Combined Boundary Treatment Method for Numerical Simulation of Seismic Wave Field of Earth-Rock Dam and Electronic Equipment

Abstract

The present application discloses a combined boundary processing method and an electronic device for numerical simulation of seismic wave fields of earth-rock dams. The method includes: Step 1: Establish an earth-rock dam model and perform discretization processing to obtain an earth-rock dam discrete grid; Step 2: Perform differential discretization through a high-order staggered semi-grid algorithm to obtain an earth-rock dam semi-grid differential model; Step 3: Set the elastic parameter types of each grid point in the earth-rock dam semi-grid differential model; Step 4: Perform average calculation on the density component and the Lame constant, calculate the shear stress, and determine the free boundary condition; Step 5: Calculate the attenuation factors of the absorption boundary regions before, after, and at the bottom of the bedrock, and determine the absorption attenuation factors of the absorption boundaries in different regions. The present invention changes the position of the earth-rock dam model in the differential grid, adaptively processes the free boundaries of the dam crest, dam slope, and dam corner, correctly simulates the wave field characteristics of surface waves, simplifies the processing method of the free boundary of the dam body, and improves the efficiency and accuracy of numerical simulation.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic exploration numerical simulation, and more particularly, to a combined boundary processing method for numerical simulation of seismic wave fields of earth-rock dams and an electronic device. Background Art

[0002] Numerical simulation of seismic wave fields of earth-rock dams can effectively reflect the dynamic and kinematic characteristics of seismic wave propagation inside the dam body, accurately infer the internal stratigraphic structure and geotechnical mechanical parameters of the earth-rock dam, and comprehensively evaluate the safety of the dam body. The high-order staggered grid finite difference method based on the elastic wave equation is the most widely used numerical simulation method at present. In the finite difference calculation process of the seismic wave field, the treatment of the geological model boundary is one of the most critical contents, which includes free boundaries and absorbing boundaries. The treatment of free boundaries can ensure that the seismic wave field satisfies the laws of elasticity at the interface between the medium and air, and simulate the surface wave field propagating on the ground surface. Currently, the main method used is the acoustic / elastic medium boundary approximation method (AEA); the treatment of absorbing boundaries can eliminate the spurious reflections at the artificial truncation boundary. The most widely used method currently is the perfectly matched layer method (PML).

[0003] For regular geological models, the free surface is a horizontal plane. The AEA method can better complete the boundary treatment and simulate the surface wave field. However, the structure of earth-rock dams is relatively complex. The crest and corners of the dam are horizontal free surfaces, while the upstream and downstream slopes of the dam are inclined free surfaces. For inclined free surfaces, they need to be discretized, decomposed into horizontal or vertical surface elements, and then the treatment scheme of the free boundary is set according to different positions to ensure that the entire inclined interface satisfies the requirements of elasticity. When the slope structure type of the earth-rock dam changes, the treatment scheme of the free boundary needs to be changed accordingly. Therefore, according to the existing free boundary treatment methods, when carrying out seismic wave field simulation of earth-rock dams, different methods need to be used to treat the free surface of the dam body in different regions. This scheme is not only complex in implementation process, poor in applicability, low in calculation efficiency, but also prone to calculation errors.

[0004] When dealing with the absorbing boundary of a conventional geological model, due to the relatively small ratio of longitudinal and transverse wave velocities and low Poisson's ratio of the formation, the PML boundary condition can well absorb the seismic wave field at the model boundary. However, earth-rock dams are built with earth-rock mixed media, which have the characteristic of high Poisson's ratio. When using the PML boundary to absorb surface waves in such media, calculation instability problems are likely to occur. Therefore, the multi-axis perfectly matched layer method (M-PML) needs to be used for the treatment of the absorbing boundary. This method uses multiple damping coefficients to absorb the boundary wave field, solves the instability problem of PML in absorbing surface waves in high Poisson's ratio media, but increases the internal storage and CPU running time in the numerical simulation process.

[0005] Therefore, it is necessary to develop a combined boundary treatment method and an electronic device for numerical simulation of the seismic wave field of earth-rock dams.

[0006] The information disclosed in the background art section of the present invention is only intended to deepen the understanding of the general background art of the present invention, and should not be regarded as an admission or any form of implication that this information constitutes the prior art known to those skilled in the art. Summary of the Invention

[0007] The present invention proposes a combined boundary treatment method and an electronic device for numerical simulation of the seismic wave field of earth-rock dams, which can simultaneously process the free boundaries of the dam crest, dam slope, and dam toe surface, ensure that the elastic parameters of all free interfaces of the dam automatically meet the requirements of elasticity mechanics, greatly simplify the treatment method of the dam free boundary, and improve the efficiency and accuracy of numerical simulation; based on the similarity between the PML and M-PML absorption boundary algorithms, on the basis of the PML boundary, a multi-axis absorption attenuation factor is introduced to realize the sub-region combination of the two absorption boundaries, and while ensuring the absorption effect, effectively reduce the storage and calculation time of numerical simulation.

