A method for inputting oblique incidence three-dimensional modeling of ground motion applied to layered strata

Abstract

The application discloses a kind of applied to layered stratum seismic motion oblique incidence three-dimensional modeling input method, belong to civil engineering technical field.The method includes the following steps: S1, modeling to each layer stratum;S2, under reflection and transmission, calculate time delay and amplitude ratio;S3, calculate model boundary point parameter;S4, to model parameter is assigned value.The application adopts the above-mentioned one applied to layered stratum seismic motion oblique incidence three-dimensional modeling input method, and the seismic motion input under layered stratum is more accurate, reduces the use of parameter on seismic wave propagation path, establishes layered stratum seismic motion input method, provides effective support for near-fault underground structure seismic motion response analysis, with very strong practicality.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of civil engineering, and particularly relates to a three-dimensional modeling input method for oblique incidence of seismic waves in layered strata. BACKGROUND

[0002] Nowadays, in the analysis of seismic response of structures, numerical simulation is an effective analysis method, mainly including static and dynamic methods. Although they can both analyze seismic response, considering that the static method is essentially a simplification process, it will have a certain influence on the final result, and under the condition of allowing, the dynamic method is often more capable of revealing the real seismic response and can reasonably deal with complex real situations, and is widely used. However, in the calculation process, a limited stratum area needs to be intercepted and an artificial boundary needs to be applied to simulate the stratum condition of an infinite half space. Considering the relationship between the crust density and the depth, the existing scheme often simplifies the input direction of the seismic wave to the vertical direction of the ground surface, or simplifies the stratum in the model area to a homogeneous body for analysis. Such a simplification process can effectively reduce the calculation complexity, and for some cases far away from the fault, it will not produce a large error, and has a certain rationality.

[0003] However, for near-fault areas, the influence of the incidence angle of the seismic wave and the layered stratum cannot be ignored, otherwise it will cause a certain error, and further affect the seismic response analysis of the structure. In this case, the seismic wave often undergoes multiple reflections and transmissions, and the propagation path is solved one by one by using a three-dimensional geometric method, which has a clear idea, mature theory and high reliability, but in the specific solving process, it is easy to produce iteration difficulty and cannot form a systematic calculation process. Limited by this, at present, there is no reasonable and effective precise modeling method for the oblique incidence of seismic waves in horizontal layered sites. SUMMARY

[0004] The purpose of the present application is to provide a three-dimensional modeling input method for oblique incidence of seismic waves in layered strata, which makes the seismic wave input under the layered strata more accurate, reduces the use of parameters on the propagation path of the seismic wave, establishes a seismic wave input method for layered strata, and provides effective support for the seismic response analysis of near-fault underground structures, and has strong practicability.

[0005] To achieve the above purpose, the present application provides a three-dimensional modeling input method for oblique incidence of seismic waves in layered strata, comprising the following steps:

[0006] S1, modeling each layer of stratum;

[0007] S2, calculating the time delay and amplitude ratio under the reflection and transmission conditions;

[0008] S3, calculating the model boundary point parameters;

[0009] S4, assigning values to the model parameters.

[0010] Preferably, in the step S1 of three-dimensionally modeling the strata, the eight-node linear hexahedron unit is used for partitioning, and the node coordinates and node control areas on the boundary surface are extracted.

[0011] Preferably, the step S2 of calculating the time delay and the amplitude ratio comprises the following steps:

[0012] S21, taking the intersection point of the zero-time wave front and the strata interface as the equivalent zero-time point;

[0013] S22, calculating the time delay;

[0014] S23, calculating the amplitude ratio;

[0015] S24, if the corresponding seismic wave transmits out of the lower boundary of the model or the amplitude is too small, the calculation is terminated, otherwise, it is taken as the incident wave to repeat the step S21 and the step S22.

[0016] Preferably, in the step S22, the time delay is calculated as follows:

[0017]

[0018] wherein, Δt i is the time delay, Δx i , Δy i , Δz i are the coordinate differences of the sought point and the equivalent zero-time point in x, y, z directions respectively, v i is the propagation speed of the corresponding type of seismic wave at the target point, α i , β i , γ i are the angles between the propagation direction of the seismic wave and the three coordinate axes respectively.

