Method for judging local influence range of cross station structure in vibration table test

Abstract

The invention belongs to the field of interaction between soil and a structure in geotechnical engineering, and provides a method for judging a local influence range of a cross station structure in a vibration table test. Comprising the steps of 1, designing a three-dimensional reduced scale model of the cross transfer station; 2, designing three-dimensional measuring points of the cross transfer station model; 3, generating an internal force characteristic curve of the cross transfer section; and 4, judging the influence range of the local cross transfer section of the station structure. According to the method, after the influence range of the cross transfer section of the cross station structure is determined, the cross transfer subway station structure can be divided into two parts to be subjected to anti-seismic analysis by adopting a segmentation processing method, and the problem of spatial effect influence factors of the cross transfer station is effectively solved.

Description

Technical Field

[0001] The invention belongs to the field of soil-structure interaction in geotechnical engineering, and provides a method for determining the local influence range of a cross station structure in a shaking table test. Background Art

[0002] Urban underground rail transit, as an important way to alleviate the shortage of urban ground transportation resources, is an important trend in the future development of cities. At the same time, my country is located between two major seismic belts, so the seismic design and safety assessment of urban underground rail transit are crucial.

[0003] Previous studies have yielded some generally accepted rules for frame-type underground structures with simple cross-sectional forms, including: the vibration modes and deformation characteristics of underground structures are primarily affected by the properties of the surrounding soil, with the inertial effect of the structure being insignificant; the seismic response of underground structures, in addition to being affected by the properties of the surrounding soil, is primarily influenced by the flexibility ratio between the soil and the structure; and for frame-type underground structures, the center column is the weak link in the seismic resistance of the underground structure, and damage to the underground structure is usually caused by the failure of the center column.

[0004] However, complex transfer subway stations, such as those with cross-junction nodes, have been largely unstudied due to their complex stress conditions, significant spatial effects, and the difficulty of preparing experimental models. The primary difference between a cross-junction transfer subway station and a traditional single-unit station is the central cross-junction section. The structural vibration modes, dynamic deformation characteristics, and impact range of this section directly impact the seismic performance of such a station. Currently, there is no widely accepted technical approach to accurately describe its seismic response characteristics and reveal its structural failure mechanisms and seismic weaknesses. Only a small number of researchers have conducted research using finite element numerical simulations. Summary of the Invention

[0005] In summary, the present invention will propose a research method based on shaking table model test, use the test collected data to establish the force system of the local cross-transfer section of the station, and propose a method for determining the influence range of the cross-transfer section. The application of this invention patent is of great significance. The ultimate goal of the seismic response analysis of underground structures is to guide the seismic design of underground structures and improve the seismic performance of underground structures. At this stage, the seismic design of underground structures is based on the cross-sectional seismic design of underground structures, which is not suitable for cross-transfer subway stations with obvious spatial effects. After using the present invention to determine the influence range of the cross-transfer section of the cross-transfer station structure, the segmentation method can be used to divide the cross-transfer subway station structure into two parts for seismic analysis, which effectively solves the problem of factors affecting the spatial effect of the cross-transfer station.

[0006] The purpose of the present invention is to propose a method for determining the local influence range of a cross-intersection station structure in a shaking table test, which effectively solves the problem of complex stress characteristics of the interaction between the complex cross-intersection transfer station structure and the surrounding soil.

[0007] The method for determining the local influence range of the cross-intersection station structure in the shaking table test includes the following steps:

[0008] Step 1: Design of a 3D scale model of the cross-transfer station;

[0009] The shaking table model similarity theory is based on Buckingham's π theorem. Plexiglas was used as the model material for the shaking table test of the cross-interchange station structure, and a scale model with a scale of 1:50 was used. Length, elastic modulus, and acceleration were selected as the fundamental physical quantities of the structural model, while shear wave velocity, density, and acceleration were selected as the fundamental physical quantities of the model soil. Similarity relationships were derived for the remaining physical quantities.

[0010] Equivalent bending moment design was performed on the side walls, roof, middle plate, and bottom plate of the underground structure, and then converted to the equivalent thickness of the organic glass using a similarity ratio. Equivalent axial force design was performed on the central column of the underground structure. The reinforced concrete cross-section of the prototype structure central column was converted to a plain concrete cross-section, and then converted to the equivalent thickness of the organic glass using a similarity ratio.

[0011] Step 2: Design of three-dimensional measurement points of the cross-transfer station model;

[0012] The core measuring points are mainly arranged along the long axis of the station, and are arranged section by section with the cross-transfer section as the dividing line. At the same time, considering the spatial effect of the cross-transfer section, the strain measuring points are arranged in three layers.

