Numerical method and system for analyzing stress field of tunnel frozen soil curtain based on finite element

Abstract

The present application relates to the technical field of electric digital data processing, in particular to a numerical method and system for analyzing stress field of tunnel frozen soil curtain based on finite element, which obtains a three-dimensional model of a tunnel construction site and geological material characteristic data; performs grid division on the three-dimensional model to obtain a finite element grid model of the three-dimensional model; performs stress simulation on the finite element grid model based on the geological material characteristic data to obtain an initial stress field of the finite element grid model before freezing; analyzes the trend of change of soil density in the freezing process based on the stress distribution of each unit grid in the initial stress field in the finite element grid model to determine a frost heaving stress field of the finite element grid model; and superimposes the initial stress field and the frost heaving stress field to determine a comprehensive stress field of the finite element grid model. The present application effectively improves the accuracy of analyzing stress field of tunnel frozen soil curtain.

Description

Technical Field

[0001] This invention relates to the field of electronic digital data processing technology, specifically to a numerical method and system for analyzing the stress field of frozen soil curtain tunnels based on the finite element method. Background Technology

[0002] Tunnel freezing construction refers to the process of using artificial cooling to freeze the water-bearing rock and soil layers surrounding the underground project into a sealed frozen wall in loose or broken water-bearing strata before construction begins. This frozen wall is used to resist ground pressure and isolate the groundwater inside and outside the project, allowing construction to proceed under its protection.

[0003] The stress field of frozen soil based on the finite element model is mainly used to describe the stress state at various points inside frozen soil under the coupled effects of external loads and temperature changes. The main stress components include: the soil's own weight and the initial geostress of the geology, and the frost heave stress generated by the volume expansion of the water-ice phase. The stress field of the finite element model can be used to conduct relevant risk analysis before the construction of frozen soil tunnels, thereby determining the feasibility of the preliminary construction plan.

[0004] Traditional stress field analysis of frozen soil curtain tunnels based on finite element models is usually conducted under assumed conditions, such as the frozen soil model being under constant low temperature conditions after freezing and the soil material having uniform density. Under these assumptions, the frost heave stress in all regions of the finite element model is assumed to be the same, so a fixed force is directly applied externally, and the mesh in the region with the highest stress in the model is judged to meet the requirements. However, in reality, freezing is a gradual and continuous process. During freezing, due to the different attraction of the freezing front to water in different regions, the density may not be uniform in some areas. In areas subjected to significant surrounding compressive stress, the increased moisture after freezing leads to a relatively higher density, resulting in significantly greater frost heave stress than other areas.

[0005] Therefore, the existing methods have a large error between the obtained freezing stress field and the actual stress field when performing stress field analysis of finite element tunnel frozen soil curtains. Summary of the Invention

[0006] To address the significant discrepancy between the existing finite element method (FEM) model-based frozen soil stress field and the actual stress field, this invention aims to provide a numerical method and system for analyzing the frozen soil curtain stress field in tunnels based on the FEM model. The specific technical solution adopted is as follows:

[0007] In a first aspect, the present invention provides a numerical method for stress field analysis of frozen soil curtain in tunnels based on the finite element method, comprising the following steps:

[0008] Obtain a 3D model of the tunnel construction site and geological material property data;

[0009] The three-dimensional model is meshed to obtain the finite element mesh model of the three-dimensional model;

[0010] Based on the geological material property data, the finite element mesh model is subjected to stress simulation to obtain the initial stress field of the finite element mesh model before freezing.

[0011] Based on the stress distribution of each element in the finite element mesh model in the initial stress field, the trend of soil density change during freezing is analyzed, and the frost heave stress field of the finite element mesh model is determined.

[0012] The initial stress field and the frost heave stress field are superimposed to determine the comprehensive stress field of the finite element mesh model.

[0013] In conjunction with the first aspect mentioned above, among some possible implementation methods, determining the frost heave stress field of the finite element mesh model includes:

[0014] Based on the stress distribution of each element mesh in the initial stress field in the finite element mesh model, the probability of density increase of each element mesh during freezing is determined.

