Method and system for determining foundation bed coefficient in underground structure reaction displacement method

Abstract

The invention relates to the technical field of anti-seismic analysis of underground structures, in particular to a method and a system for determining a foundation bed coefficient in an underground structure reaction displacement method. The method comprises the following steps: acquiring working condition parameters of an underground structure; obtaining an influence factor curve of the foundation bed coefficient; obtaining a simplified formula of the foundation bed coefficient; calculating foundation bed coefficients under the working condition of the homogeneous site and the working condition of the layered site by utilizing a reaction displacement method; performing comparative analysis on the foundation bed coefficient and a foundation bed coefficient calculated by an existing standard method; analyzing the structural response under the working condition of the homogeneous site and the working condition of the layered site; verifying the applicability of the simplified formula; according to the applicability, the foundation bed coefficient in the underground structure reaction displacement method is determined. According to the method, static finite element analysis does not need to be repeated for multiple times, the calculation efficiency is high, the calculation precision can be guaranteed, the method has good applicability to different sites and structural forms, and important reference can be provided for anti-seismic analysis of underground structures.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic analysis of underground structures, and in particular to a method and system for determining a base bed coefficient in a reaction displacement method of an underground structure. Background Art

[0002] In recent years, with the development of urbanization, the development and utilization of underground space has become increasingly extensive. Among them, subway stations, as an important part of urban underground infrastructure, have attracted much attention for their seismic performance. Traditionally, underground structures have been considered to have strong seismic resistance, so the level of attention paid to disaster prevention and mitigation of underground projects is relatively low. However, observation data from multiple strong earthquakes have shown that underground structures are also at risk of suffering serious damage, which has prompted the academic and engineering communities to re-examine the seismic design of underground structures. Against this background, the theory and methods of seismic analysis of underground structures have developed rapidly. Among them, the response displacement method has been widely used in practical engineering due to its high calculation accuracy and simple operation.

[0003] Although the reaction displacement method has achieved remarkable results in the seismic analysis of underground structures, there are still many challenges in determining its bed coefficient. As a key parameter in the reaction displacement method, the value of the bed coefficient directly affects the accuracy of the analysis results.

[0004] At present, scholars at home and abroad have proposed a variety of methods to determine the foundation coefficient, including the free field deformation method, the flexibility coefficient method and the reaction displacement method. However, most of these methods only consider the influence of a single factor in the structure size or soil properties on the foundation coefficient, ignoring the comprehensive effect of site conditions, structure size and structure burial depth parameters on the foundation coefficient. In addition, the application effect of the traditional reaction displacement method in the analysis of certain specific underground structures is not ideal, and there is a problem of insufficient calculation accuracy. Therefore, how to accurately and simply determine the foundation coefficient has become a key issue that needs to be solved in the current field of seismic analysis of underground structures.

[0005] In order to overcome the problems existing in the prior art in determining the base bed coefficient, domestic and foreign scholars have conducted a lot of research and proposed a variety of improved methods, including the longitudinal integral reaction displacement method, the inertia force displacement method and the generalized reaction displacement method. These methods have improved the accuracy of determining the base bed coefficient to a certain extent, but they still have the limitations of complex operation and limited scope of application. In contrast, the present invention proposes a simpler and more widely applicable method for determining the base bed coefficient in the underground structure reaction displacement method. This method comprehensively considers the influence of multiple parameters such as site conditions, structural dimensions, and structural burial depth on the base bed coefficient, and realizes the rapid and accurate calculation of the base bed coefficient by establishing a simplified formula; by setting up homogeneous site and layered site conditions for comparative analysis, and comparing with the calculation results of the traditional reaction displacement method and the inertia force displacement method, the calculation accuracy and rationality of the method of the present invention are verified. Summary of the invention

[0006] In view of the defects in the prior art, the present invention provides a method and system for determining the base coefficient in the underground structure reaction displacement method.

[0007] In a first aspect, the present invention provides a method for determining a base bed coefficient in a reaction displacement method for an underground structure, comprising the following steps: obtaining operating parameters of an underground structure, the operating parameters including elastic modulus, aspect ratio, burial depth ratio and bedrock ratio parameters of the soil; using the operating parameters to obtain an influencing factor curve of the base bed coefficient; obtaining a simplified formula of the base bed coefficient based on the influencing factor curve; using the simplified formula, using the reaction displacement method, calculating the base bed coefficient under homogeneous site conditions and stratified site conditions; comparing and analyzing the base bed coefficient with the base bed coefficient calculated by the existing specification method to obtain a comparative analysis result; based on the comparative analysis result, analyzing the structural response under the homogeneous site condition and the stratified site condition to obtain a structural response analysis result; verifying the applicability of the simplified formula through the comparative analysis result and the structural response analysis result; and determining the base bed coefficient in the reaction displacement method for an underground structure based on the applicability. The present invention achieves accurate quantitative description of complex geological conditions by acquiring the working parameters of underground structures and drawing the influencing factor curve of the bed coefficient, breaking through the limitation of traditional methods on simplifying geological parameters; deriving a simplified formula of the bed coefficient through the influencing factor curve significantly improves the calculation efficiency and simplifies the traditional calculation mode that relies on complex numerical simulation; by applying the simplified formula to the reaction displacement method and calculating the bed coefficient under homogeneous and layered site conditions, unified processing of different site conditions is achieved, breaking through the constraints of traditional methods on site type restrictions; by comparing and analyzing the calculation results with a variety of existing standard methods, the universality and accuracy of the simplified formula are verified, subverting the single applicability of traditional standard methods; by analyzing the structural response and verifying the applicability of the simplified formula, accurate prediction of underground structure behavior is achieved, breaking through the empirical dependence of traditional methods in structural response analysis; by realizing the scientific determination of the bed coefficient in the reaction displacement method of underground structures, an important solution is provided for the seismic analysis of underground structures, overcoming the limitations of traditional methods for determining the bed coefficient.

[0008] Optionally, the use of the operating conditions parameters to obtain the curve of factors affecting the base bed coefficient includes: keeping the aspect ratio, burial depth ratio and bedrock ratio parameters of the soil unchanged, changing the elastic modulus parameters of the soil, and obtaining the relationship curve between the elastic modulus parameters and the base bed coefficient; keeping the elastic modulus, the burial depth ratio and the bedrock ratio parameters unchanged, changing the aspect ratio parameters, and obtaining the relationship curve between the aspect ratio parameters and the base bed coefficient; keeping the elastic modulus, the aspect ratio and the bedrock ratio parameters unchanged, changing the burial depth ratio parameters, and obtaining the relationship curve between the burial depth ratio parameters and the base bed coefficient; keeping the elastic modulus, the aspect ratio and the burial depth ratio parameters unchanged, changing the bedrock ratio parameters, and obtaining the relationship curve between the bedrock ratio parameters and the base bed coefficient. The present invention changes the elastic modulus, aspect ratio, burial depth ratio and bedrock ratio parameters of the soil one by one and keeps other parameters unchanged, obtains the relationship curve between the base bed coefficient and various influencing factors, realizes the accurate quantitative analysis of the influence of a single variable, breaks through the complexity of multivariate coupling analysis in traditional methods, and provides a clear theoretical basis for the scientific determination of the base bed coefficient; by systematically analyzing the influence of the elastic modulus, aspect ratio, burial depth ratio and bedrock ratio on the base bed coefficient, the independent action mechanism of each parameter on the base bed coefficient is revealed, the limitation of the general treatment of influencing factors in traditional methods is overcome, and a targeted solution is provided for the calculation of the base bed coefficient under different geological conditions; by establishing the relationship curve between the base bed coefficient and various influencing factors, data support is provided for the derivation of a simplified formula for the base bed coefficient, which significantly improves the calculation efficiency and accuracy.