[0008] In a first aspect, an embodiment of the present disclosure provides a combined boundary treatment method for numerical simulation of the seismic wave field of earth-rock dams, including:

[0009] Step 1: Establish an earth-rock dam model and perform discretization processing to obtain an earth-rock dam discrete grid;

[0010] Step 2: For the earth-rock dam discrete grid, perform difference discretization through a high-order staggered semi-grid algorithm to obtain an earth-rock dam semi-grid difference model;

[0011] Step 3: Set the elastic parameter types of each grid point in the earth-rock dam semi-grid difference model, where the elastic parameters include normal stress, shear stress, horizontal velocity component, vertical velocity component, horizontal density component, vertical density component, and Lame constant;

[0012] Step 4: Perform an average calculation on the density component and Lame constant μ of each grid point xz to calculate the shear stress and determine the free boundary condition;

[0013] Step 5: Calculate the attenuation factors of the absorption boundary regions before and after the bedrock and at the bottom, and determine the absorption attenuation factors of the absorption boundaries in different regions.

[0014] Preferably, the normal stress is set at the integer grid points of the earth-rock dam semi-grid difference model, and the shear stress, the horizontal velocity component, the vertical velocity component, the horizontal density component, the vertical density component, and the Lame constant μ xz are set at the semi-grid points of the earth-rock dam semi-grid difference model.

[0015] Preferably, step 2 further includes:

[0016] Set the free boundaries of the dam crest, dam slope, and dam toe in the semi-grid region of the earth-rock dam semi-grid differential model, and assign an elastic parameter value of 0 to all grid points outside the earth-rock dam model.

[0017] Preferably, step 3 includes:

[0018] For the horizontal density component, the vertical density component, and the Lame constant μ xz Perform average calculations respectively, so that the horizontal density component and the vertical density component at the free boundary are half of the density value of the dam body or bedrock, and the Lame constant μ xz at the free boundary all have a value of 0;

[0019] Calculate the shear stress according to the averaged Lame constant μ xz so that the shear stress values at the free boundary are all 0.

[0020] Preferably, the average calculation for the horizontal density component and the vertical density component includes:

[0021]

[0022]

[0023] where ρ x is the horizontal density component, ρ z is the vertical density component, and ρ i，j represents the density value of the node at the horizontal direction i and vertical direction j in the discrete grid.

[0024] Preferably, the average calculation for the Lame constant μ xz is performed through formula (3):

[0025]

[0026] Preferably, the shear stress is calculated through formula (4):

[0027]

[0028] where τ xz is the shear stress, represents the time as n + 1, the grid node position as i + 1 / 2, j + 1 / 2, △t is the time interval of numerical calculation, and D z v x represents the partial derivative of the horizontal velocity component v x with respect to the z direction.

[0029] Preferably, the absorption attenuation factors of the absorption boundaries before and after the bedrock include the absorption attenuation factor d in the x direction xx and the absorption attenuation factor d in the z direction xz .

[0030] Preferably, the absorption attenuation factor d in the z direction of the absorption boundaries before and after the bedrock is calculated by formula (5) xz :

[0031] d xz = pd xx (5)

[0032] where p is a constant coefficient between 0 and 1.

[0033] As a specific implementation manner of the embodiments of the present disclosure

[0034] In a second aspect, the embodiments of the present disclosure further provide an electronic device, which includes:

[0035] a memory storing executable instructions;

[0036] a processor that runs the executable instructions in the memory to implement the combined boundary processing method for the numerical simulation of the seismic wave field of the earth-rock dam.

[0037] Its beneficial effects are as follows:

[0038] 1. Aiming at the deficiencies of the traditional free boundary method in dealing with various types of free boundaries of the dam body, such as complex processing process, poor applicability, low calculation accuracy and efficiency, by changing the position of the earth-rock dam model in the staggered finite difference grid, setting the shear wave velocity, longitudinal wave velocity, and density outside the dam body model to 0, and setting elastic parameters such as normal stress, shear stress, Lame constant, and density during the difference calculation, and using the average calculation principle to adaptively process the free boundaries of the dam crest, dam slope, and dam corner, ensuring that the elastic parameters of all free interfaces of the dam body automatically meet the requirements of elasticity mechanics, correctly simulating the wave field characteristics of surface waves, greatly simplifying the processing method of the free boundary of the dam body, and improving the efficiency and accuracy of numerical simulation.