[0015] Based on the probability of density increase, the soil density of each cell grid after freezing is determined;

[0016] Based on the soil density after freezing and the relationship between the thermal conductivity coefficient and the soil density, the thermal conductivity coefficient of each unit grid after freezing is determined.

[0017] Based on the thermal conductivity coefficient and the distance of each unit grid to the nearest freezing tube, the frost heave stress of each unit grid is determined;

[0018] By integrating the frost heave stresses of all element meshes in the finite element mesh model, the frost heave stress field of the finite element mesh model is obtained.

[0019] In conjunction with the first aspect above, in some possible implementations, determining the probability of an increase in density for each cell mesh upon freezing includes:

[0020] Obtain the compression vector of each element mesh in the finite element mesh model, which is compressed by its neighboring element meshes.

[0021] Determine the angle of difference between the extrusion vector and the stress vector of each adjacent cell grid in the initial stress field;

[0022] Based on the difference angle and the magnitude of the stress vector of each adjacent cell grid in the initial stress field, the probability of density increase of each cell grid during freezing is determined.

[0023] In conjunction with the first aspect above, in some possible implementations, determining the probability of an increase in density for each cell mesh upon freezing includes:

[0024] The stress components are obtained by multiplying the magnitude of the stress vector in the initial stress field of each adjacent cell grid with the cosine of the difference angle.

[0025] The sum of the stress components is normalized to obtain the probability of increased density of each unit mesh during freezing.

[0026] In conjunction with the first aspect above, in some possible implementations, determining the soil density of each cell grid after freezing includes:

[0027] The product of the density increase probability and the preset maximum probability density increment is used to obtain the soil density increment of each cell after freezing.

[0028] The soil density increment is superimposed with the initial global assumption of frozen soil density to obtain the soil density of each cell grid after freezing.

[0029] In conjunction with the first aspect above, in some possible implementations, determining the thermal conductivity coefficient of each cell grid after freezing includes:

[0030] Obtain the thermal conductivity coefficient of the tunnel construction site under different soil densities;

[0031] The least squares function was used to fit the thermal conductivity coefficient under different soil densities to obtain the fitting curve of thermal conductivity coefficient as a function of soil density.

[0032] The soil density after freezing is substituted into the fitted curve, and the thermal conductivity coefficient of each cell grid after freezing is determined by the fitted curve.

[0033] In conjunction with the first aspect above, in some possible implementations, determining the frost heave stress of each element grid includes:

[0034] Determine the thermal conductivity coefficient and the ratio of the distance from each cell grid to the nearest frozen tube;

[0035] The ratio is normalized to obtain the degree of frost heave stress for each unit grid.

[0036] The product of the degree of frost heave stress and the set maximum frost heave force is determined to obtain the frost heave stress of each unit grid.

[0037] In conjunction with the first aspect above, in some possible implementations, obtaining the initial stress field of the finite element mesh model before freezing includes:

[0038] Based on the geological material property data, the parameters of the finite element mesh model are set;

[0039] Pressure is applied to the finite element mesh model to simulate the actual stress on the frozen wall, and the initial stress field of the finite element mesh model is obtained.

[0040] In conjunction with the first aspect described above, in some possible implementations, the method further includes:

[0041] Based on the comprehensive stress field, determine whether the stress distribution of each element mesh in the finite element mesh model meets the actual requirements.

[0042] Secondly, the present invention also provides a numerical system for stress field analysis of frozen soil curtain tunnels based on the finite element method, comprising a memory and a processor. The memory is used to store executable computer program code, and the processor is used to call and run the executable computer program code from the memory, causing the system to execute the numerical method for stress field analysis of frozen soil curtain tunnels based on the finite element method in the first aspect or any possible implementation thereof.