[0009] Optionally, the simplified formula for obtaining the bed coefficient according to the influencing factor curve includes: extracting data of elastic modulus, aspect ratio, burial depth ratio and bedrock ratio parameters of the soil according to the influencing factor curve; fitting the data to obtain the simplified formula for the bed coefficient. The present invention realizes the comprehensive quantification of factors affecting the bed coefficient by extracting data of elastic modulus, aspect ratio, burial depth ratio and bedrock ratio parameters of the soil, and combining the influencing factor curve for systematic analysis, breaking through the limitation of fuzzy processing of parameter relationships in traditional methods, and laying a data foundation for the accurate calculation of the bed coefficient; by fitting the extracted data, a simplified formula for the bed coefficient is obtained, which significantly reduces the calculation complexity and overturns the inefficient mode of traditional methods relying on complex numerical simulation; by combining the simplified formula with actual working condition parameters, a rapid prediction of the bed coefficient under different geological conditions is realized, breaking through the limitations of traditional methods in terms of applicability and versatility.

[0010] Optionally, the simplified formula is as follows: , in, is the base bed coefficient, , , , , is a constant, for , for , for , is the elastic modulus of the soil, is the structure width, is the structure height, is the depth of structure, is the distance from the bottom plate of the structure to the bedrock. The present invention realizes mathematical modeling of complex geological conditions by expressing the bed coefficient as a linear combination of the soil elastic modulus, aspect ratio, burial depth ratio and bedrock ratio, breaking through the limitation of the traditional method of single reliance on experience or simplified assumptions for the bed coefficient, and providing a theoretical basis for the scientific calculation of the bed coefficient. By incorporating the parameters of structural width, height, burial depth and the distance from the bottom plate to the bedrock into the formula, the applicability and accuracy of the formula are significantly improved, subverting the processing mode of simplifying structural geometric parameters and geological conditions in traditional methods, and providing a unified framework for the calculation of bed coefficients under different working conditions; by using simplified formulas to quickly calculate the bed coefficient, the calculation complexity and time cost are greatly reduced, breaking through the inefficiency of traditional methods that rely on complex numerical simulations.

[0011] Optionally, the calculation of the base bed coefficient under the homogeneous site condition and the stratified site condition by using the reaction displacement method according to the simplified formula includes: calculating the base bed coefficient under the homogeneous site condition by using the reaction displacement method according to the simplified formula, the reaction displacement method includes the traditional reaction displacement method and the inertia force reaction displacement method; simplifying the stratified site to a homogeneous site, and constructing a conversion model of equivalent shear wave velocity, the conversion model is used to convert the shear wave velocity of the soil into the equivalent shear wave velocity, and the conversion model satisfies the following expression:

[0012] in, is the equivalent shear wave velocity, To calculate the depth, To calculate the depth range The thickness of the soil layer, To calculate the depth range The shear wave velocity of each soil layer; according to the simplified formula, combined with the conversion model, the reaction displacement method is used to calculate the base bed coefficient under the stratified site condition. The present invention calculates the base bed coefficient under the homogeneous site condition by simplifying the formula and combining the reaction displacement method, thereby realizing the accurate solution of the base bed coefficient of the homogeneous site, breaking through the limitation of the simplification of site conditions in the traditional method; by simplifying the stratified site into a homogeneous site and constructing a conversion model of the equivalent shear wave velocity, the scientific simplification of the complex stratified site conditions is realized, subverting the high complexity and inefficiency of the stratified site treatment in the traditional method, and providing an important solution for the calculation of the base bed coefficient of the stratified site; by combining the simplified formula and the equivalent shear wave velocity conversion model, the reaction displacement method is used to calculate the base bed coefficient under the stratified site condition, which significantly improves the calculation efficiency and accuracy, and breaks through the technical bottleneck of the traditional method in the analysis of stratified sites.

[0013] Optionally, the reaction displacement method includes: selecting a two-story three-span frame structure of an underground station as an analysis object; based on the analysis object, setting basic parameters and obtaining setting results; according to the setting results, optimizing the site structure and obtaining calculation results that eliminate the influence of site boundary effects. The present invention selects a two-story three-span frame structure of an underground station as an analysis object, thereby realizing targeted research on complex underground structures and breaking through the limitations of traditional methods on structural types and scales; by using the analysis object to set basic parameters and obtain setting results, it realizes systematic optimization of structural parameters, subverts the traditional method of relying on experience or simplified processing mode for parameter setting, and provides a scientific basis for the accuracy and reliability of structural analysis; by optimizing the site structure according to the setting results and eliminating the influence of site boundary effects, the accuracy and practicality of the calculation results are significantly improved, and the problem of boundary effect interference analysis in traditional methods is effectively solved.

[0014] Optionally, optimizing the site structure according to the setting results to obtain calculation results that eliminate the influence of site boundary effects includes: determining the site calculation width according to the setting results, and the site calculation width is taken as 7 times the structure width; determining the site calculation height based on the site calculation width, and the site calculation height is the distance from the ground surface to the bedrock position; based on the site calculation height, discretizing the structure using beam units and discretizing the soil using plane strain units; determining the grid size based on the discretization of the structure and the discretization of the soil, and the grid size is taken as 0.5m near the structure position; and obtaining calculation results that eliminate the influence of site boundary effects based on the grid size. The present invention determines the calculated width and height of the site and optimizes the site structure based on the distance from the surface to the bedrock, thereby achieving scientific control of the site boundary effect, breaking through the limitations of the simplified processing of boundary conditions in traditional methods, and providing reliable boundary condition support for the precise analysis of underground structures; by using beam units for structural discretization and plane strain units for soil discretization, refined modeling of structure and soil is achieved, subverting the low-precision mode of simplified simulation of the interaction between structure and soil in traditional methods, and providing a high-fidelity numerical model for the mechanical behavior analysis of complex underground structures; by determining the grid size based on the discrete results and obtaining the calculation results that eliminate the influence of the site boundary effect, the calculation accuracy and efficiency are significantly improved, breaking through the shortcomings of the traditional method of grid division relying on experience or extensive processing, and providing an important technical path for the real working condition simulation and response prediction of underground structures.

[0015] Optionally, the base bed coefficient is compared and analyzed with the base bed coefficient calculated by the existing standard method to obtain a comparative analysis result, including: comparing and analyzing the base bed coefficient under homogeneous site conditions with the base bed coefficient calculated by the existing standard method to obtain a first comparative analysis result, the first comparative analysis result including: the base bed coefficient under the homogeneous site condition is applicable to the traditional reaction displacement method and the inertia force displacement method; comparing and analyzing the base bed coefficient under layered site conditions with the base bed coefficient calculated by the existing standard method to obtain a second comparative analysis result, the second comparative analysis result including: the base bed coefficient under the layered site condition is applicable to the traditional reaction displacement method and the inertia force displacement method. By comparing and analyzing the base bed coefficient under homogeneous site conditions with the existing standard methods, the present invention verifies the applicability and accuracy of the simplified formula in homogeneous sites, breaking through the limitations of traditional standard methods in homogeneous site analysis; by comparing and analyzing the base bed coefficient under layered site conditions with a variety of standard methods, the universality and accuracy of the simplified formula in layered sites are proved, subverting the complexity and inefficiency of traditional methods in layered site analysis, and providing an important solution for the calculation of the base bed coefficient of layered sites; through comparative analysis results, it is clarified that the simplified formula is applicable to the traditional reaction displacement method and the inertia force displacement method, which significantly improves the applicability and calculation efficiency of the reaction displacement method under different site conditions, and breaks through the limitations of traditional methods on site types and calculation modes.