[0039] 2. Based on the similarity between the PML and M-PML absorption boundary algorithms, on the basis of the PML boundary, multi-axis absorption attenuation factors are introduced to realize the sub-region combination of the two absorption boundaries. Compared with the conventional single use of the PML boundary or M-PML boundary, under the condition of ensuring the absorption effect, the storage amount and calculation time of numerical simulation are effectively reduced.

[0040] The method and apparatus of the present invention have other characteristics and advantages, which will be apparent from the accompanying drawings incorporated herein and the subsequent detailed description, or will be described in detail in the accompanying drawings incorporated herein and the subsequent detailed description, and these accompanying drawings and detailed description are used together to explain the specific principles of the present invention. Description of the Drawings

[0041] By describing the exemplary embodiments of the present invention in more detail in conjunction with the accompanying drawings, the above and other objects, features, and advantages of the present invention will become more apparent, wherein, in the exemplary embodiments of the present invention, the same reference numerals generally represent the same components.

[0042] Figure 1 A schematic diagram showing an earth-rock dam model and boundary setting according to an embodiment of the present invention is shown.

[0043] Figure 2 A flowchart showing the steps of a combined boundary processing method for numerical simulation of the seismic wave field of an earth-rock dam according to an embodiment of the present invention is shown.

[0044] Figure 3 A schematic diagram showing a numerical model of an earth-rock dam according to an embodiment of the present invention is shown.

[0045] Figure 4 A schematic diagram showing a seismic wave field simulation seismic source according to an embodiment of the present invention is shown.

[0046] Figure 5 A schematic diagram showing the staggered grid difference calculation of elastic waves in the dam body according to an embodiment of the present invention is shown.

[0047] Figure 6 A schematic diagram showing the absorption boundary setting in the seismic wave field simulation of an earth-rock dam according to an embodiment of the present invention is shown.

[0048] Figures 7a - 7f Respectively show the earth-rock dam v obtained by numerical simulation according to an embodiment of the present invention z Schematic diagrams of wave field snapshots at 20 ms, 40 ms, 80 ms, 120 ms, 180 ms, and 240 ms of the component.

[0049] Figure 8a and Figure 8b Respectively show the earth-rock dam v obtained by numerical simulation according to an embodiment of the present invention x and v z Schematic diagrams of seismic records of the component. Detailed Description of the Invention

[0050] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein.

[0051] The present invention provides a combined boundary treatment method for numerical simulation of seismic wave fields of earth-rock dams, including:

[0052] Step 1: Establish an earth-rock dam model and perform discretization processing to obtain an earth-rock dam discrete grid;

[0053] Step 2: For the earth-rock dam discrete grid, perform difference discretization through a high-order staggered semi-grid algorithm to obtain an earth-rock dam semi-grid difference model;

[0054] Step 3: Set the elastic parameter types of each grid point in the earth-rock dam semi-grid difference model. The elastic parameters include normal stress, shear stress, horizontal velocity component, vertical velocity component, horizontal density component, vertical density component, and Lame constant;

[0055] Step 4: Perform an average calculation on the density component and Lame constant μ xz of each grid point, and then calculate the shear stress to determine the free boundary condition;

[0056] Step 5: Calculate the attenuation factors of the absorption boundary regions before, after, and at the bottom of the bedrock, and determine the absorption attenuation factors of the absorption boundaries in different regions.

[0057] In one example, the normal stress is set at the integer grid points of the earth-rock dam semi-grid difference model, and the shear stress, horizontal velocity component, vertical velocity component, horizontal density component, vertical density component, and Lame constant μ xz are set at the semi-grid points of the earth-rock dam semi-grid difference model.

[0058] In one example, Step 2 further includes:

[0059] Set the free boundaries of the dam crest, dam slope, and dam corner in the semi-grid region of the earth-rock dam semi-grid difference model, and assign all the elastic parameters of the grid points outside the earth-rock dam model to 0.

[0060] In one example, Step 3 includes:

[0061] Perform average calculations on the horizontal density component, vertical density component, and Lame constant μ xz respectively, so that the horizontal density component and vertical density component at the free boundary are half of the density values of the dam body or bedrock, and the values of the Lame constant μ xz at the free boundary are all 0;

[0062] According to the averaged Lame constant μ xzCalculate the shear stress so that the values of the shear stress at the free boundaries are all 0.

[0063] In one example, the average calculation for the horizontal density component and the vertical density component includes:

[0064]

[0065]

[0066] where ρ x is the horizontal density component, ρ z is the vertical density component, and ρ i，j represents the density value of the node at the horizontal direction i and the vertical direction j in the discrete grid.