[0043] Thirdly, the present invention also provides a numerical device for analyzing the stress field of a tunnel frozen soil curtain based on the finite element method, the device comprising:

[0044] The data acquisition module is used to acquire a three-dimensional model of the tunnel construction site and geological material property data;

[0045] The model acquisition module is used to perform mesh generation on the three-dimensional model and obtain the finite element mesh model of the three-dimensional model.

[0046] The initial stress field acquisition module is used to perform stress simulation on the finite element mesh model based on the geological material property data, and to acquire the initial stress field of the finite element mesh model before freezing.

[0047] The frost heave stress field acquisition module is used to analyze the trend of soil density change during freezing based on the stress distribution of each element mesh in the initial stress field of the finite element mesh model, and to determine the frost heave stress field of the finite element mesh model.

[0048] The integrated stress field acquisition module is used to superimpose the initial stress field and the frost heave stress field to determine the integrated stress field of the finite element mesh model.

[0049] Fourthly, the present invention also provides a computer program product comprising: computer program code, which, when run on a computer, causes the computer to execute the numerical method for stress field analysis of tunnel frozen soil curtain based on finite element method in the first aspect or any possible implementation thereof.

[0050] Fifthly, the present invention also provides a computer-readable storage medium storing computer program code that, when executed on a computer, causes the computer to perform the numerical method for stress field analysis of tunnel frozen soil curtain based on finite element method in the first aspect or any possible implementation thereof.

[0051] The present invention has the following beneficial effects: First, it obtains a three-dimensional model of the tunnel construction site and geological material property data, and obtains the initial stress field of the finite element mesh model corresponding to the three-dimensional model; then, based on the stress distribution of each unit mesh in the initial stress field, it analyzes the magnitude of freezing heave force of different unit meshes caused by the initial stress field during the freezing process, and obtains the frost heave stress field of the finite element mesh model; finally, by superimposing the initial stress field and the frost heave stress field, a comprehensive stress field distribution that conforms to the actual situation is obtained, which effectively improves the accuracy of the stress field analysis of the frozen soil curtain in tunnels. Attached Figure Description

[0052] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a flowchart illustrating the steps of a numerical method for analyzing the stress field of a tunnel frozen soil curtain based on the finite element method, according to an embodiment of the present invention.

[0054] Figure 2 This is a schematic diagram of the element mesh stress according to an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of the structure of a numerical system for analyzing the stress field of a tunnel frozen soil curtain based on the finite element method, according to an embodiment of the present invention.

[0056] Figure 4 This is a schematic diagram of the structure of a numerical device for analyzing the stress field of a tunnel frozen soil curtain based on the finite element method, according to an embodiment of the present invention. Detailed Implementation

[0057] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific embodiments and in conjunction with the accompanying drawings.

[0058] Embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While some embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the invention. It should be understood that the accompanying drawings and embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the invention.

[0059] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0060] The term "comprising" and its variations as used herein are open-ended inclusions, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the description below.

[0061] It should be noted that the concepts of "first" and "second" mentioned in this invention are only used to distinguish different devices, modules or units, and are not used to limit the order of functions performed by these devices, modules or units or their interdependencies.

[0062] Although operations or steps are described in a specific order in the accompanying drawings in the embodiments of the present invention, this should not be construed as requiring these operations or steps to be performed in the specific order or serial order shown, or requiring all of the shown operations or steps to be performed to obtain the desired result. In the embodiments of the present invention, these operations or steps may be performed serially; they may be performed in parallel; or a portion of these operations or steps may be performed.

[0063] Furthermore, it is understood that the data involved in the technical solutions of this invention (including but not limited to the data itself, the acquisition or use of the data) shall comply with the requirements of relevant laws, regulations and related provisions. Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains, and all parameters or indicators in the formulas involved in this invention are normalized values ​​that have eliminated the influence of dimensions.