[0016] Optionally, based on the comparative analysis results, analyzing the structural responses under the homogeneous site conditions and the layered site conditions, obtaining the structural response analysis results includes: based on the comparative analysis results, extracting internal force data and error data of the structural side walls, center columns, top plates and bottom plates, the internal force data including shear force, bending moment and axial force data, and the error data including error data of the shear force, the bending moment and the axial force; based on the internal force data and the error data, obtaining the structural response analysis results, the structural response analysis results include: the overall error of the internal force data is extremely small, and the base bed coefficient solved based on the internal force data is applicable to the traditional reaction displacement method and the inertia force displacement method. The present invention realizes a refined analysis of the structural response by extracting the internal force data and error data of the structural side walls, central columns, top plates and bottom plates, breaking through the limitations of the simplified processing of the structural internal force distribution in traditional methods, and providing high-precision data support for the study of the mechanical behavior of underground structures. By analyzing the internal force data and error data, it is found that the overall error is extremely small, which verifies the applicability of the simplified formula in the traditional reaction displacement method and inertia force displacement method, and subverts the inherent perception of insufficient accuracy of the calculation of the base bed coefficient in traditional methods.

[0017] In a second aspect, the present invention provides a system for determining a base bed coefficient in an underground structure reaction displacement method, comprising an input device, a processor, an output device and a memory, wherein the input device, the processor, the output device and the memory are interconnected, wherein the memory is used to store a computer program, the computer program comprises program instructions, the processor is configured to call the program instructions, and the system uses the method for determining a base bed coefficient in an underground structure reaction displacement method. The system for determining the base coefficient in the underground structure reaction displacement method provided by the present invention has a high degree of integration and smooth information transmission between various components. By integrating the acquisition of working condition parameters, the drawing of influencing factor curves, the derivation of simplified formulas and the calculation of the reaction displacement method, unified processing of complex geological conditions and structural forms is achieved, breaking through the limitations of the traditional methods of dispersed parameter processing and separation of calculation steps, and providing a systematic solution for the scientific determination of the base coefficient; by comparing and analyzing the simplified formula with a variety of standard methods and verifying its applicability in homogeneous sites and layered sites, the accuracy and universality of the base coefficient calculation are significantly improved, and the defect of the traditional method's insufficient adaptability to different site conditions is overcome; by extracting structural internal force data and verifying the accuracy of the simplified formula, a refined analysis of the structural response is achieved, and the defect of simplified processing of the structural internal force distribution in the traditional method is overcome, providing important technical support for the mechanical behavior research and safety assessment of underground structures, and promoting the innovation of underground engineering design and analysis methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of a method for determining a base bed coefficient in an underground structure response displacement method according to an embodiment of the present invention; Figure 2 is a schematic diagram of underground structure parameters in soil according to an embodiment of the present invention; Figure 3 This is a curve diagram showing the influence of different calculation parameters on the base bed coefficient according to an embodiment of the present invention; Figure 4 It is a structural schematic diagram of a station cross section calculated by a traditional reaction displacement method model according to an embodiment of the present invention; Figure 5 It is a structural schematic diagram of a station cross section calculated by an inertial force displacement method model according to an embodiment of the present invention; Figure 6 The shear force diagrams obtained by using the reaction displacement method under homogeneous site conditions according to the four methods of the embodiments of the present invention; Figure 7 The shear force diagrams obtained by using the reaction displacement method under layered site conditions according to the four methods of the embodiments of the present invention; Figure 8 The bending moment diagrams are obtained by using the reaction displacement method under homogeneous site conditions according to the four methods of the embodiments of the present invention; Fig. 9 The bending moment diagrams are obtained by using the reaction displacement method under layered site conditions according to the four methods of the embodiments of the present invention; Fig.10 The axial force diagrams obtained by using the reaction displacement method under homogeneous site conditions according to the four methods of the embodiments of the present invention; Fig.11 The axial force diagrams obtained by using the reaction displacement method under layered site conditions according to the four methods of the embodiments of the present invention; Fig.12 The shear force diagram calculated by the inertial force displacement method of the embodiment of the present invention and the reaction displacement method of the method of the present invention under homogeneous site conditions; Fig.13 The shear force diagram calculated by the inertial force displacement method of the embodiment of the present invention and the reaction displacement method of the method of the present invention under layered site conditions; Fig.14 The bending moment diagram is calculated by the inertial force displacement method of the embodiment of the present invention and the reaction displacement method of the method of the present invention under homogeneous site conditions; Fig.15 The bending moment diagram calculated by the inertial force displacement method of the embodiment of the present invention and the reaction displacement method of the method of the present invention under layered site conditions; Fig.16 The axial force diagram calculated by the inertial force displacement method of the embodiment of the present invention and the reaction displacement method of the method of the present invention under homogeneous site conditions; Fig.17 The axial force diagram calculated by the inertial force displacement method of the embodiment of the present invention and the reaction displacement method of the method of the present invention under layered site conditions; Fig.18 It is a structural schematic diagram of a system for determining a base coefficient in an underground structure response displacement method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are only for illustration and are not intended to limit the present invention. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details do not need to be adopted to implement the present invention. In other examples, in order to avoid confusing the present invention, known circuits, software or methods are not specifically described.

[0020] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "in one embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or subcombination. In addition, it should be understood by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale.

[0021] See also Figure 1 The embodiment of the present invention provides a method for determining a base bed coefficient in an underground structure reaction displacement method, the method comprising the following steps: S1. Obtain the working parameters of the underground structure.

[0022] In one embodiment, elastic modulus, aspect ratio, burial depth ratio and bedrock ratio parameters of the soil are obtained.

[0023] Specifically, a subway station is taken as an example to set up different working conditions for research. , the soil elastic modulus is 3MPa, the soil Poisson's ratio is 0.3; the station structure is 12m high, 20m wide, and the top slab depth is 5m. It should be noted that the size of the foundation coefficient reflects the restraint capacity of the soil around the structure.

[0024] Furthermore, by keeping the basic parameters unchanged and changing a variable such as the elastic modulus of the soil, the specific conditions of the working parameters are obtained. The working condition settings are shown in Table 1. The schematic diagram of the underground structure parameters in the soil is shown in Figure 2 As shown. Among them, is the structure width (m), is the structure height (m), is the buried depth of the structure (m), is the distance from the structure bottom plate to the bedrock (m). It should be noted that when discussing the influence of the structure aspect ratio, the structure aspect ratio is changed by changing the structure height, and the soil width is taken as 7 times the structure width.

[0025]

[0026] S2. Using the operating parameters, obtain a curve of factors affecting the base bed coefficient.

[0027] In one embodiment, based on Table 1 and using the operating parameters, relationship curves between the soil elastic modulus, aspect ratio, burial depth ratio, bedrock ratio and bed coefficient are plotted respectively.

