CN113987888A - A Numerical Separation Method of Bedrock Incident-Down Waves Based on Array Observation - Google Patents

A Numerical Separation Method of Bedrock Incident-Down Waves Based on Array Observation Download PDF

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CN113987888A
CN113987888A CN202111355758.3A CN202111355758A CN113987888A CN 113987888 A CN113987888 A CN 113987888A CN 202111355758 A CN202111355758 A CN 202111355758A CN 113987888 A CN113987888 A CN 113987888A
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阮滨
吉瀚文
王苏阳
苗雨
贺鸿俊
叶宜培
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Huazhong University of Science and Technology
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Abstract

The invention provides a matrix incident-downlink wave number value separation method based on array observation, which comprises the steps of establishing a two-dimensional stratified field finite element model according to wave speed structure information of a field where an array is located, inputting array matrix observation waves into grid nodes at the bottom, extracting a counter force time course RF (t) from middle grid nodes at the bottom after submitting operation, dividing the counter force time course by the grid node width L to obtain a node counter force time course F (t) with unit length, and converting the station matrix observation waves a (t) into an equivalent node force time course F (t)1And (t) calculating an equivalent node force time course f (t) of the bedrock incident wave, substituting the equivalent node force time course of the bedrock incident wave into an equivalent node force calculation formula, and performing inverse solution calculation to obtain a bedrock incident wave u (t). The method can separate the incident wave and the down-going wave reflected by the earth surface in the observation record of the vertical array bedrock, obtain the accurate input data for the earthquake-resistant analysis of the underground structure, and realize the accurate analysis of the earthquake field reaction.