[0064] To address the significant discrepancy between the existing frozen stress field obtained from the finite element model and the actual stress field, this invention provides a numerical method and system for analyzing the stress field of a tunnel frozen soil curtain based on the finite element method. By obtaining the initial stress field before freezing and the frost heave stress field caused by freezing, a stress field distribution that closely matches the actual model can be obtained, effectively reducing the error with the actual stress field.

[0065] The following will, with reference to the accompanying drawings, provide a detailed description of a numerical method and system for stress field analysis of frozen soil curtain tunnels based on the finite element method, as provided in an embodiment of the present invention.

[0066] Figure 1 This diagram illustrates the basic flowchart of a numerical method for analyzing the stress field of a tunnel frozen soil curtain based on the finite element method, as provided in an embodiment of the present invention. Figure 1 As shown, the method specifically includes the following steps:

[0067] Step S100: Obtain a 3D model of the tunnel construction site and geological material property data;

[0068] Step S200: Mesh the three-dimensional model to obtain the finite element mesh model of the three-dimensional model;

[0069] Step S300: Based on the geological material property data, perform stress simulation on the finite element mesh model to obtain the initial stress field of the finite element mesh model before freezing;

[0070] Step S400: Based on the stress distribution of each element mesh in the initial stress field in the finite element mesh model, analyze the trend of soil density change during freezing and determine the frost heave stress field of the finite element mesh model.

[0071] Step S500: Superimpose the initial stress field and the frost heave stress field to determine the comprehensive stress field of the finite element mesh model.

[0072] In the numerical method for stress field analysis of frozen soil curtain in tunnels based on finite element method provided in the above embodiments of the present invention, in order to realize the finite element numerical analysis of frozen soil curtain in tunnels, firstly, a three-dimensional model of the tunnel construction site and geological material property data are obtained, and the initial stress field of the finite element mesh model corresponding to the three-dimensional model is obtained; secondly, based on the stress distribution of each unit mesh in the initial stress field in the finite element mesh model, the magnitude of freezing expansion force of different unit meshes caused by the initial stress field during the freezing process is analyzed, thereby obtaining the frost expansion stress field of the finite element mesh model during the freezing process; finally, by superimposing the initial stress field and the frost expansion stress field, a comprehensive stress field distribution that conforms to the actual situation is finally obtained, which effectively improves the accuracy of stress field analysis of frozen soil curtain in tunnels.

[0073] The following is a detailed description of each step in the numerical method for stress field analysis of frozen soil curtain tunnels based on the finite element method provided in the embodiments of the present invention.

[0074] Step S100: Obtain a three-dimensional model of the tunnel construction site and geological material property data.

[0075] When using the finite element method (FEM) to analyze the stress field of frozen soil, a three-dimensional model of the tunnel construction site can be obtained through field investigation. This three-dimensional model is based on the actual geological environment. Simultaneously, geological material property data of the tunnel construction site can be obtained through literature references or experimental methods. These geological material property data refer to relevant attribute data of geological materials, including the elastic modulus, Poisson's ratio, and initial global average density of the frozen soil. Since the specific implementation process of obtaining the three-dimensional model of the construction site during the FEM stress field analysis is existing technology, it will not be elaborated here.

[0076] Step S200: Mesh the three-dimensional model to obtain the finite element mesh model of the three-dimensional model.

[0077] The above step S100 obtains relevant data about the tunnel permafrost curtain, such as basic data like three-dimensional models and geological material property data. Using these data, a basic finite element mesh model of the three-dimensional model can be constructed under existing technology.

[0078] In a specific example, based on a 3D model of the tunnel construction site, SolidWorks uses a curvature-based method to perform tetrahedral meshing on the 3D model, thereby obtaining the finite element mesh model of the 3D model. Since the specific implementation process of meshing a 3D model based on the actual geological environment to obtain the corresponding finite element mesh model is existing technology, it will not be elaborated here.

[0079] Step S300: Based on the geological material property data, perform stress simulation on the finite element mesh model to obtain the initial stress field of the finite element mesh model before freezing.