[0028] Specifically, by keeping the aspect ratio, burial depth ratio and bedrock ratio parameters of the soil unchanged, changing the elastic modulus parameter of the soil, a relationship curve between the elastic modulus parameter and the bed coefficient is obtained. The relationship curve is as follows: Figure 3 As shown in (a); Furthermore, by keeping the elastic modulus, the burial depth ratio and the bedrock ratio parameters unchanged and changing the aspect ratio parameter, a relationship curve between the aspect ratio parameter and the bed coefficient is obtained, such as Figure 3 As shown in (b); Furthermore, by keeping the elastic modulus, the aspect ratio and the bedrock ratio parameters unchanged and changing the burial depth ratio parameter, a relationship curve between the burial depth ratio parameter and the bed coefficient is obtained, such as Figure 3 As shown in (c); Furthermore, by keeping the elastic modulus, the aspect ratio and the burial depth ratio parameters unchanged and changing the bedrock ratio parameter, a relationship curve between the bedrock ratio parameter and the bed coefficient is obtained, such as Figure 3 As shown in (d) in .

[0029] Furthermore, the above relationship curves are analyzed to obtain the following analysis results: Depend on Figure 3 It can be seen from (a) that ~ As the elastic modulus of the soil increases, the base coefficient increases linearly with the increase of the elastic modulus of the soil. It can be considered that the elastic modulus is one of the important factors affecting the base coefficient. Figure 3 In (b), we can see that as The increase of , Gradually decrease, , It increases accordingly, and , Basically unchanged; , The rate of change in When it is 1, it is the turning point. When it is less than 1, , The rate of decrease is faster when When greater than 1, , The rate of decrease is slow; , along with The increase of is basically linear. , Although with increases with the increase of, but the change is very limited; it can be considered It is one of the important factors affecting the tangential and normal base coefficients of the structural side walls. Figure 3 As can be seen from (c) in The increase of ~ Gradually increases, and when When it is greater than 0.35, ~ along with The increase of shows a linear growth trend. Figure 3 As can be seen from (d) in The increase of ~ Gradually decreases. , along with and The change of is basically unchanged, so it can be considered and yes ~ important influencing factors.

[0030] S3. According to the influencing factor curve, a simplified formula of the base bed coefficient is obtained.

[0031] In one embodiment, firstly, the data of elastic modulus, aspect ratio, burial depth ratio and bedrock ratio parameters of the soil are extracted according to the influencing factor curve.

[0032] Furthermore, the data are fitted to obtain a simplified formula for the base bed coefficient, which is as follows: , in, is the base bed coefficient, , , , , is a constant, for , for , for , is the elastic modulus of the soil, is the structure width, is the structure height, is the depth of structure, is the distance from the structural bottom plate to the bedrock. The relevant parameters of this simplified formula are shown in Table 2.

[0033]

[0034] It should be noted that since the simplified formula has multiple sets of parameters, the base bed coefficient obtained by solving the simplified formula needs further comparative analysis and error analysis to determine a high-precision base bed coefficient.

[0035] S4. Based on the simplified formula, the reaction displacement method is used to calculate the base bed coefficient under homogeneous site conditions and stratified site conditions.

[0036] The reaction displacement method includes the traditional reaction displacement method and the inertia force displacement method; The traditional reaction displacement method assumes that the response of underground structures during earthquakes mainly depends on the deformation of the surrounding soil layers. At the same time, considering the difference in lateral stiffness between the underground structure and the surrounding soil, the interaction between the structure and the soil is quantitatively represented by introducing foundation springs. The traditional reaction displacement method is mainly applicable to box-type or arched structures with relatively regular structural forms, especially to situations where the geological conditions are relatively clear.

[0037] The inertia force displacement method is designed to improve the traditional reaction displacement method by ignoring the situation that the overburden of the structure generates a large vertical inertia force after losing its constraint due to shear failure under earthquake action when analyzing the seismic response of shallow underground structures. Compared with the traditional reaction displacement method, the calculation model eliminates the normal and tangential springs at the top of the structure, and considers the inertia force generated by the overburden after shear failure and the underground structure itself under vertical earthquake action. The inertia force displacement method is generally applicable to the seismic analysis of shallow underground structures under strong earthquake action.

[0038] Regarding the calculation method of the base bed coefficient, the existing technologies include the Japanese standard method, the plate width correction method, the Chinese standard method and the inertia force displacement method.

[0039] Specifically, the Japanese Railway Seismic Design Code proposes a method for determining the value of the foundation coefficient based on the width and height of the structure. This method is recorded as the Japanese standard method, and its specific calculation is shown in the following formula:

[0040] Where: ,in, is the dynamic deformation modulus of the soil layer, in units of ; is the soil Poisson’s ratio, is the dynamic shear stiffness of the soil, in units of ; is the structure width, in units of ; is the height of the structural side wall, in units of ; is the normal bed coefficient of the top and bottom plates, in units of ; is the tangential bed coefficient of the top and bottom plates, in units of ; is the side wall tangential bed coefficient, in units of ; is the shear bed coefficient of the side wall, in units of .

[0041] Through comparative analysis of underground structure seismic design methods, Bian Jin et al. found that the response displacement method can reasonably reflect the impact of seismic loads on the structure, and pointed out a method for calculating the base coefficient that considers the impact of the structure width on the base coefficient. This method is called the plate width correction method, and its specific calculation is shown in the following formula:

[0042] Where: is the resistance coefficient of soil, which is taken as 1.0; is the lateral correction coefficient, which is taken as 1.0. is the dynamic deformation modulus of the soil layer, in units of , is the structure width, in units of , is the normal bed coefficient of the top and bottom plates, in units of ; is the tangential bed coefficient of the top and bottom plates, in units of ; is the side wall tangential bed coefficient, in units of ; is the shear bed coefficient of the side wall, in units of .

[0043] The Code for Seismic Design of Urban Rail Transit Structures (GB 50909-2014) states that the base coefficient can be calculated using the static finite element method, which is recorded as the standard method in my country. The specific calculation expression is as follows:

[0044] in, is the base bed coefficient, is the uniformly distributed load applied around the hole, is the deformation under each load.

[0045] The foundation spring stiffness coefficient in the inertia force displacement method draws on the static finite element method for determining the spring stiffness coefficient in the traditional reaction displacement method. The expression for calculating the foundation coefficient is consistent with the standard method in my country, but it ignores the interaction between the overlying soil on the structure and other soils around the structure. This means that the inertia force displacement method has improved the traditional reaction displacement method as a new reaction displacement method.

[0046] In one embodiment, the finite element software ABAQUS is used to establish a soil structure finite element model, and a two-story three-span frame structure of an underground station is used as an example for calculation. The soil structure finite element model is a reaction displacement method model. The elastic modulus of the top plate, bottom plate, middle plate and side wall of the station structure is 32.5 GPa, and the density is 2400 The spacing between the columns of the station structure is 9 m. According to certain equivalent principles, the elastic modulus of the columns is 3.61 GPa and the density is The cross section of the station is as follows Figure 4 As shown in (a), four typical sections are selected, including the top plate, bottom plate, side wall and center column, for the subsequent analysis of the internal force value and error of each section. Among them, the top plate of the station structure is buried at a depth of 3.5 m, the bottom plate of the structure is buried at a depth of 26.5 m, and the bedrock depth is 64 m.

[0047] Furthermore, the Chi-Chi ground motion was used to adjust the peak acceleration to 0.1 g and the ground motion duration to 40 s.

[0048] Furthermore, in order to eliminate the influence of the site boundary effect as much as possible, the calculated site width is taken as 7 times the structure width, that is, 210m. The site height is 64m from the surface down to the bedrock position, as shown in Figure 4 As shown in (b), the figure shows the dimensions of the finite element model of the soil structure.