[0067] In one example, the average calculation for the Lame constant μ xz is performed through formula (3):

[0068]

[0069] In one example, the shear stress is calculated through formula (4):

[0070]

[0071] where τ xz is the shear stress, represents that the time is n + 1, the grid node position is i + 1 / 2, j + 1 / 2, △t is the time interval of the numerical calculation, and D z v x represents taking the partial derivative of the horizontal velocity component v x in the z direction.

[0072] In one example, the absorption attenuation factors of the absorption boundaries before and after the bedrock include the absorption attenuation factor d xx in the x direction and the absorption attenuation factor d xz in the z direction.

[0073] In one example, the absorption attenuation factor d xz in the z direction of the absorption boundaries before and after the bedrock is calculated through formula (5):

[0074] d xz = pd xx (5)

[0075] where p is a constant coefficient between 0 and 1.

[0076] Figure 1 Shows a schematic diagram of an earth-rock dam model and boundary setting according to an embodiment of the present invention. The top of the dam, the dam slope, and the dam corner are free boundaries, and the periphery of the bedrock is an absorption boundary.

[0077] Specifically, the setting of the boundary of the earth-rock dam in the present invention is as follows Figure 1 shown. The core content is that during the differential calculation of the seismic wave field, the normal stress is set at integer grid points, the shear stress, horizontal velocity, and vertical velocity are set at half grid points, the free boundary of the earth-rock dam is set along the half grid points, the shear wave velocity, longitudinal wave velocity, and density outside the dam body model are assigned 0, and through the density and Lame constant μ xz average calculation principle, it is ensured that the elastic parameters of all free interfaces of the dam body automatically meet the requirements of elasticity mechanics and adaptively meet the requirements of dam surface wave field simulation. For the absorbing boundary of the dam body, the M-PML boundary is used to absorb the artificial truncation boundary reflection in the areas with strong surface wave energy in front of and behind the bedrock, and the conventional PML boundary is used in the areas with weak surface wave energy at the bottom of the bedrock. The combination of this absorbing boundary not only ensures the boundary absorption effect but also effectively improves the calculation efficiency.

[0078] The combined boundary processing method for numerical simulation of the seismic wave field of the earth-rock dam includes the following steps:

[0079] Step 1: According to the actual structural characteristics of the earth-rock dam, set the crest width, slope ratio, dam height, and bedrock thickness, and establish an earth-rock dam model; discretize the earth-rock dam model according to the grid spacing dx and dz of numerical calculation to obtain the earth-rock dam discrete grid. The grid spacing dx and dz should be less than 1 / 20 of the minimum wavelength of the seismic wave field propagating in the earth-rock dam, that is:

[0080]

[0081] where f is the main frequency of the numerical simulation seismic source, and V s1 is the minimum shear wave velocity in the model.

[0082] Step 2: Based on the earth-rock dam discrete grid, use the staggered grid finite difference method of sixth order in space and second order in time to obtain the earth-rock dam half-grid difference model. Set the free boundaries of the dam crest, dam slope, and dam corners in the half-grid area of the earth-rock dam half-grid difference model, and assign all elastic parameters of the grid points outside the earth-rock dam model to 0.

[0083] Step 3: Set the types of elastic parameters of each grid node of the earth-rock dam. The elastic parameters include normal stress, shear stress, horizontal velocity component, vertical velocity component, horizontal density component, vertical density component, and Lame constant. Set the normal stress τ xx , τ zz , λ, and μ at integer grid points, and set the shear stress τ xz , the horizontal velocity component v x , and the vertical velocity component v z at half grid points. Set the horizontal density component ρ x , and the vertical density component ρz and the Lame constant μ for calculating the shear stress xz is also set at the half grid points.

[0084] Step 4: Calculate the average of the density components and the Lame constant at each grid point, and then calculate the Lame constant μ xz , determine the free boundary conditions; for the density components ρ x 、ρ z perform the average calculation in the following way:

[0085]

[0086]

[0087] Since the physical property parameters outside the earth-rock dam model are all 0, after the density components at the horizontal and inclined free boundaries are calculated by the above average algorithm, their values at the free boundaries are all half of the density values of the surrounding medium, that is

[0088]

[0089] where ρ1 is the density of the dam body and ρ2 is the density of the bedrock.

[0090] Perform the average calculation for the Lame constant μ through formula (3) xz , the Lame constant μ at the free boundary xz After being calculated by the above average algorithm, its value is all 0, and then the shear stress τ is calculated through formula (4) xz When calculating xz = 0.