Description

Bedrock incident-downlink wave number value separation method based on array observation
Technical Field
The invention relates to a matrix incident-downlink wave number value separation method based on array observation, which can be used for separating incident waves contained in a field matrix observation record of a vertical array of a global strong earthquake observation platform network and belongs to the technical field of earthquake engineering.
Background
The complex field reaction caused by the near-surface propagation of the vibration is always an important subject of seismic engineering. Researches show that the propagation process of seismic motion on the near-surface comprises incident waves transmitted from bedrock to the surface and downlink waves reflected to the bedrock through the surface, which causes certain difficulties in the analysis of the propagation process of the seismic on the near-surface and the seismic analysis of underground structures. The accurate input of the earthquake motion of the bedrock is very important, the existing simulation analysis underground structure earthquake resistance mostly adopts a mode of combining equivalent node force and a viscoelastic boundary as an earthquake motion input mode and a bottom boundary condition, bedrock waves recorded by a typical station field close to a researched engineering field are selected as input waves, and the wave band is superposed waves of incident waves and reflected waves of the bedrock of the station observation field, so that the superposed waves are directly converted into estimated earthquake motion input energy with overhigh equivalent node force, and the adverse effect is generated on the analysis of damage of the underground structure in the earthquake.
Based on the fact that the existence of the down waves causes that the bedrock observation records are directly converted into seismic force input is inaccurate, and a more reasonable calculation result can be obtained only by converting bedrock incident waves into the seismic force as the input, so that the research of the incident wave separation method has important value for analyzing the underground structure seismic design.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a bedrock incident-downlink wave number value separation method based on array observation, which can separate incident waves and downlink waves reflected by the earth surface in the observation records of the bedrock of a vertical array by applying finite element numerical simulation software ABAQUS and the analysis algorithm provided by the invention, obtain accurate input data for performing earthquake-resistant analysis of an underground structure and realize accurate reaction analysis of an earthquake field.
The technical scheme adopted by the invention for solving the technical problem is as follows: the utility model provides a bedrock incident-downlink wave number value separation method based on array observation, which comprises the following steps:
s1, establishing a two-dimensional layered site finite element model according to wave velocity structure data, provided by a seismic observation table network, of S waves and P waves of a site soil layer where a vertical array is located, changing along the depth of the soil layer, inputting an array bed rock observation wave a (t) recorded by an array bed rock at the bottom of the two-dimensional layered site finite element model, establishing a dynamic analysis step, and submitting the dynamic analysis step to matrix iterative operation;
s2, extracting a mesh node reaction time course RF (t) at the middle node at the bottom of the calculated two-dimensional layered field finite element model, and dividing the mesh node reaction time course RF (t) by the mesh node width L to obtain a node reaction time course F (t) of unit length;
s3, converting the array bedrock observation wave a (t) into an equivalent node force time course F by adopting an equivalent node force calculation formula1(t)；
S4, calculating the equivalent node force time course f (t) of the bedrock incident wave by the following formula:
f(t)＝(F(t)+F1(t))/2
and S5, substituting the equivalent node force time course of the bedrock incident wave into an equivalent node force calculation formula for inverse solution calculation to obtain an incident velocity time course u (t).
In step S1, a two-dimensional layered site finite element model is established by using ABAQUS/CAE, and both the lateral boundary and the bottom boundary of the two-dimensional layered site finite element model adopt vertical constraints to control the mesh nodes of the two-dimensional layered site finite element model to move only in the horizontal direction.
In step S3, the following equivalent node force calculation formula is used to convert the array bedrock observation wave path a (t) into an equivalent node force time path F1(t)：
F1(t)＝AbVsρu0(t)
Wherein A isbDenotes the grid size, p denotes the material density, VsDenotes the material shear wave velocity u0(t) represents the observation speed of the bedrock of the station, and is calculated by the following formula:
Figure BDA0003357513120000021
step S5 specifically uses the following formula to calculate the incident velocity time interval u (t):
u(t)＝f(t)/(AbρVs)。
the invention has the beneficial effects based on the technical scheme that: the existing simulation analysis of underground structure earthquake resistance mostly adopts a mode of combining equivalent node force and viscoelastic boundary as an earthquake motion input form and bottom boundary condition, selects basement wave recorded by a typical station field close to a researched engineering field as input wave, but the wave band is superposition wave of basement incident wave and reflected wave of the station observation field, directly converts the superposition wave into energy of estimation earthquake motion input with overhigh equivalent node force, and generates adverse effect on the evaluation of damage of the underground structure in the earthquake. The matrix incident-downlink wave number value separation method based on array observation provided by the invention can separate incident waves in vertical array matrix observation records from the downlink waves reflected by the earth surface, obtain accurate input data for underground structure earthquake resistance analysis, realize accurate reaction analysis of earthquake fields, and has important engineering significance for underground structure earthquake resistance simulation.
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Fig. 1 is a schematic flow chart of a matrix incident-downlink wave number value separation method based on array observation provided by the invention.
Figure 2 is a schematic diagram of a vertical array bedrock and surface accelerometer arrangement.
FIG. 3 is a schematic diagram of a two-dimensional layered yard finite element model.
Fig. 4 is a schematic structural diagram of the S wave and P wave speed of the soil layer of the field where the array is located.
Fig. 5 is a schematic diagram of incident waves and observed waves under an ideal two-dimensional field model.
FIG. 6 is a schematic diagram of an equivalent node force and a unit node counter force time course.