[0049] It should be noted that when the model is established, the structure is discretized using beam elements (B21) and the soil is discretized using plane strain elements (CPE4R). When dividing the mesh, the mesh size should be less than 1 / 8~1 / 10 λ (wavelength). The seismic wave energy selected in the present invention is concentrated in the range of 0-10 Hz, and the minimum shear wave velocity of the soil is 200 ,at this time To ensure the accuracy of the model calculation, the longitudinal size of the grid near the structure is 0.5 m, and that of the rest is 1 m.

[0050] Furthermore, in order to verify the applicability and reliability of the method of solving the base bed coefficient using the simplified formula in the traditional reaction displacement method, two basic working conditions, layered and homogeneous site, are set for calculation. The working condition settings are as follows: Working condition 1: In a homogeneous site, the base bed coefficient is calculated using the Japanese standard method, the plate width correction method, the Chinese standard method and the simplified formula calculation method of the present invention, and then the traditional reaction displacement method is used to calculate and extract the internal force of the structure. The soil layer parameters of working condition 1 are shown in Table 3.

[0051] Working condition 2: The homogeneous site is ideal. The actual soil distribution is very complex. The layered site is designed. The base bed coefficient is calculated using the Japanese standard method, the plate width correction method, the Chinese standard method and the method of the present invention. The traditional reaction displacement method is used to calculate and extract the internal force of the structure. The soil layer parameters of working condition 2 are shown in Table 3.

[0052]

[0053] Furthermore, based on the simplified formula, the reaction displacement method model is used to calculate the base bed coefficient under homogeneous site conditions.

[0054] Furthermore, the layered site is simplified into a homogeneous site, and a conversion model of equivalent shear wave velocity is constructed. The conversion model is used to convert the shear wave velocity of the soil into an equivalent shear wave velocity. The conversion model satisfies the following expression:

[0055] in, is the equivalent shear wave velocity, To calculate the depth, To calculate the depth range The thickness of the soil layer, To calculate the depth range Shear wave velocity of the soil layer.

[0056] Furthermore, based on the simplified formula, combined with the conversion model, the reaction displacement method model is used to calculate the base bed coefficient under the layered site conditions.

[0057] Furthermore, the calculation results of the base bed coefficient for the homogeneous site condition (condition 1) and the stratified site condition (condition 2) were obtained.

[0058] In another embodiment, an inertial force displacement method model is established.

[0059] Specifically, a two-story three-span frame structure of an underground station is used as an example for calculation. The elastic modulus of the station structure top plate, bottom plate, middle plate and side wall is 32.5 GPa, and the density is 2400 kg / m3. The interval between the columns of the station structure is 6 m. After a certain equivalent principle, the elastic modulus of the column is 4.43 GPa, and the density is 320 The cross section of the station is as follows Figure 5 As shown in (a) in . Furthermore, four typical sections including top plate, bottom plate, side wall and center column were selected to analyze the internal force value and error of each section. Among them, the top plate of the structure is buried at a depth of 2 m, the bottom plate of the structure is buried at a depth of 17 m, the bedrock depth is 52 m, and the dimensions of the soil structure finite element model are as follows: Figure 5 As shown in (b) in .

[0060] Furthermore, Chi-Chi earthquake motion was used to adjust the peak acceleration to 0.1 g and the earthquake motion duration to 40 s.

[0061] Furthermore, similar to the model verification of the reaction displacement method, the model verification of the inertia force displacement method also uses the homogeneous site condition (condition three) and the layered site condition (condition four) to verify the applicability of the empirical formula. The condition settings are shown in Table 4.

[0062]

[0063] Furthermore, according to the simplified formula, the inertial force displacement method model is used to calculate the base bed coefficient under different site conditions. It should be noted that for layered site conditions, the conversion model also needs to be used for calculation, just like the traditional reaction displacement method.

[0064] S5. Compare and analyze the base bed coefficient with the base bed coefficient calculated by the existing standard method to obtain a comparative analysis result.

[0065] In one embodiment, the calculation results of the base bed coefficient obtained in step S4 are first counted, and the statistical results are shown in Table 5, where: , , , , , is the base bed coefficient of different groups.

[0066]

[0067] Furthermore, a comparative analysis was conducted between the base bed coefficients calculated by the method of the present invention and those calculated by the existing standard method.

[0068] Specifically, it can be seen from Table 5 that the method of the present invention calculates , , The result of the base bed coefficient calculated by the standard method of our country is the closest; the result calculated by the method of the present invention is Although it is several times the result calculated by the Chinese standard method, it is still better than the result calculated by the Japanese standard method and the plate width correction method. The results calculated by the method of the present invention are closer to those calculated by the standard method of my country. In general, the base bed coefficient calculated by the method of the present invention is more consistent with the base bed coefficient calculated by the standard method of my country than the other two methods.

[0069] In another embodiment, the inertial force displacement method and the method of the present invention were used to calculate the base bed coefficient under different site conditions, and the calculation results are shown in Table 6.

[0070]

[0071] Furthermore, a comparative analysis was conducted between the base bed coefficient calculated by the method of the present invention and the inertial force displacement method.

[0072] Specifically, it can be seen from Table 6 that under the conditions of homogeneous and stratified sites, the The results calculated by the inertial force displacement method are relatively close. , , Under different site conditions, the results calculated by the method of the present invention are different from those calculated by the inertial force displacement method. , , the calculation result of the method of the present invention is too small. , the calculation result of the method of the present invention is too large.

[0073] S6. Based on the comparative analysis results, analyze the structural responses under the homogeneous site condition and the layered site condition to obtain structural response analysis results.

[0074] In one embodiment, based on the comparative analysis results, the internal forces of the structural side walls, central columns, top plates, and bottom plates are extracted. The measuring points of the structural side walls and central columns are numbered from top to bottom, and the measuring points of the structural top plates and structural bottom plates are numbered from left to right.

[0075] Furthermore, the extracted internal forces are analyzed to obtain the following structural response analysis results: See also Figure 6 , Figure 6 The shear force diagrams calculated by the reaction displacement method under homogeneous site conditions are shown in the following figure. Figure 6 (a), (b), (c), and (d) represent the side wall shear force, middle column shear force, top plate shear force, and bottom plate shear force diagrams of the structure respectively. Figure 6 It can be seen from (a) and (d) in that the maximum shear force obtained by the Chinese standard method, the Japanese standard method and the method of the present invention are very close in value, while the maximum shear force obtained by the plate width correction method is too large. This is because this method ignores the influence of the structure height when calculating the base bed coefficient, and thus cannot simulate the constraint effect of the soil on the structure very well, resulting in a large difference between the maximum shear force of the side wall and the bottom plate of the structure and the other three methods. Figure 6 It can be seen from (b) in the figure that the Chinese standard method and the method of the present invention obtain the maximum shear force in the lower half of the middle column, while the Japanese standard method and the plate width correction method obtain the maximum shear force in the upper half of the middle column. This is because the Japanese standard method and the plate width correction method are relatively rough in calculating the tangential base coefficient of the structural side wall, resulting in different locations for the maximum shear force of the middle column. Figure 6 It can be seen from (c) in that the maximum value of the structural top plate shear force obtained by the Japanese standard method and the plate width correction method is much larger than the maximum value of the top plate shear force obtained by the Chinese standard method and the method of the present invention. This is because the Japanese standard method and the plate width correction method ignore the influence of the position of the structure in the soil when calculating the base bed coefficient, resulting in a large deviation in the results when calculating the structural top plate shear force.

[0076] In the layered site, four methods are used to calculate the internal force results of each part of the structure. Figure 7 As shown, Figure 7 (a), (b), (c), and (d) represent the side wall shear force, middle column shear force, top plate shear force, and bottom plate shear force diagrams of the structure respectively. Figure 7 and Figure 6 It can be seen that the shear force variation trends of the four methods in various parts of the structure in homogeneous and stratified sites are consistent, and the shear force results calculated by the method of the present invention are closer to the standard method of my country than the other two methods.