[0091] Step 5: For the absorbing boundary, first process the entire absorbing boundary region of the bedrock at the bottom of the dam using the PML boundary condition algorithm, and calculate the absorption attenuation factor d(x) of each region according to the following formula:

[0092]

[0093] where R is the reflection coefficient, and its value selection is related to the thickness of the absorbing layer, L is the thickness of the absorbing layer, V pmax is the maximum longitudinal wave velocity in the model, x is the abscissa of the grid point, and when calculating the attenuation factor d(z) at the bottom of the bedrock, x is changed to the ordinate z of the grid point.

[0094] Since the PML boundary condition is unidirectional absorption, there is only an absorption attenuation factor d xx in the x direction in the absorbing boundary regions in the front and back of the bedrock, and there is only an absorption attenuation factor d zz, there are two absorption attenuation factors \(d\) in the overlapping area of the bottom corner absorption regions on both sides of the bedrock xx , \(d\) zz .

[0095] To enhance the absorption effect of the bedrock front and back absorption boundaries on the surface waves, in addition to the original absorption attenuation factor \(d\) xx , the absorption attenuation factor \(d\) along the \(z\)-direction is calculated through formula (5), and the original uniaxial PML boundary condition is changed to the multi-axis absorption M-PML boundary condition along the \(x\) and \(z\) directions. xz

[0096] The present invention also provides an electronic device, which includes: a memory storing executable instructions; a processor that runs the executable instructions in the memory to implement the above-mentioned combined boundary processing method for numerical simulation of the seismic wave field of an earth-rock dam.

[0097] To facilitate understanding of the solution and its effects of the embodiments of the present invention, the following gives two specific application examples. Those skilled in the art should understand that this example is only for facilitating the understanding of the present invention, and any specific details are not intended to limit the present invention in any way.

[0098] Example 1

[0099] Figure 2 The flowchart showing the steps of the combined boundary processing method for numerical simulation of the seismic wave field of an earth-rock dam according to an embodiment of the present invention is shown.

[0100] As Figure 2 shown, the combined boundary processing method for numerical simulation of the seismic wave field of an earth-rock dam includes:

[0101] Step 1: Establish an earth-rock dam model and perform discretization processing to obtain an earth-rock dam discrete grid;

[0102] Step 2: For the earth-rock dam discrete grid, perform difference discretization through a high-order staggered semi-grid algorithm to obtain an earth-rock dam semi-grid difference model;

[0103] Step 3: Set the elastic parameter types of each grid point in the earth-rock dam semi-grid difference model, and the elastic parameters include normal stress, shear stress, horizontal velocity component, vertical velocity component, horizontal density component, vertical density component, and Lame constant;

[0104] Step 4: Perform an average calculation on the density component and the Lame constant \(\mu\) xz of each grid point, and then calculate the shear stress to determine the free boundary condition;

[0105] Step 5: Calculate the attenuation factors of the absorption boundary regions in front of, behind, and at the bottom of the bedrock to determine the absorption attenuation factors of the absorption boundaries in different regions.

[0106] Figure 3 Shows a schematic diagram of the numerical model of an earth-rock dam according to an embodiment of the present invention.

[0107] According to the actual structural characteristics of the earth-rock dam, the crest width of the earth-rock dam is set to 10 m, the slope ratio is 1:2, the dam height is 20 m, and the bedrock thickness is 5 m, and an earth-rock dam model is established, as Figure 3 shown.

[0108] The earth-rock dam model is discretized according to the grid spacing dx = dz = 0.05 m of the numerical calculation. The longitudinal wave velocity V p1 of the medium in the dam body area is 650 m / s, the transverse wave velocity V s1 is 300 m / s, and the density ρ1 = 1700 kg / m 3 . Similarly, the longitudinal wave velocity V p2 of the medium in the bedrock area is 3500 m / s, the transverse wave velocity V s2 is 2000 m / s, and the density ρ2 = 2600 kg / m 3 .

[0109] Figure 4 Shows a schematic diagram of the seismic source for seismic wave field simulation according to an embodiment of the present invention.

[0110] The seismic source for numerical simulation uses a Gaussian first derivative wavelet. The total calculation duration ns = 0.25 s, and the time interval Δt = 1.0×10 -6 s, as Figure 4 shown. The seismic source position is set in the middle of the dam crest.

[0111]

[0112] In the formula, f is the main frequency of the seismic source, its value is 150 Hz, t is the time, and t0 is the delay time.

[0113] Using the physical property parameters of the model, the corresponding Lame constants λ and μ are calculated:

[0114]

[0115] Figure 5 Shows a schematic diagram of the staggered grid difference calculation of elastic waves in the dam body according to an embodiment of the present invention. The free boundary of the dam body model is set at the half grid point, and the thick dashed line represents the free boundary.