[0080] Traditional finite element analysis of frozen soil in tunnels assumes that a stable temperature is reached after freezing, and only analyzes the geological stress caused by freezing, ignoring the possible differences in frost heave stress in different areas before and after freezing. Therefore, we consider performing an initial stress analysis on the three-dimensional geological model before freezing, and then simulating the heat transfer during the freezing process to obtain the frost heave stress distribution of the three-dimensional model, which is then superimposed on the original geological stress model, making the final stress field have a smaller error compared with the actual stress field distribution.

[0081] Therefore, for the finite element mesh model, based on the geological material property data of the tunnel construction site, an initial constant temperature field is set, and the actual geological stress is simulated according to the geological stress conditions, so as to obtain the initial stress field of the finite element mesh model before freezing.

[0082] Furthermore, step S300 above, which obtains the initial stress field of the finite element mesh model before freezing, includes: setting the parameters of the finite element mesh model based on the geological material property data; applying pressure to the finite element mesh model to simulate the actual stress condition of the frozen wall, thereby obtaining the initial stress field of the finite element mesh model.

[0083] In a specific example, obtaining the initial stress field of the finite element mesh model includes the following steps:

[0084] First, assuming the area affected by the project consists of a single soil layer, and the material of the frozen soil curtain is set to an elastic material, the parameters of the unit model are set using the geological material property data obtained in step S100 above. For example, the elastic modulus of the frozen soil is set to 150 MPa, the Poisson's ratio to 0.3, and the global average density to 1800 kg / m³. 3 The model consists of a frozen structural wall, with the initial frozen soil curtain set as an isothermal body and the global constant temperature set at 0.5℃ (before the freezing pipe freezes the soil).

[0085] Secondly, the stress distribution on the outer wall of the structure is obtained, mainly by using the structural mechanics solver SM Solver to obtain the pressure distribution on the outside of the frozen wall.

[0086] Finally, by applying pressure to the outer contour of the finite element mesh model after meshing based on the stress distribution of the frozen structure's outer wall, the actual stress condition of the frozen wall is simulated. The stress on each elastic material element in the outermost layer of the finite element model is set, and the deformation of each elastic element (element mesh) is determined according to Hooke's law. The force is then transmitted to other inner elements, thereby calculating the stress on each element mesh. Based on the stress on all element meshes in the finite element mesh model, the initial stress field, i.e., the geological stress field under pressure load, is obtained and denoted as […]. .

[0087] Thus, under the preset temperature field, by simulating the stress on the finite element mesh model in the real environment, the geological stress distribution field of the tunnel under the initial unfrozen condition was obtained. In other words, the initial stress field before freezing was obtained through simulation before actual construction.

[0088] Step S400: Based on the stress distribution of each element mesh in the initial stress field in the finite element mesh model, analyze the trend of soil density change during freezing and determine the frost heave stress field of the finite element mesh model.

[0089] The influence of the initial stress field on frost heave stress during freezing is generally concentrated in areas of higher stress, which often exhibit different density variation trends. Specifically, during freezing, areas with a higher density trend have higher heat transfer efficiency and freeze faster than low-density areas. Moisture in these areas is more easily migrated by the ice front before freezing, resulting in greater freezing and a higher likelihood of frost heave stress. Conversely, areas with a lower density trend have lower heat transfer efficiency and freeze more slowly. During freezing, the frozen ice front has a lower capacity to absorb moisture from the surrounding area, resulting in lower frost heave stress.

[0090] Therefore, by analyzing the stress distribution of each unit grid in the initial stress field in the finite element mesh model, the trend of soil density change during freezing can be obtained, and the corresponding trend of thermal conductivity change can be obtained. Then, by using the thermal conductivity of the unit grid and its distance from the freezing pipe, the distribution of frost heave force caused by geological stress during freezing can be obtained. By combining the initial stress field and the frost heave stress field, the stress field distribution before tunnel construction can be finally formed.