[0077] The structural bending moment data calculated by the above four methods are extracted under homogeneous site conditions. The results are as follows: Figure 8 As shown, Figure 8 (a), (b), (c), and (d) represent the side wall bending moment, middle column bending moment, top plate bending moment, and bottom plate bending moment diagrams of the structure respectively. Figure 8 It can be seen from (a), (b), and (c) in the figure that the bending moment results of the structural side walls, middle columns, and top plates calculated by the method of the present invention are basically consistent with the results calculated by the Chinese standard method, while the results calculated by the Japanese standard method and the plate width correction method are slightly different from those of the Chinese standard method. Figure 8 It can be seen from (d) in Figure 1 that the bottom plate bending moments calculated by the Japanese standard method, the Chinese standard method and the method of the present invention are highly consistent, and the results of the bottom plate bending moments calculated by the plate width correction method are larger than those of the other three methods. Figure 8It can be seen that at the endpoints of the structural side walls, middle columns, top plates and bottom plates, the bending moment results obtained by the method of the present invention are closer to those obtained by the Chinese standard method, while the bending moment results of at least one endpoint of the Japanese standard method and the plate width correction method are too different from the bending moment results obtained by the Chinese standard method. The maximum positive bending moment of the structure is obtained at the bottom of the structural side wall and the leftmost end of the structural bottom plate, and the maximum negative bending moment is obtained at the rightmost end of the structural bottom plate. By comparing the bending moment results of the structural side walls, middle columns, top plates and bottom plates, it can be seen that the bending moment results of each part obtained by the method of the present invention and the Chinese standard method are relatively close, while the bending moment solved by the plate width correction method is quite different from the bending moment results calculated by other methods, with the largest difference being nearly 1000kN·m.

[0078] Fig. 9 The calculation results of the bending moments of various parts of the structure using the reaction displacement method in stratified strata by four methods are shown in Figure 1. Fig. 9 (a), (b), (c), and (d) represent the side wall bending moment, middle column bending moment, top plate bending moment, and bottom plate bending moment diagrams of the structure respectively. Fig. 9 and Figure 8 It can be seen that the variation trend of the bending moment in each part of the structure is the same as that in the layered and homogeneous sites. The calculation results of the bending moment of the side wall, middle column, bottom plate and top plate of the structure are more consistent with the calculation results of the method of the present invention and the standard method of my country than the other two methods. For the bending moment at the left end of the bottom plate of the structure, the calculation error between the method of the present invention and the standard method of my country is only 5%.

[0079] Fig.10 The following is a comparison diagram of the axial forces of various parts of the structure calculated by the four methods under working condition 1. Fig.10 (a), (b), (c), and (d) represent the axial force diagrams of the side wall, middle column, top plate, and bottom plate of the structure, respectively. Fig.10 As can be seen from (a) in the figure, the axial force gradually decreases from measuring point 0 to 18, that is, the closer the upper side wall is to the top plate, the greater the axial force is. The axial force at measuring points 19 to 46 first decreases and then increases, and the rate of change is significantly larger after measuring point 34. Fig.10 It can be seen from (b) in Figure 1 that the shear force of the structure column calculated by the method of the present invention is closer to the calculation result of the standard method of my country. Fig.10 As can be seen from (d) in the figure, the calculation results of the structural bottom plate axial force by the Japanese standard method are quite different from those by the Chinese standard method, while the calculation results by the Japanese standard method and the method of the present invention are similar. Fig.10 As can be seen from (c) in the figure, for the axial force of the middle span of the structure top plate, the results of the four calculation methods are basically consistent, while for the axial force of the two side spans of the structure top plate, the result calculated by the method of the present invention is smaller than that of the other three methods.

[0080] The above four methods are used to extract the axial forces of different parts of the structure in the layered site, such as Fig.11 As shown, Fig.11 (a), (b), (c), and (d) represent the axial forces of the side walls, middle columns, top plate, and bottom plate of the structure, respectively. Fig.11 and Fig.10 It can be seen that the axial force variation trend of the side wall, top plate and bottom plate of the structure under the layered site condition is consistent with that of the homogeneous site. For the axial force of the middle column of the upper layer of the structure, the calculation results of the method of the present invention are close to those of the plate width correction method, and for the axial force of the middle column of the lower layer of the structure, the calculation results of the method of the present invention are close to those of the standard method of my country.

[0081] Table 7 shows the shear force, bending moment, axial force values ​​of typical sections calculated by four methods under different site conditions and the errors between the calculation results of different calculation methods and the calculation results of the Chinese standard method. It can be seen from Table 7 that the bending moment of each typical section calculated by the method of the present invention is very close to the bending moment results calculated by the Chinese standard, and except for the bending moment error at the bottom of the middle column in the homogeneous site, the remaining bending moment error values ​​are all within 10%, and the minimum bending moment error is only -0.08%. For the shear force at the bottom of the side wall, the axial force at the bottom of the middle column, and the shear force at the left end of the bottom plate, the results calculated by the method of the present invention under different site conditions are close to those calculated by the Chinese standard method. For the second working condition, the bending moment at the bottom of the side wall, the shear force at the bottom of the middle column, the shear force at the left end of the top plate, and the axial force internal force results at the left end of the bottom plate calculated by the method of the present invention have larger errors compared with the Chinese standard method, but smaller errors compared with the Japanese standard method and the plate width correction method. In summary, the method of the present invention has good applicability in calculating the base coefficient in the reaction displacement method under different site conditions.

[0082]

[0083] In another embodiment, based on the comparative analysis results, structural response analysis results of the method of the present invention and the inertial force displacement method are obtained.

[0084] Specifically, see Fig.12 , Fig.12 The calculation results of shear force at each part of the structure in the inertia force displacement method by the method of the present invention and the calculation method of the base bed coefficient of the inertia force displacement method under homogeneous site conditions are as follows: Fig.12 (a), (b), (c), and (d) represent the side wall shear force, middle column shear force, top plate shear force, and bottom plate shear force diagrams of the structure respectively. Fig.12 It can be seen that the bed coefficient calculated by the simplified formula of the present invention also has a high accuracy when used in the inertial force displacement method, especially Fig.12 In (c) and (d), the results calculated by the two methods are highly consistent. Fig.12It can be seen from (a) and (b) in that, before measuring point 15, the shear forces of the structural side walls and central columns calculated by the method of the present invention are basically consistent with the results calculated by the inertia force displacement method. However, after measuring point 15, the results calculated by the method of the present invention are slightly larger than those calculated by the inertia force displacement method and are more conservative.

[0085] For further information, see Fig.13 , Fig.13 This is a comparison diagram of the shear forces at various parts of the structure obtained by the method of the present invention and the method for calculating the base coefficient of the inertial force displacement method in a layered site. Fig.13 (a), (b), (c), and (d) represent the side wall shear force, middle column shear force, top plate shear force, and bottom plate shear force diagrams of the structure respectively. Fig.13 and Fig.12 It can be seen that the errors of the shear force results calculated by the two methods are increased in the layered site, especially for the shear force at the center column and the top plate of the structure. However, for the side wall and the bottom plate of the structure, the results calculated by the method of the present invention are highly consistent with the results calculated by the inertial force displacement method.