[0116] Based on the discrete grid of the earth-rock dam, the staggered grid finite difference method of six-order in space and second-order in time is adopted to discretize the derivatives in the elastic wave stress-velocity equation into differences. To improve the accuracy of the numerical calculation of the seismic wave field, a half-grid algorithm is used for difference discretization, and the normal stress τ xx , τzz 、 λ and μ are set at integer grid points, and τ xz Shearing stress, v x Horizontal velocity component, v z The vertical velocity component is set at half grid points, and the horizontal ρ x 、Vertical component ρ z And the Lame constant μ for calculating the shearing stress xz Are also set at half grid points. The schematic diagram of the staggered grid difference calculation of elastic waves in the earth-rock dam is as Figure 5 Shown;

[0117] Set the free boundaries of the dam crest, dam slope, and dam corner of the earth-rock dam in the half grid area of the staggered finite difference, and at the same time assign all the elastic parameters of the grid points outside the earth-rock dam model to 0;

[0118] For the density components ρ x 、ρ z And the Lame constant μ xz Perform average calculation in the following way:

[0119]

[0120]

[0121]

[0122] Since the physical property parameters outside the earth-rock dam model are all 0, the density components at the horizontal and inclined free boundaries are all half of the density values of the surrounding media after being calculated by the above average algorithm, that is

[0123]

[0124] Where ρ1 is the density of the dam body and ρ2 is the density of the bedrock.

[0125] The Lame constant μ at the free boundary xz After being calculated by the above average algorithm, the value at the free boundary is all 0, and then when calculating the shearing stress τ using the following stress-velocity difference equation xz All the shearing stress τ at the free boundaries can be made xz = 0;

[0126]

[0127] Where Indicates that the time is n + 1, the grid node position is i + 1 / 2, j + 1 / 2, △t is the time interval of numerical calculation, D z v x Indicates taking the partial derivative of the horizontal velocity component with respect to the z direction.

[0128] According to the above scheme, the free boundaries of each area of the dam body can be processed simply and efficiently, so that the elastic parameters of the free boundaries of each area meet the requirements of elasticity mechanics, that is

[0129]

[0130] In the formula, ρ0 and μ0 respectively represent the density and Lame constant μ of the medium around the free boundary xz , since the free boundaries are all set at the semi-grid nodes, the normal stress τ is not involved in the process of dealing with the free boundaries zz .

[0131] The front and rear areas of the bedrock at the bottom of the dam intersect with the free boundaries at the dam corners. To effectively absorb the surface wave field at the dam bottom corners and ensure the stability of numerical simulation calculations, the M-PML boundary condition is used to process the absorption boundaries in front of and behind the bedrock. Since the surface wave energy at the bottom of the bedrock is weak, to reduce the storage capacity of the calculation and improve the calculation efficiency, the PML boundary condition is used to process the absorption boundary at the bottom of the bedrock. The thicknesses of both the PML and M-PML boundaries are L = 150 grid points;

[0132] All the absorption boundary areas are processed using the PML boundary condition algorithm, and the absorption attenuation factor d(x) of each area is calculated according to the following formula;

[0133]

[0134] In the formula, R is the reflection coefficient, and its value is set to 1.0×10 -6 , V pmax is the maximum longitudinal wave velocity in the model, that is, V pmax =V p2 =3500 m / s, x is the abscissa of the grid point. When calculating the attenuation factor d(z) at the bottom of the bedrock, x is changed to the ordinate z of the grid point.

[0135] Since the PML boundary condition is unidirectional absorption, there is only an absorption attenuation factor d in the x direction in the absorption boundary areas in the front and rear areas of the bedrock xx , there is only an absorption attenuation factor d in the z direction at the bottom of the bedrock zz , and there are absorption attenuation factors d in two directions in the overlapping area of the absorption areas at the bottom corners on both sides of the bedrock xx , d zz ;

[0136] Figure 6 shows a schematic diagram of the setting of the absorption boundary in the seismic wave field simulation of an earth-rock dam according to an embodiment of the present invention. The M-PML boundary condition is used in the front and rear areas of the bedrock, and there are a horizontal attenuation factor d xx and a vertical attenuation factor d xz, the bottom of the bedrock adopts the PML boundary condition, and there is only a vertical attenuation factor d zz .

[0137] To enhance the absorption effect of the surface wave by the absorption boundary in front of and behind the bedrock, in addition to the original absorption attenuation factor d xx , an absorption attenuation factor d along the z direction is introduced xz , changing the original uniaxial PML boundary condition to the multi-axis absorption M-PML boundary condition along the x and z directions, as Figure 6 shown, the calculation method of d xz is as follows:

[0138] d xz = pd xx

[0139] In the formula, p is a constant coefficient between 0 and 1, and the value in the example is 1.