[0091] Furthermore, step S400 above determines the frost heave stress field of the finite element mesh model, including:

[0092] Step S401: Based on the stress distribution of each element mesh in the initial stress field in the finite element mesh model, determine the probability of density increase of each element mesh during freezing.

[0093] Step S300 above obtains the initial stress field of the finite element mesh model under initial unfrozen conditions. Based on this initial stress field, the stress of each element mesh in the finite element mesh model can be obtained. After a certain period of time, the element mesh (finite element element) will experience local density changes due to stress. These local density changes will cause changes in the thermal conductivity of the material, resulting in local temperature changes. Since the frost heave force of frozen soil is closely related to temperature, it is necessary to analyze the stress situation around each element mesh, determine the change in its thermal conductivity, and thus obtain the feedback temperature field and the corresponding change in frost heave force.

[0094] When the stress of surrounding grid cells compresses and approaches the cell, the density of that cell increases more significantly; conversely, when the stress of surrounding grid cells disperses, the density of that cell decreases more significantly. The thermal conductivity of frozen soil is positively correlated with its density; that is, the higher the density of frozen soil, the stronger its thermal conductivity. Near the freezing point, soil with a high thermal conductivity cools faster and forms ice more quickly. During freezing, unfrozen water migrates towards the freezing front, and a high thermal conductivity accelerates this process, leading to more water accumulation and a more significant volume expansion after freezing, resulting in greater frost heave force. Conversely, soil with a lower thermal conductivity near the freezing point experiences relatively less frost heave force during freezing.

[0095] Furthermore, step S401 above, determining the probability of density increase for each unit mesh during freezing, includes: obtaining the compression vector of each unit mesh in the finite element mesh model being squeezed by its neighboring unit meshes; determining the difference angle between the compression vector and the stress vector of each neighboring unit mesh in the initial stress field; and determining the probability of density increase for each unit mesh during freezing based on the difference angle and the magnitude of the stress vector of each neighboring unit mesh in the initial stress field.

[0096] Determining the probability of density increase for each unit grid during freezing includes: determining the product of the magnitude of the stress vector in the initial stress field of each adjacent unit grid and the cosine of the difference angle to obtain each stress component; and normalizing the sum of the stress components to obtain the probability of density increase for each unit grid during freezing.

[0097] The stress experienced by each element in the initial stress field of the finite element mesh model mainly includes the magnitude and direction of the stress. Since the density of each element is generally related to the force during the freezing process, areas with higher density generally have inward squeezing forces around them. Therefore, the more obvious the tendency of squeezing stress around the element, the more the external pressure inhibits the expansion of the ice volume and makes it easier for water from other areas to accumulate there. The higher the probability of the density of this area increasing during the freezing process.

[0098] Therefore, by quantifying whether the stress around each individual cell tends to compress towards it, the density variation trend of the individual cell can be obtained. Specifically, when the stress of other cells near a given cell is directed towards that cell, the more pronounced the stress concentration and the more obvious the trend of increasing density.

[0099] In a specific example, the spatial coordinates of the core (centroid) of each element in the finite element mesh model are obtained, and the stress direction of each element is also obtained. This stress direction is usually a three-dimensional vector, referred to here as the stress vector. The vector pointing from the core of an adjacent element to the core of the current element represents the stress compressing the current element. Therefore, if the compressive vector formed by an element and its surrounding elements is in the same direction as the stress vector it experiences, it indicates that the higher the compressive stress on the current element, the greater its tendency to increase density upon freezing. Figure 2 A schematic diagram of the stress in the element mesh is shown. Figure 2 In the diagram, A and C represent the adjacent meshes of mesh B, respectively, and the solid arrows indicate the stress conditions experienced by each mesh. Taking mesh A as an example, 'a' represents the stress experienced by mesh A itself. Let a represent the vector pointing from the core of cell A to the core of cell B, if a and The smaller the angle between them, the higher the compressive force on cell B from cell A, and the higher the possibility of density increase during freezing.