[0013] Step 3: Generation of internal force characteristic curve of cross-transfer section;

[0014] During the test, strain gauges were pasted vertically at the same position on both the inside and outside of each component of the structural model to reflect the strain conditions at each position of the structural model within the observation section.

[0015] M=E·I·ε / y

[0016] Where E is the material elastic model; I is the section moment of inertia, ε is the surface strain, and y is the distance from the strain gauge position to the neutral axis.

[0017] The above formula is used to calculate the bending moment values of the side walls and center columns of the model structure. Based on the similarity principle, the bending moment values of the side walls and center columns of the prototype structure are obtained. Similarly, the axial force values of the side walls and center columns of the prototype structure are obtained.

[0018] The internal force peak value in the dynamic time history process is selected as the representative value, and the internal force peak point of the side wall and center column of the cross station structure along the horizontal axial direction is calibrated with the end of the station intersection transfer as the starting point. The polynomial fitting is performed based on the measured test data. The best polynomial fitting curve is determined based on the principle of

[0019] Where x i is the test point data, y i is the target parameter converted from the test point data, δ i 2 is the square of the target deviation.

[0020] Step 4: Determine the impact range of the local cross-transfer section of the station structure;

[0021] The influence range is determined by using the internal force characteristic change curve along the axial direction of the cross transfer section of the cross station structure.

[0022] The concept of curve gradient is introduced, which represents the rate and direction of change of a function at a certain point. In one-dimensional space, the gradient is the derivative of the function, which represents the rate of change of the function at a certain point.

[0023]

[0024] Where, X n-1 、X n 、X n+1 Y is the distance between the N-1, N, and N+1 measuring points and the intersection end. n-1 、Y n 、Y n+11 The peak values of the bending moment responses at the N-1, N, and N+1 measuring points;

[0025] When the distance from the cross transfer end is X n When the above formula is satisfied, the difference before and after the peak of the structural internal force response is within 5%, and the curve trend is considered to be approaching zero. Therefore, when the difference is less than this threshold, it is determined that the corresponding N point has reached the maximum influence range of the cross-transfer section of the cross-transfer station.

[0026] This paper proposes a method for determining the local influence range of a cross-intersection station structure using a shaking table test, which has the following innovative features:

[0027] Innovation point 1: Due to the limitations of the vibration table model size and the test material, the similarity ratio between the scaled model of the vibration table of underground structures and the prototype can only be 1:20 to 1:30 at most. When the underground station structure is complex enough, its corresponding scale ratio is far from meeting the requirements. The reinforced concrete scaled model made at this time is extremely difficult to form, and it is also impossible to truly reflect the material properties of the prototype structure. Therefore, the present invention uses organic glass material as a model material for the vibration table test of the cross-interchange transfer station structure, which is a new attempt. This type of material can effectively realize a scaled model with a scale ratio of more than 1:50. At the same time, the new method of equivalent bending moment and equivalent axial force is used to control the cross-sectional size of the scaled model to effectively restore the mechanical properties of the prototype, making the reinforced concrete prototype structure similar to the scaled organic glass model.

[0028] Innovation point 2: Design and arrange a distribution pattern of strain sensors suitable for the local influence range of the cross-intersection station structure model, fully considering the influence of the cross-transfer section of the cross-intersection transfer station structure, and reproducing the strain distribution trend along the axis of the cross-intersection station shaking table model through sensor arrangement.

[0029] Innovation point three: Based on the model strain distribution points collected in the test, considering the similarity ratio between the model material parameters and the prototype structure parameters, polynomial fitting of the internal force distribution curve is performed. At the same time, based on the concept of curve gradient, a method for judging the influence range based on the structural internal force distribution curve is proposed. The basic indicator for judgment is the 5% difference between the peak internal forces of the previous and subsequent structures. When the difference is less than the threshold, it can be judged that the cross-transfer section of the cross-transfer station has reached the maximum influence range. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Schematic diagram of the cross station structure model of the present invention

[0031] Figure 2 Schematic diagram of the cross-sectional dimensions of the vibration table model structure of the present invention (mm);

[0032] Figure 3 for Figure 2 1-1 cross-sectional view;

[0033] Figure 4 for Figure 2 2-3 cross-section diagram;

[0034] Figure 5 The distribution of strain measurement points on the longitudinal section of the structural model of the present invention;

[0035] Figure 6 The strain measurement point distribution of the outer wall of the structural model of the present invention;

[0036] Figure 7The distribution of measuring points of the top cross section of the structural model of the present invention;

[0037] Figure 8 Schematic diagram of the curve gradient of the present invention. DETAILED DESCRIPTION