[0140] Figures 7a - 7f respectively show the schematic diagrams of the wave field snapshots at 20ms, 40ms, 80ms, 120ms, 180ms, and 240ms of the v z component of the earth-rock dam obtained by numerical simulation according to an embodiment of the present invention.

[0141] The wave field snapshots of the v z component of the earth-rock dam at different moments obtained by numerical simulation are as Figures 7a - 7f shown. From the wave field snapshot at 20ms in Figure 7a , it can be seen that according to the treatment method of the free boundary of the present invention, after the source is excited, a surface wave with strong energy is generated at the dam crest, and the surface wave propagates along the dam crest towards the dam slope. From the wave field snapshot at 40ms in Figure 7b , it can be seen that when the surface wave at the dam crest propagates to the dam apex angle, a reverse surface wave reflection is generated at the dam apex angle, that is, the surface wave propagating to the left generates a reflected surface wave propagating to the right at the left apex angle of the dam body, and the surface wave propagating to the right generates a reflected surface wave propagating to the left at the right apex angle of the dam body.

[0142] From the wave field snapshots of the v Figures 7b - 7f component at 40ms, 80ms, 120ms, 180ms, and 240ms in z , it can be seen that after the free boundary of the inclined dam slope is processed according to the present invention, the surface wave excited at the dam crest continuously propagates along the surface of the dam slope to the bottom corner of the dam body, and a reflected surface wave is generated at the bottom corner of the dam body, and the reflected surface wave propagates along the dam slope towards the dam crest. At the same time, from the wave field snapshot at 240ms, it can be seen that no wave field reflection is seen in the bedrock boundary region, which fully proves that the combined boundary of M-PML and PML in the present invention absorbs the surface wave, longitudinal wave, converted wave, transverse wave and other wave fields propagating from the dam body to the bedrock boundary well.

[0143] Figure 8a and Figure 8b respectively show the schematic diagrams of the seismic records of the v x and v z components obtained by numerical simulation according to an embodiment of the present invention.

[0144] Geophones are arranged along the surface of the dam slope and the dam crest, with a trace interval of 0.5 m. The seismic records of the v x and v z components obtained by numerical simulation are as shown in Figure 8a and Figure 8b . It can be seen from the seismic records that the surface waves excited by the seismic source and the linear travel-time curves of the reflected surface waves generated at the dam apex and the dam base angle. Since the physical property parameters in the surface wave propagation region remain unchanged, the travel-time curves of the three types of surface waves are parallel.

[0145] The above examples prove the accuracy and effectiveness of the adaptive free boundary and combined absorbing boundary processing proposed by the present invention in the numerical simulation of the seismic wave field of earth-rock dams. By changing the position of the earth-rock dam model in the differential grid, the shear wave velocity, longitudinal wave velocity, and density outside the dam body model are assigned 0. During the differential calculation process, the normal stress, shear stress, Lame constant μ xz , density and other elastic parameters are set specifically. Using the average calculation principle, the free boundaries of the dam crest, dam slope, and dam corners are adaptively processed to ensure that the elastic parameters of all free interfaces of the dam body automatically meet the requirements of elasticity mechanics, and the wave field characteristics of the surface waves are correctly simulated, greatly simplifying the processing method of the dam body free boundary and improving the efficiency and accuracy of the numerical simulation. Based on the similarity between the PML and M-PML absorbing boundary algorithms, on the basis of the PML boundary, a multi-axis absorption attenuation factor is introduced to realize the sub-region combination of the two absorbing boundaries, effectively reducing the storage and calculation time of the numerical simulation while ensuring the absorption effect.

[0146] Example 2

[0147] The present disclosure provides an electronic device, which includes: a memory storing executable instructions; a processor that runs the executable instructions in the memory to implement the combined boundary processing method for the numerical simulation of the seismic wave field of the earth-rock dam as described above.

[0148] The electronic device according to an embodiment of the present disclosure includes a memory and a processor.

[0149] The memory is used to store non - transitory computer - readable instructions. Specifically, the memory may include one or more computer program products, and the computer program products may include various forms of computer - readable storage media, such as volatile memory and / or non - volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory, etc. The non - volatile memory may include, for example, read - only memory (ROM), hard disk, flash memory, etc.

[0150] The processor may be a central processing unit (CPU) or other forms of processing units having data - processing capabilities and / or instruction - execution capabilities, and may control other components in the electronic device to perform desired functions. In an embodiment of the present disclosure, the processor is used to run the computer - readable instructions stored in the memory.