Fig. 7 is a schematic diagram of the time course of the incident wave calculated by the separation of the incident-downlink wave number values from the theoretical solution.
Fig. 8 is a schematic diagram of seismic simulation analysis of a two-dimensional field tunnel cross section.
FIG. 9 is a schematic diagram of the effect of separating the downgoing wave on the bending moment envelope of the tunnel cross section.
Detailed Description
The invention is further illustrated by the following figures and examples.
The invention provides a bedrock incident-downlink wave number value separation method based on array observation, which comprises the following steps with reference to fig. 1:
s1, arranging the seismic observation station net as shown in figure 2, providing wave velocity structure data of S waves and P waves of a soil layer of a vertical station array as shown in figure 4, and establishing a two-dimensional layered site finite element model shown in figure 3 in ABAQUS/CAE according to the data. The ABAQUS/CAE is a preprocessing module of ABAQUS software and can directly establish a finite element model. The height of the two-dimensional layered field finite element model is the drilling depth of a vertical array, square grids with the side length of L are used for grid dispersion in ABAQUS, grid nodes of the lateral boundary and the bottom boundary of the two-dimensional layered field finite element model both adopt vertical constraint conditions provided by ABAQUS, the lateral boundary and the bottom boundary grid nodes of the two-dimensional layered field finite element model are controlled to move only along the horizontal direction, the acceleration time course a (t) recorded by array bed rock is input to the grid nodes at the bottom of the model, and dynamic analysis step submission matrix iterative operation is established.
S2, extracting a reaction force time course RF (t) at the middle node at the bottom of the calculated two-dimensional layered field finite element model, and dividing the node reaction force time course RF (t) by the grid node width L to obtain a node reaction force time course F (t) with unit length.
S3, converting the array bedrock observation wave path a (t) into an equivalent node force time path F by adopting the following equivalent node force calculation formula1(t)：
F1(t)＝AbVsρu0(t)
Wherein A isbDenotes the grid size, pDenotes the density of the material, VsDenotes the material shear wave velocity u0(t) represents the observation speed of the bedrock of the station, and is calculated by the following formula:
Figure BDA0003357513120000031
s4, calculating the equivalent node force time course f (t) of the bedrock incident wave by the following formula:
f(t)＝(F(t)+F1(t))/2
s5, substituting the equivalent node force time course of the bedrock incident wave into an equivalent node force calculation formula to perform inverse solution calculation to obtain the bedrock incident wave, and specifically calculating by adopting the following formula to obtain an incident velocity time course u (t):
u(t)＝f(t)/(AbρVs)。
the feasibility can be verified through an ideal two-dimensional field model:
a finite field with the height of 50m and the length of 2m is established in the ABAQUS/CAE to serve as a research area, and middle nodes at the top and the bottom of an ideal two-dimensional field finite element model serve as monitoring points A and B of the model. The material parameters were as follows: density rho 1000kg/m3Elastic modulus E is 24MPa, Poisson ratio V is 0.2, and material shear wave velocity VsAnd (3) performing grid discretization on the ideal two-dimensional site finite element model by adopting a four-node plane strain unit (CPE4) at 100m/s, wherein the unit size is equal to Δ x and equal to Δ y and equal to 1 m. Applying a unit pulse wave of the following formula to the bottom boundary in the X direction:
Figure BDA0003357513120000041
under an ideal two-dimensional field model, the obtained pulse wave is used as an input wave, converted into an equivalent node force adapted to a viscoelastic boundary and used as the input wave to the model bedrock, and the time course of the observation wave at the bottom of the model is shown in fig. 5.
Regarding the model bottom observation wave of FIG. 5 as an array bedrock observation record, extracting a middle node reaction time course RF (t) at the bottom of the model, wherein the node reaction is a unit node reaction F (t) because the size of a model unit is 1 m; the time courses of the bedrock observation wave, F1(t), F (t) and F1(t) are converted by applying the formula (1) to the equivalent node force time course as shown in fig. 6, and it can be seen that the first peaks of F (t) and F1(t) are identical and the second peaks are opposite.
Unit node reaction force F (t) at bottom of model and equivalent node force time course F recorded by bedrock observation1The first peak of (t) is the same, and the second peak is exactly opposite, so F (t) ═ F (t) + F is used1(t))/2, the equivalent node force f (t) corresponding to the incident wave can be calculated, and u (t) is obtained by inverse solution of an equivalent node force calculation formula, wherein u (t) is the bedrock wave time course, and the node force f (t) and the bedrock wave u (t) are shown in fig. 7. As can be seen from fig. 7, the time course of incident wave displacement obtained by applying the method is basically consistent with the theoretical solution of fig. 5, and the feasibility and effectiveness of the method are proved.
The method provided by the invention is applied to the anti-seismic simulation analysis of the cross section of a tunnel in a two-dimensional field, the matrix incident wave obtained by separating the matrix incident wave value and the downlink wave value in the array observation field is used as the matrix seismic input, and the influence of the separated and undiseparated downlink wave on the anti-seismic analysis of the tunnel is compared:
fig. 8 is a schematic diagram of seismic simulation analysis of a two-dimensional field tunnel cross section, in which acceleration time courses of separated and non-separated traveling waves are applied to the bottom boundary of a numerical model of the two-dimensional field tunnel cross section as input waves respectively, and a bending moment envelope curve of the tunnel cross section is calculated. Fig. 9 shows the effect of separating and not separating the down-traveling wave on the bending moment envelope curve of the cross section of the tunnel, and it can be seen from fig. 9 that the incident wave obtained by applying the method of the present invention is used as the seismic input of the bedrock, and the calculated bending moment envelope curve of the cross section of the tunnel is smaller compared with the traditional input method, which shows that the energy of the seismic input is estimated in consideration of the over-high input method of the down-traveling wave separation.
According to the matrix incident-downlink wave number value separation method based on array observation provided by the invention, incident waves in vertical array matrix observation records and downlink waves reflected by the earth surface can be separated, accurate input data for underground structure seismic analysis is obtained, and accurate reaction analysis of a seismic field can be realized.