[0038] The following is a further description of the method for determining the local influence range of a cross-intersection station structure using a shaking table test proposed by the present invention. The specific calculation steps are as follows:

[0039] Step 1: Design of a 3D scale model of the cross-transfer station;

[0040] The similarity theory of the vibration table model is based on Buckingham's π theorem, that is, if a physical system has n different physical quantities, of which k physical quantities have independent dimensions, then the n physical quantities can be represented by similarity criteria π1, π2, ..., π n-k The functional relationship between them is expressed. Plexiglas was used as the model material for the shaking table test of the cross-interchange station structure, and a scale model with a scale of 1:50 was used. In the test, length, elastic modulus, and acceleration were selected as the basic physical quantities of the structural model, and shear wave velocity, density, and acceleration were selected as the basic physical quantities of the model soil. Similar relationships were derived for the remaining physical quantities, as shown in Table 1.

[0041] Table 1 Model similarity ratio

[0042]

[0043] Symbol u r ,L r ,σ r ,E r ,ρ r ,v r ,t r ,w r ,a r ,g r They represent the similarity ratios of displacement, geometric dimensions, stress, elastic modulus, mass density, velocity, time, frequency, acceleration, and gravitational acceleration respectively.

[0044] An underground structure that has undergone a reasonable shear resistance design can significantly improve its shear resistance, thereby avoiding simple shear failure. Therefore, the present invention performs an equivalent bending moment design on the side walls, top, middle plate, and bottom plate of the underground structure, i.e., E1I1=E2I2, and the reinforced concrete cross-sections of the side walls, top, middle plate, and bottom plate of the prototype structure are equivalent to plain concrete cross-sections, and then converted into equivalent thicknesses of organic glass using a similarity ratio. At the same time, an equivalent axial force design is performed on the columns of the underground structure, i.e., E1A1=E2A2, and the reinforced concrete cross-sections of the columns of the prototype structure are equivalent to plain concrete cross-sections, and then converted into equivalent thicknesses of organic glass using a similarity ratio. This achieves the process of making the reinforced concrete prototype structure similar to a scaled organic glass model.

[0045] In this embodiment, some minor auxiliary structures were removed during the model preparation process. The overall structural model is cross-shaped in the top view. The structural cross-sections of the model in two directions are respectively a three-story three-span structural cross-section and a two-story three-span structural cross-section. Figure 1 、 Figure 2 、 Figure 3 and Figure 4 shown.

[0046] Step 2: Design of three-dimensional measurement points of the cross-transfer station model;

[0047] The arrangement of the test measuring points is ultimately intended to test the distribution of deformation characteristics of the model structure along the axial direction. Therefore, the core measuring points are mainly arranged along the long axis of the station, and are arranged section by section with the cross-transfer section as the dividing line. At the same time, considering the spatial effect of the cross-transfer section, the strain measuring points are arranged in three layers.

[0048] In this embodiment, the model can be set up with 8 strain observation sections, each of which has 10 measuring points to measure the strain responses of the top, middle, and bottom of the side walls and the top and bottom of the center column respectively; the strain gauge sensors are represented by the letter S, and there are 78 in total, such as Figure 5 、 Figure 6 and Figure 7 shown.

[0049] Step 3: Generation of internal force characteristic curve of cross-transfer section;

[0050] During the test, strain gauges can be vertically pasted at the same position on both the inside and outside sides of each component of the structural model to reflect the strain conditions at various positions of the structural model within the observation section.

[0051] M=E·I·ε / y

[0052] Where E is the material elastic model; I is the section moment of inertia, ε is the surface strain, and y is the distance from the strain gauge position to the neutral axis.

[0053] The above formula can be used to calculate the bending moment values of the side walls and center columns of the model structure. Based on the similarity principle, the bending moment values of the side walls and center columns of the prototype structure can be obtained. Similarly, the axial force values of the side walls and center columns of the prototype structure can be obtained.

[0054] The internal force peak value (bending moment, axial force) in the dynamic time history process is selected as the representative value. The internal force peak point of the side wall and center column of the cross station structure along the horizontal axial direction is calibrated with the cross transfer end of the station as the starting point. The polynomial fitting is performed based on the measured test data. The best polynomial fitting curve is determined based on the principle of i is the test point data, y i is the target parameter converted from the test point data, is the square of the target deviation.

[0055] Step 4: Determine the impact range of the local cross-transfer section of the station structure;

[0056] The influence range is determined by using the internal force characteristic change curve along the axial direction of the cross transfer section of the cross station structure (the curve generated in the third step).