[0019] Preferably, in the step S23, the amplitude ratio before and after the conversion is calculated, and the amplitude ratios obtained from each conversion process on the path are multiplied to obtain the amplitude ratio with the incident wave.

[0020] Preferably, the time delay and the amplitude ratio are used to calculate the equivalent node force in combination with the node control area.

[0021] Preferably, the termination condition of the loop calculation includes that the amplitude ratio is less than 0.01, and the seismic wave is located in the lowermost stratum and propagates downward.

[0022] Therefore, this invention adopts the above-mentioned three-dimensional modeling input method for oblique incidence of seismic motion in strata, which makes the input of seismic motion in strata more accurate, reduces the use of parameters on the propagation path of seismic waves, establishes a seismic motion input method for strata, provides effective support for the seismic response analysis of near-fault underground structures, and has strong practicality.

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of oblique incidence seismic motion modeling in strata, which is an input method for three-dimensional modeling of oblique incidence seismic motion in strata according to the present invention.

[0025] Figure 2 This is a schematic diagram of the time delay of the reflected wave in a three-dimensional model of a three-dimensional modeling input method for oblique incidence seismic motion in strata, according to the present invention.

[0026] Figure 3 This is a schematic diagram of the time delay of the transmitted wave in a three-dimensional model of a three-dimensional modeling input method for oblique incidence seismic motion in strata, which is an application of the present invention. Detailed Implementation

[0027] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0028] A method for inputting 3D seismic motion oblique incidence modeling in stratified strata includes the following steps:

[0029] S1. Model each stratum;

[0030] S2. Calculate the time delay and amplitude ratio under both reflection and transmission conditions;

[0031] S3. Calculate the boundary point parameters of the model;

[0032] S4. Assign values ​​to the model parameters.

[0033] Example

[0034] This invention provides a three-dimensional modeling input method for oblique incidence seismic motion in strata, comprising four parts: modeling of each stratum, calculation of time delay and amplitude ratio under reflection and transmission conditions, calculation of model boundary point parameters, and assignment of model parameters.

[0035] like Figure 1 As shown, a finite element analysis model was established, and parameters were assigned to each stratum. Eight-node linear hexahedral elements were used for partitioning. Seismic waves were introduced into the model at an incident angle α, and the coordinates of each node on the boundary surface and the node control area were further extracted.

[0036] The analysis of the node control area can be performed by applying a load with a size of 1 on each boundary surface of the model except the free surface, the direction of the load being perpendicular to the model boundary and pointing to the interior of the model, and applying a fixed boundary at each boundary node of the non-free surface, and the node reaction force thus obtained is the node control area.

[0037] Considering that the number of nodes involved in the extraction process of the node coordinates and the node control area is usually large, the process analysis can be performed by programming.

[0038] The calculation of the reflection and transmission time delay according to the present application takes the intersection point of the zero-time wave front and the stratum interface as the equivalent zero-time point, which can be selected as any point on the intersection line of the zero-time wave front and the stratum interface in the three-dimensional model, such as point A in Figure 2 and Figure 3 .

[0039] Therefore, the calculation of the time delay is as follows:

[0040]

[0041] where Δt i is the time delay, Δx i , Δy i , Δz i are the coordinate differences of the sought point and point A in the x, y and z directions respectively, v i is the propagation velocity of the corresponding type of seismic wave at the target point, α i , β i , γ i are the angles between the propagation direction of the sought seismic wave and the three coordinate axes respectively.

[0042] The amplitude ratio before and after the conversion is calculated according to the propagation relationship of the wave, and the amplitude ratios obtained in each conversion process on the path are multiplied to obtain the amplitude ratio between the incident wave, i.e., the amplitude ratio of the target wave and the incident wave, which is:

[0043] E=ΠABCD

[0044] where A is the amplitude ratio of the same type of seismic wave in the reflected wave to the corresponding incident wave, B is the amplitude ratio of the same type of seismic wave in the transmitted wave to the corresponding incident wave, C is the amplitude ratio of different types of seismic waves in the reflected wave to the corresponding incident wave, and D is the amplitude ratio of different types of seismic waves in the reflected wave to the corresponding incident wave.

[0045] The reflection and transmission calculation involves multiple conversions in layered strata, and cannot be naturally terminated, and therefore needs to be ensured to be effectively performed by defining the termination condition of the iteration of the conversion process.