[0086] Furthermore, the calculation results of the bending moment obtained by the inertial force displacement method and the method of the present invention in a homogeneous site are extracted, such as Fig.14 As shown, Fig.14 (a), (b), (c), and (d) represent the side wall bending moment, middle column bending moment, top plate bending moment, and bottom plate bending moment diagrams of the structure respectively. Fig.14 It can be seen that for the bending moments at various parts of the structure, the calculation results of the calculation method of the present invention are highly consistent with those of the inertia force displacement method. The errors of the bending moments at the side walls and the bottom of the middle column are 5.4% and 1.8%, respectively.

[0087] For further information, see Fig.15 , Fig.15 The calculation results of the bending moment of each part of the structure in the layered site by the inertial force displacement method and the method of the present invention are as follows: Fig.15 (a), (b), (c), and (d) represent the side wall bending moment, middle column bending moment, top plate bending moment, and bottom plate bending moment diagrams of the structure respectively. Fig.15 and Fig.14 It can be seen that in the layered site, the bending moment results of each part of the structure calculated by the method of the present invention and the inertia force displacement method can still maintain good consistency. And for the bending moment at the bottom of the side wall of the structure and the bending moment at the bottom of the center column of the structure, the error of the results calculated by the two methods is only -0.78% and -0.55%.

[0088] For further information, see Fig.16 , Fig.16 This is a comparison diagram of the axial forces of various parts of the structure calculated by the inertial force displacement method and the method of the present invention in a homogeneous site. Fig.16(a), (b), (c), and (d) represent the axial force diagrams of the side wall, middle column, top plate, and bottom plate, respectively. Fig.16 It can be seen from (c) in Figure 1 that the axial force results of the top plate of the structure calculated by the two base coefficient calculation methods are close. Fig.16 As can be seen from (d) in the figure, the axial force results of the middle span of the structural base plate calculated by the two methods are highly consistent. For the spans on both sides, the results calculated by the method of the present invention are more conservative.

[0089] Furthermore, the above two methods are used to extract the axial forces of different parts of the structure in the layered site, such as Fig.17 As shown, Fig.17 (a), (b), (c), and (d) represent the axial forces of the side walls, middle columns, top plate, and bottom plate of the structure, respectively. Fig.17 and Fig.16 It can be seen that the change trend of the axial forces of the side walls, top plates and bottom plates of the structure under the layered site condition is consistent with that of the homogeneous site. For the axial forces of the top plates and middle columns of the structure, the results calculated by the two methods are very close, but for the axial forces of the side walls and bottom plates of the structure, the error between the calculation results of the method of the present invention and the inertia force displacement method is increased.

[0090] Furthermore, through the above two methods of calculating the base coefficient, the shear force, bending moment and axial force values ​​of the typical sections of the structure for different site types are calculated respectively, and the errors of the calculation results of the two methods are obtained, as shown in Table 8.

[0091]

[0092] It can be seen from Table 8 that the error of the results calculated by the method of the present invention and the inertia force displacement method under homogeneous site conditions is within ±15%, among which the smallest error is only -0.22%, and the results calculated by the method of the present invention are more conservative than those calculated by the inertia force displacement method. It can be seen from Table 8 that in layered sites, the errors of the axial force at the bottom of the side wall, the shear force at the bottom of the middle column, and the axial force at the left end of the bottom plate calculated by the method of the present invention and the inertia force displacement method are relatively large, but the errors of the internal forces of the structures in other parts are still within ±15%, among which the errors of the bending moment at the bottom of the side wall, the bending moment at the bottom of the middle column, the bending moment at the left end of the top plate, and the bending moment at the left end of the bottom plate are -0.78%, -0.55%, 8.39%, and -2.83%, respectively. This shows that the method of the present invention has good applicability in calculating the base bed coefficient under different site conditions.

[0093] S7. Verify the applicability of the simplified formula through the comparative analysis results and the structural response analysis results.

[0094] In one embodiment, based on steps S5 and S6, the applicability of the method of the present invention in the reaction displacement method is verified, that is, the applicability of the simplified formula in the reaction displacement method.

[0095] In another embodiment, based on steps S5 and S6, the applicability of the method of the present invention in the inertia force displacement method is verified, that is, the applicability of the simplified formula in the inertia force displacement method.

[0096] S8. According to the applicability, the base coefficient in the underground structure response displacement method is determined.

[0097] In one embodiment, it is determined that the simplified formula can be well applied to the traditional reaction displacement method and the inertial force displacement method. Therefore, it is possible to simultaneously solve the high-precision bed coefficient that is closer to the standard specifications of my country in the traditional reaction displacement method and the inertial force displacement method. It should be noted that, compared with the existing calculation method, the method of the present invention has the characteristics of high applicability in the reaction displacement method, a relatively simple process for solving the bed coefficient, and high precision.

[0098] See also Fig.18 , Fig.18 The present invention is a schematic diagram of the structure of a system for determining a bed coefficient in an underground structure reaction displacement method in an embodiment of the present invention. The system includes an input device, a processor, an output device, and a memory, wherein the input device, the processor, the output device, and the memory are interconnected, wherein the memory is used to store a computer program, the computer program includes program instructions, the processor is configured to call the program instructions, and the system uses the method for determining a bed coefficient in an underground structure reaction displacement method.

[0099] In this embodiment, the input device includes a parameter input module, a data import module and an interactive interface; Specifically, the parameter input module includes a keyboard, a touch screen or a data interface, which is used to input working parameters such as the elastic modulus, aspect ratio, burial depth ratio, bedrock ratio, structure width, height, burial depth and distance from the bottom plate to the bedrock of the soil; the data import module supports the import of geological survey data and structural design parameters from an external database or file; the interactive interface provides a graphical user interface, and users can intuitively input or adjust parameters through drop-down menus, sliders, etc.

[0100] The processor includes a data preprocessing unit, a computing core unit and a comparison and analysis unit; Specifically, the data preprocessing unit is used to verify and standardize the input operating parameters to ensure that the data meets the calculation requirements; the calculation core unit includes a simplified formula calculation module for the base coefficient, a reaction displacement method analysis module and an equivalent shear wave velocity conversion module, which are used to calculate the base coefficient and structural response; the comparative analysis unit compares and analyzes the calculation results with the Japanese standard method, the plate width correction method, the Chinese standard method and the inertia force displacement method to generate error data and comparison results.

[0101] The output device includes a graphic display module, a data export module and a printing module; Specifically, the graphic display module includes a display or projection device for displaying the influencing factor curve of the base coefficient, the structural internal force distribution diagram and the error analysis results; the data export module supports exporting the calculation results as a report file or a data file; the printing module is connected to a printer for outputting paper reports or charts.

[0102] The memory adopts a high-speed solid-state hard disk, which has the characteristics of fast reading and writing speed, large capacity and high reliability, can meet the needs of large data storage, and is mainly used to store data input by the input device and data processed by the processor.

[0103] In summary, the present invention selects a variety of factors that affect the size of the base bed coefficient, namely site conditions, structural geometric parameters and structural burial depth, quantitatively analyzes the key parameters and degrees that affect the base bed coefficient, and proposes a corresponding simplified formula. The present invention compares the differences between this formula and several other base bed coefficient calculation methods under homogeneous site and stratified site conditions. At the same time, considering the homogeneous site and stratified site conditions, the calculation accuracy applied to the traditional reaction displacement method and inertial force displacement method is analyzed. The main conclusions obtained are as follows: (1) There is a linear correlation between the base coefficient and the soil elastic modulus. The change in the aspect ratio of the structure has a greater impact on the base coefficient of the side wall and bottom plate of the structure. The change in the buried depth of the structure has a greater impact on the base coefficient of the top plate and side wall of the structure, and the impact on the base coefficient of the top plate is more obvious.