[0100] Therefore, based on the spatial coordinates of the core (centroid) of each element in the finite element mesh model, a vector pointing from the core of the adjacent element to the core of that element is obtained. This vector is called the compression vector of the adjacent element. Using the coordinate form of the vector, the difference in direction between the stress vector and the compression vector experienced by all adjacent element meshes is calculated and denoted as the difference angle.

[0101] ;

[0102] In the formula, This represents the angle of difference between the compression vector and the stress vector of the j-th adjacent cell in each cell. This indicates the dimensions of the compression vector and the stress vector; the dimensions of the two vectors are the same. This represents the i-th value in the stress vector coordinate form of the j-th adjacent element of each element mesh; This represents the i-th value in the extrusion vector coordinate form of the j-th adjacent cell of each cell.

[0103] Furthermore, for each adjacent element of a given element, the larger the stress component of the adjacent element relative to the corresponding element in the direction of the compression vector, the more pronounced the compression tendency of the corresponding element is to the adjacent element, and the higher the probability of density increase during freezing. Therefore, by combining all adjacent elements, the probability of density increase during freezing for each element is determined as follows:

[0104] ;

[0105] In the formula, This indicates the probability that the density of the i-th cell will increase when the cell is frozen. This represents the number of adjacent cell grids surrounding the i-th cell grid; This represents the magnitude of the stress in the initial stress field of the j-th adjacent cell surrounding the i-th cell (the magnitude of the stress vector in the initial stress field). This represents the stress vector of the j-th adjacent cell surrounding the i-th cell in the initial stress field; The angle representing the difference between the compression vector and the stress vector of the j-th adjacent cell around the i-th cell; This represents a normalization function used to normalize values ​​to the range [0,1].

[0106] Step S401 above determines the difference angle between the compression vector of each element mesh in the finite element mesh model, which is squeezed by its neighboring element meshes, and the stress vector of each neighboring element mesh in the initial stress field. Based on this difference angle, the stress component of the neighboring element mesh relative to the current element mesh in the direction of the compression vector is calculated. This allows for an accurate assessment of the possibility that the density of each element mesh in the finite element mesh model will increase when frozen.

[0107] Step S402: Based on the probability of density increase, determine the soil density of each cell grid after freezing.

[0108] In the finite element mesh model, each element can obtain a density increase probability. By pre-quantifying the relationship between this density increase probability and the density of the soil after freezing, the density of each element can be determined after freezing based on this relationship and the density increase probability of each element.

[0109] Furthermore, step S402 above, which determines the soil density of each cell grid after freezing, includes: determining the product of the density increase probability and the preset maximum probability density increment to obtain the soil density increment of each cell grid after freezing; and superimposing the soil density increment with the initial global assumption of frozen soil density to obtain the soil density of each cell grid after freezing.

[0110] In a specific example, based on experience, the percentage by which the density increases the most is set to the original value. times, such as The value is set to 0.05, meaning that when the probability of density increase is 1, the maximum density increase is 0.05 times the initial preset value. Because the volume of water increases after freezing, water migrates during the freezing process, and the ice structure is compressed, the density of frozen soil will increase and will not fall below the initial state. Therefore, based on the preset soil density... (Initial global average density in geological material property data) and multiples Determine the preset maximum probability density increment Then, for any i-th cell, the final density increment of the frozen soil is:

[0111] ;

[0112] In the formula, This represents the soil density increment of the i-th cell after freezing; This indicates the probability that the density of the i-th cell will increase when the cell is frozen.

[0113] Furthermore, based on the preset soil density and / or the resulting element mesh's soil density increment after freezing The soil density of the element mesh after freezing is obtained. .

[0114] Step S402 above determines the soil density increment based on the density increase probability of each cell grid, and superimposes the soil density increment with the initial global assumption of the frozen soil density, thereby accurately obtaining the soil density of each cell grid after freezing.

[0115] Step S403: Based on the soil density after freezing and the relationship between the thermal conductivity coefficient and the soil density, determine the thermal conductivity coefficient of each cell grid after freezing.