[0046] The termination condition defined in the application includes two kinds, one is that the seismic wave is located in the lowermost layer and the propagation direction is downward, this type of seismic wave will be out of the model area, so only the seismic wave is considered, and the subsequent conversion condition does not need to be considered; the second is that the amplitude of the generated seismic wave is too small, the amplitude ratio of the target seismic wave and the original incident wave is less than 0.01, then the seismic wave and the subsequent seismic wave can be ignored; otherwise, the calculated process of the reflection and transmission of the incident wave is repeated, and the iterative calculation is carried out.

[0047] In terms of convergence of the termination condition, considering the diffusion attenuation characteristics of the actual seismic wave propagation process, the iteration converges.

[0048] On this basis, the equivalent node force is:

[0049]

[0050] Wherein, K b is the spring stiffness matrix, C b is the damping coefficient matrix, u b is the free field displacement vector, is the free field velocity vector, sigma b is the free field stress, and n is the boundary outer normal direction vector; A l is the node control area of the node to be solved.

[0051] For the spring stiffness matrix, in the tangential direction In the normal direction Wherein, G is the shear modulus of the layer, and R is the distance from the scattering wave source to the viscoelastic boundary.

[0052] For the damping coefficient matrix, in the tangential direction C bT = rho * c s , in the normal direction C bN = rho * c p , wherein, rho is the density of the layer, c s is the shear wave velocity, and c p is the compression wave velocity.

[0053] For the free field displacement vector and the free field velocity vector, the conversion of the seismic wave on the layered interface is obtained according to the Snell equation, and the space-time relationship between the incident wave and the seismic wave is analyzed, and then the wave superposition principle is used to solve. The calculation of the reflection and transmission time delay proposed in the application can be effectively applied to this.

[0054] The equivalent node force calculated at each time is applied to the corresponding boundary point of the model, so that the seismic oblique incidence calculation of the three-dimensional layered stratum model can be carried out, and the seismic response of the model stratum is solved.

[0055] When the method is applied to analyze the seismic response of underground structures, the structures can be considered and calculated in the model to analyze the seismic response of the underground structures; when the method is applied to analyze the above-ground structures, the stratum can be solved first, and the calculation results of the stratum model are applied to the structure analysis.

[0056] Therefore, the application adopts the above-mentioned input method of oblique incidence of seismic waves for layered stratum, so that the input of seismic waves under the layered stratum is more accurate, the use of parameters on the seismic wave propagation path is reduced, the input method of seismic waves for layered stratum is established, effective support is provided for the seismic response analysis of near-fault structures, and the method has strong practicability.

[0057] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit it. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or equivalent replacements should not make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. An input method for oblique incidence three-dimensional modeling of ground motion applied to a layered ground, characterized by, The method comprises the following steps: S1, modeling each layer of stratum; S2, calculating time delay and amplitude ratio in reflection and transmission, comprising the following steps: S21, taking the intersection of zero time wave front and stratum interface as equivalent zero time point; S22, calculating time delay as follows: ； wherein, is the time delay, , , are the coordinate differences of the sought point and the equivalent zero-time point in the directions of the three coordinate axes, respectively, x , y , z is the propagation speed of the corresponding type of seismic wave at the target point, , , are the angles between the direction of propagation of the sought seismic wave and the three coordinate axes, respectively.​ S23, calculating amplitude ratio before and after conversion according to wave propagation relationship, and multiplying the amplitude ratio obtained in each conversion process on the path to obtain amplitude ratio with incident wave; S24, if the corresponding seismic wave transmits out the lower boundary of the model or the amplitude is too small, the calculation is terminated, otherwise it is taken as incident wave to repeat step S21 and step S22; S3, calculating model boundary point parameters; S4, assigning values to model parameters.

2. The method of claim 1, wherein the method is applied to a layered formation. In step S1 of three-dimensional modeling of each layer of stratum, eight-node linear hexahedral elements are used for division, and node coordinates and node control area on the boundary surface are extracted.

3. The method of claim 1, wherein: Time delay and amplitude ratio are used to calculate equivalent node force in combination with node control area.

4. The method of claim 1, wherein, Termination condition of loop calculation: including amplitude ratio less than 0.01; seismic wave is located in the lowermost layer of stratum and the propagation direction is downward.

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