[0151] Those skilled in the art should understand that, in order to solve the technical problem of how to obtain good user - experience effects, this embodiment may also include well - known structures such as communication buses, interfaces, etc., and these well - known structures should also be included in the protection scope of the present disclosure.

[0152] For a detailed description of this embodiment, reference may be made to the corresponding descriptions in the foregoing embodiments, and details will not be repeated here.

[0153] Those skilled in the art should understand that the purpose of the above description of the embodiments of the present invention is only to exemplarily illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any of the examples given.

[0154] The above has described the embodiments of the present invention. The above description is exemplary and not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes are obvious to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A combined boundary treatment method for numerical simulation of seismic wave fields in earth-rock dams, characterized in that, Including: Step 1: Establish a soil-rock dam model and perform discretization processing to obtain a discretized grid of the soil-rock dam; Step 2: For the discretized grid of the soil-rock dam, perform difference discretization through a high-order staggered semi-grid algorithm to obtain a semi-grid difference model of the soil-rock dam; Step 3: Set the elastic parameter types of each grid point in the semi-grid difference model of the soil-rock dam. The elastic parameters include normal stress, shear stress, horizontal velocity component, vertical velocity component, horizontal density component, vertical density component, and Lame constant; Step 4: Average the density components and Lame constant μ of each grid point xz to calculate the shear stress and determine the free boundary conditions; Step 5: Calculate the attenuation factors of the absorption boundary regions before and after the bedrock and at the bottom, and determine the absorption attenuation factors of the absorption boundaries in different regions.

2. The combined boundary treatment method for numerical simulation of seismic wave field of earth-rock dams according to claim 1, wherein, The normal stress is set at the integer grid points of the semi-grid differential model of the earth-rock dam, and the shear stress, the horizontal velocity component, the vertical velocity component, the horizontal density component, the vertical density component, and the Lame constant μ xz are set at the semi-grid points of the semi-grid differential model of the earth-rock dam.

3. The combined boundary treatment method for numerical simulation of seismic wave field of earth-rock dams according to claim 1, wherein, The said Step 2 further includes: Set the free boundaries of the dam crest, dam slope, and dam corner in the semi-grid region of the semi-grid difference model of the soil-rock dam, and assign all elastic parameters of the grid points outside the soil-rock dam model to 0.

4. The combined boundary treatment method for numerical simulation of seismic wave field of earth-rock dams according to claim 1, wherein, The said Step 3 includes: For the horizontal density component, the vertical density component, and the Lame constant μ xz perform average calculations respectively, so that the horizontal density component and the vertical density component at the free boundary are half of the density values of the dam body or the bedrock, and the Lame constant μ xz at the free boundary all have a value of 0; According to the Lame constant μ after average calculation xz Calculate the shear stress so that the values of the shear stress at the free boundary are all 0.

5. The combined boundary treatment method for numerical simulation of earthquake wave field of earth-rock dams according to claim 4, wherein, The average calculation for the horizontal density component and the vertical density component includes: where ρ x is the horizontal density component, ρ z is the vertical density component, and ρ i，j represents the density value of the node at the horizontal direction i and the vertical direction j in the discrete grid.

6. The combined boundary treatment method for numerical simulation of seismic wave field of earth-rock dams according to claim 4, wherein, Calculate the average for the Lamé constant μ according to formula (3). xz The calculation is as follows:

7. The combined boundary treatment method for numerical simulation of seismic wave field of earth-rock dams according to claim 6, wherein, Calculate the shear stress through formula (4): where τ xz is the shear stress, represents the time of n + 1, the grid node position of i + 1 / 2, j + 1 / 2, △t is the time interval of numerical calculation, D z v x represents the partial derivative of the horizontal velocity component v x with respect to the z direction.

8. The combined boundary treatment method for numerical simulation of the seismic wave field of an earth-rock dam according to claim 1, wherein, The absorption attenuation factors of the absorption boundaries before and after the bedrock include the absorption attenuation factor d in the x direction xx and the absorption attenuation factor d in the z direction xz .

9. The combined boundary treatment method for numerical simulation of seismic wave field of earth-rock dams according to claim 8, wherein, Calculate the absorption attenuation factor d of the absorption boundaries before and after the bedrock along the z direction through formula (5). xz : d xz = pd xx (5) Where p is a constant coefficient between 0 and 1.

10. An electronic device, characterized in that, The said electronic device includes: A memory storing executable instructions; A processor that runs the executable instructions in the memory to implement the combined boundary processing method for numerical simulation of the seismic wave field of the soil-rock dam according to any one of claims 1-9.

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