[0057] Introducing the concept of curve gradient, such as Figure 8 , which represents the rate and direction of change of a function at a certain point. In one-dimensional space, the gradient is the derivative of the function, which represents the rate of change of the function at a certain point.

[0058]

[0059] Where, X n-1 、X n 、X n+1 Y is the distance between the N-1, N, and N+1 measuring points and the intersection end. n-1 、Y n 、Y n+11 The peak values of the bending moment responses at the N-1, N, and N+1 measuring points;

[0060] When the distance from the cross transfer end is X n When the above formula is satisfied, the difference between the peak value of the structural internal force response before and after is within 5%, and the curve trend can be considered to be approaching zero. Therefore, when the difference is less than this threshold, it can be determined that the corresponding N point has reached the maximum influence range of the cross-transfer section of the cross-transfer station.

[0061] The impact range determined by the above-mentioned discrimination method is of great significance. Based on this indicator, a seismic design for the structure of a cross-transfer station can be proposed. The splitting method is used to divide the cross-transfer subway station structure into two parts for separate seismic analysis, effectively solving the problem of factors affecting the spatial effect of the cross-transfer station.

Claims

1. The method for determining the local influence range of the cross station structure in the shaking table test is characterized by: The following steps are involved: Step 1: Design of a 3D scale model of the cross-transfer station; The shaking table model similarity theory is based on Buckingham's π theorem. Plexiglas is used as the model material for the shaking table test of the cross-interchange station structure, and the scale model is 1:

50. Step 2: Design of three-dimensional measurement points of the cross-transfer station model; The core measuring points are mainly arranged along the long axis of the station, with the cross-transfer section as the dividing line. Taking the spatial effect of the cross-transfer section into consideration, the strain measuring points are arranged in three layers. Step 3: Generation of internal force characteristic curve of cross-transfer section; During the test, strain gauges are attached vertically at the same position on both sides of the inner and outer parts of each component of the structural model to reflect the strain conditions at each position of the structural model within the observation section. Calculate the bending moment values of the side walls and center columns of the model structure, and then obtain the bending moment values of the side walls and center columns of the prototype structure based on the similarity principle. Similarly, obtain the axial force values of the side walls and center columns of the prototype structure. The internal force peak value during the dynamic time history is selected as the representative value. Starting from the station intersection transfer end, the internal force peak points of the side walls and center columns of the intersection station structure along the horizontal axial direction are calibrated. Based on the measured test data, a polynomial fitting is performed. The optimal polynomial fitting curve is determined using the principle of minimizing the sum of squared deviations. Step 4: Determine the impact range of the local cross-transfer section of the station structure; The influence range is determined by using the internal force characteristic change curve along the axial direction of the cross transfer section of the cross station structure.

2. The method for determining the local influence range of a cross station structure in a shaking table test according to claim 1 is characterized in that: In step 1, length, elastic modulus, and acceleration are selected as the basic physical quantities of the structural model, and shear wave velocity, density, and acceleration are selected as the basic physical quantities of the model soil, and similar relationships of the remaining physical quantities are derived; Conduct equivalent bending moment design for the side walls, top, middle plate and bottom plate of the underground structure, and then convert the equivalent thickness of the organic glass into equivalent thickness by similarity ratio; The equivalent axial force design is carried out on the central column of the underground structure. The reinforced concrete section of the central column of the prototype structure is equivalent to the plain concrete section, and then converted into the equivalent thickness of organic glass of the same width by similarity ratio.

3. The method for determining the local influence range of a cross station structure in a shaking table test according to claim 1 is characterized in that: In step 3, the bending moment values of the side walls and center columns of the model structure are calculated using the following formula: M=E·I·ε / y Where E is the material elastic model; I is the section moment of inertia, ε is the surface strain, and y is the distance from the strain gauge position to the neutral axis.

4. The method for determining the local influence range of a cross station structure in a shaking table test according to claim 1 is characterized in that: Step 4 introduces the concept of curve gradient, which represents the rate of change and direction of a function at a certain point. In one-dimensional space, the gradient is the derivative of the function, which represents the rate of change of the function at a certain point. Where, X n-1 、X n 、X n+1 Y is the distance between the N-1, N, and N+1 measuring points and the intersection end. n-1 、Y n 、Y n+11 The peak values of the bending moment responses at the N-1, N, and N+1 measuring points; When the distance from the cross transfer end is X n When the above formula is satisfied, the difference before and after the peak value of the structural internal force response is within 5%, and the curve change trend is considered to be approaching zero; therefore, when the difference is less than the threshold, it is judged that the corresponding N point has reached the maximum influence range of the cross-transfer section of the cross-transfer station.

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