[0104] (2) Under different site conditions, the calculation results of the four methods for calculating the base coefficient in the reaction displacement method are compared. The base coefficient result calculated by the method of the present invention is closest to the static finite element method. The method of the present invention is simpler in calculation than the static finite element method, and is superior to the Japanese standard method and the plate width correction method in reliability, indicating that the method of the present invention has good applicability in calculating the base coefficient of the reaction displacement method under different site conditions.

[0105] (3) Under different site conditions, the method of the present invention is applied to the traditional reaction displacement method and the inertia force displacement method. Comparing the internal force results of the measuring points at various parts of the structure under the two calculation methods, the error value of the calculation results of the method of the present invention is generally within 20%, among which the error of the bending moment is generally below 10%, and the minimum error value is only -0.08%, indicating that under different site conditions, the base coefficient calculated by the method of the present invention can be well applied to the traditional reaction displacement method and the inertia force displacement method.

[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A method for determining the base coefficient in the underground structure reaction displacement method, characterized in that: The method comprises the following steps: Obtaining working parameters of the underground structure, wherein the working parameters include elastic modulus, aspect ratio, burial depth ratio and bedrock ratio parameters of the soil; Using the working condition parameters, obtaining a curve of factors affecting the base bed coefficient; According to the influencing factor curve, a simplified formula of the base bed coefficient is obtained; According to the simplified formula, the reaction displacement method is used to calculate the base bed coefficient under homogeneous site conditions and stratified site conditions; Compare and analyze the base bed coefficient with the base bed coefficient calculated by the existing standard method to obtain a comparative analysis result; Based on the comparative analysis results, analyzing the structural responses under the homogeneous site condition and the layered site condition to obtain structural response analysis results; Verifying the applicability of the simplified formula through the comparative analysis results and the structural response analysis results; According to the applicability, the determination of the base bed coefficient in the underground structure reaction displacement method is achieved.

2. The method for determining the base coefficient in the underground structure reaction displacement method according to claim 1, characterized in that: The method of obtaining the influencing factor curve of the base bed coefficient by using the working condition parameters includes: By keeping the aspect ratio, burial depth ratio and bedrock ratio parameters of the soil body unchanged, changing the elastic modulus parameter of the soil body, and obtaining a relationship curve between the elastic modulus parameter and the bed coefficient; By keeping the elastic modulus, the burial depth ratio and the bedrock ratio parameters unchanged and changing the aspect ratio parameter, a relationship curve between the aspect ratio parameter and the bed coefficient is obtained; By keeping the elastic modulus, the aspect ratio and the bedrock ratio parameters unchanged and changing the burial depth ratio parameter, a relationship curve between the burial depth ratio parameter and the bed coefficient is obtained; By keeping the elastic modulus, the aspect ratio and the burial depth ratio parameters unchanged and changing the bedrock ratio parameter, a relationship curve between the bedrock ratio parameter and the bed coefficient is obtained.

3. The method for determining the base bed coefficient in the underground structure reaction displacement method according to claim 1, characterized in that: The simplified formula for obtaining the bed coefficient according to the influencing factor curve includes: Extracting data of elastic modulus, aspect ratio, burial depth ratio and bedrock ratio parameters of the soil according to the influencing factor curve; The data are fitted to obtain a simplified formula for the base bed coefficient.

4. The method for determining the base coefficient in the underground structure reaction displacement method according to claim 3 is characterized in that: The simplified formula is as follows: , in, is the base bed coefficient, , , , , is a constant, for , for , for , is the elastic modulus of the soil, is the structure width, is the structure height, is the depth of structure, is the distance from the structure base to the bedrock.

5. The method for determining the base coefficient in the underground structure reaction displacement method according to claim 1, characterized in that: According to the simplified formula, the calculation of the base bed coefficient under homogeneous site conditions and layered site conditions using the reaction displacement method includes: According to the simplified formula, the base bed coefficient under the homogeneous site condition is calculated using the reaction displacement method, and the reaction displacement method includes the traditional reaction displacement method and the inertia force reaction displacement method; The layered site is simplified into a homogeneous site, and a conversion model of equivalent shear wave velocity is constructed. The conversion model is used to convert the shear wave velocity of the soil into the equivalent shear wave velocity. The conversion model satisfies the following expression: , in, is the equivalent shear wave velocity, To calculate the depth, To calculate the depth range The thickness of the soil layer, To calculate the depth range Shear wave velocity of each soil layer; According to the simplified formula, combined with the conversion model, the reaction displacement method is used to calculate the base bed coefficient under the layered site conditions.

6. The method for determining the base coefficient in the underground structure reaction displacement method according to claim 5, characterized in that: The reaction displacement method comprises: The two-story three-span frame structure of the underground station was selected as the analysis object; Based on the analysis object, basic parameters are set and setting results are obtained; According to the setting results, the site structure is optimized to obtain calculation results that eliminate the influence of site boundary effects.

7. The method for determining the base coefficient in the underground structure reaction displacement method according to claim 6, characterized in that: The method of optimizing the site structure according to the setting result to obtain the calculation result of eliminating the influence of the site boundary effect includes: According to the setting result, the calculated width of the site is determined, and the calculated width of the site is taken as 7 times of the structure width; Based on the calculated width of the site, determine the calculated height of the site, where the calculated height of the site is the distance from the ground surface to the bedrock position; According to the calculated height of the site, the structure is discretized using beam elements, and the soil is discretized using plane strain elements; Based on the discretization of the structure and the discretization of the soil, a grid size is determined, wherein the grid size is 0.5 m near the structure; According to the grid size, a calculation result is obtained which eliminates the influence of the site boundary effect.

8. The method for determining the base coefficient in the underground structure reaction displacement method according to claim 1, characterized in that: The base bed coefficient is compared and analyzed with the base bed coefficient calculated by the existing standard method, and the comparative analysis results obtained include: Comparing and analyzing the base bed coefficient under the homogeneous site condition with the base bed coefficient calculated by the existing standard method, a first comparative analysis result is obtained, wherein the first comparative analysis result includes: the base bed coefficient under the homogeneous site condition is applicable to the traditional reaction displacement method and the inertia force displacement method; The base bed coefficient under the layered site condition is compared and analyzed with the base bed coefficient calculated by the existing standard method to obtain a second comparative analysis result, which includes: the base bed coefficient under the layered site condition is applicable to the traditional reaction displacement method and the inertia force displacement method.

9. The method for determining the base bed coefficient in the underground structure reaction displacement method according to claim 1, characterized in that: The analyzing the structural responses under the homogeneous site condition and the layered site condition based on the comparative analysis result to obtain the structural response analysis result comprises: Based on the comparative analysis results, extract the internal force data and error data of the structural side walls, center columns, top plates and bottom plates, wherein the internal force data include shear force, bending moment and axial force data, and the error data include error data of the shear force, bending moment and axial force; Based on the internal force data and the error data, a structural response analysis result is obtained, and the structural response analysis result includes: the overall error of the internal force data is extremely small, and the base bed coefficient solved based on the internal force data is applicable to the traditional reaction displacement method and the inertia force displacement method.

10. A system for determining a base bed coefficient in an underground structure reaction displacement method, the system using a method for determining a base bed coefficient in an underground structure reaction displacement method according to any one of claims 1 to 9, characterized in that: The system includes an input device, a processor, an output device and a memory, wherein the input device, the processor, the output device and the memory are connected to each other, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions.

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