Claims (4)

1.一种基于台阵观测的入射-下行波场分离方法，其特征在于包括以下步骤：1. an incident-downward wave field separation method based on stage array observation, is characterized in that comprising the following steps: S1、根据地震观测台网提供的竖向台阵所在场地土层的S波和P波沿土层深度变化的波速结构数据，建立二维成层场地有限元模型，在二维成层场地有限元模型的底部输入台阵基岩记录的台阵基岩观测波a(t)，建立动力分析步，提交矩阵迭代运算；S1. According to the wave velocity structure data of the S-wave and P-wave of the soil layer at the site where the vertical array is located, provided by the seismic observation network, a two-dimensional layered site finite element model is established, and the finite element model of the two-dimensional layered site is established. Input the observation wave a(t) of the array bedrock recorded by the array bedrock at the bottom of the model, establish a dynamic analysis step, and submit the matrix iterative operation; S2、在计算完成的二维成层场地有限元模型底部中间节点提取网格节点反力时程RF(t)，将网格节点反力时程RF(t)除以网格节点宽度L，得到单位长度的节点反力时程F(t)；S2. Extract the grid node reaction force time history RF(t) at the middle node at the bottom of the calculated two-dimensional layered site finite element model, and divide the grid node reaction force time history RF(t) by the grid node width L, Get the nodal reaction time history F(t) of unit length; S3、采用等效节点力计算公式将台阵基岩观测波a(t)转化为等效节点力时程F1(t)；S3. Convert the observation wave a(t) of the array bedrock into the equivalent nodal force time history F 1 (t) by using the equivalent nodal force calculation formula; S4、通过以下公式计算基岩入射波的等效节点力时程f(t)：S4. Calculate the equivalent nodal force time history f(t) of the bedrock incident wave by the following formula: f(t)＝(F(t)+F1(t))/2f(t)=(F(t)+F 1 (t))/2 S5、将基岩入射波的等效节点力时程代入等效节点力计算公式反解计算得到入射速度时程u(t)。S5. Substitute the equivalent nodal force time history of the incident wave of the bedrock into the equivalent nodal force calculation formula and calculate the inverse solution to obtain the incident velocity time history u(t). 2.根据权利要求1所述的基于台阵观测的入射-下行波场分离方法，其特征在于：步骤S1中，采用ABAQUS/CAE建立二维成层场地有限元模型，二维成层场地有限元模型的侧向边界和底部边界均采用竖向约束，以控制二维成层场地有限元模型的网格节点仅沿水平方向运动。2. the incident-downward wave field separation method based on the observation of the stage array according to claim 1, is characterized in that: in step S1, adopt ABAQUS/CAE to establish the finite element model of two-dimensional layered site, and the two-dimensional layered site is limited Both the lateral boundary and the bottom boundary of the element model adopt vertical constraints to control the mesh nodes of the two-dimensional layered site finite element model to move only in the horizontal direction. 3.根据权利要求1所述的基于台阵观测的入射-下行波场分离方法，其特征在于：步骤S3中，采用以下等效节点力计算公式将台阵基岩观测波程a(t)转化为等效节点力时程F1(t)：3. The incident-downward wave field separation method based on array observation according to claim 1, characterized in that: in step S3, the following equivalent nodal force calculation formula is used to observe the wave path a(t) of the array bedrock Converted to equivalent nodal force time history F 1 (t): F1(t)＝AbVsρu0(t)F 1 (t)=A b V s ρu 0 (t) 其中，Ab表示网格尺寸，ρ表示材料密度，Vs表示材料剪切波速，u0(t)表示台站基岩观测速度，通过以下公式计算得到：Among them, A b is the grid size, ρ is the material density, V s is the material shear wave velocity, and u 0 (t) is the observation velocity of the bedrock of the station, which is calculated by the following formula:
Figure FDA0003357513110000011
Figure FDA0003357513110000011
 4.根据权利要求1所述的基于台阵观测的入射-下行波场分离方法，其特征在于：步骤S5具体采用以下公式计算得到入射速度时程u(t)：4. the incident-downward wavefield separation method based on stage array observation according to claim 1, is characterized in that: step S5 adopts the following formula to calculate and obtains the incident velocity time course u(t) specifically: u(t)＝f(t)/(AbρVs)。u(t)=f(t)/(A b ρV s ).
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