[0116] By using experimental methods to obtain the relationship curve between soil density and thermal conductivity, and then substituting the soil density of each cell after freezing into this relationship curve, the thermal conductivity of each cell after the change can be obtained.

[0117] Furthermore, step S403 above, which determines the thermal conductivity coefficient of each cell grid after freezing, includes: obtaining the thermal conductivity coefficient of the tunnel construction site under different soil densities; using the least squares function to perform curve fitting on the thermal conductivity coefficients under different soil densities to obtain a fitting curve of the thermal conductivity coefficient changing with soil density; substituting the soil density after freezing into the fitting curve, and determining the thermal conductivity coefficient of each cell grid after freezing from the fitting curve.

[0118] In a specific example, firstly, through manual experiments, the thermal conductivity coefficients of the soil at multiple tunnel construction sites under different soil densities were obtained. Different soil densities can be obtained by mechanical pressure application. For example, if the soil density is... The thermal conductivity is Next, using soil density as the abscissa and thermal conductivity as the ordinate, a least squares algorithm is used for curve fitting to obtain a fitted curve showing the change in soil density with thermal conductivity. Then, based on the soil density of each cell obtained in step S402 after freezing, the thermal conductivity of each cell is matched to the fitted curve. Let the thermal conductivity of the i-th cell be denoted as... .

[0119] Step S403 above obtains the fitting curve of the soil density at the tunnel construction site as a function of the thermal conductivity coefficient, and substitutes the obtained soil density of each unit grid after freezing into the fitting curve, thereby obtaining the thermal conductivity coefficient of each unit grid in the finite element mesh model after freezing.

[0120] Step S404: Determine the frost heave stress of each unit grid based on the thermal conductivity coefficient and the distance of each unit grid to the nearest freezing tube.

[0121] In grid cells with high thermal conductivity, heat transfer is rapid. The closer a cell is to the freezing point, the faster it freezes, and the more likely it is to absorb moisture from nearby cells, leading to greater frost heave. By determining the distance from each cell to the nearest freezing point and combining this distance with the corresponding thermal conductivity, a smaller distance and a higher thermal conductivity indicate greater frost heave stress in that cell. This allows us to determine the frost heave stress of each cell.

[0122] Furthermore, step S404 above, which determines the frost heave stress of each unit grid, includes: determining the ratio of the thermal conductivity coefficient to the distance from each unit grid to the nearest freezing pipe; normalizing the ratio to obtain the degree of frost heave stress of each unit grid; and determining the product of the degree of frost heave stress and a set maximum frost heave force to obtain the frost heave stress of each unit grid.

[0123] In a specific example, firstly, for any i-th cell mesh, based on its thermal conductivity... and the distance to the nearest freezing tube Calculate the degree of frost heave stress In the formula, This represents a normalization function used to normalize values ​​to the range [0,1].

[0124] Secondly, a maximum frost heave force is defined, which refers to the frost heave force value corresponding to a frost heave stress level of 1. This maximum frost heave force is then calculated in relation to the frost heave stress level of any i-th element mesh. The product of these factors is used as the magnitude of the frost heave stress in any i-th element mesh.

[0125] Step S404 above determines the degree of frost heave stress of each unit grid based on the thermal conductivity coefficient of each unit grid and the distance of each unit grid to the nearest freezing pipe, and obtains the magnitude of frost heave stress of the unit grid after freezing based on the degree of frost heave stress.

[0126] Step S405: Integrate the frost heave stresses of all element meshes in the finite element mesh model to obtain the frost heave stress field of the finite element mesh model.

[0127] The above steps S401-S404 analyze the behavior of the initial stress field of the finite element mesh model during the freezing process, simulate the frost heave stress of each element mesh in the finite element mesh model, and fuse the frost heave stress of all element meshes to obtain the frost heave stress field of the finite element mesh model during the freezing process, which is denoted as G1.

[0128] Step S500: Superimpose the initial stress field and the frost heave stress field to determine the comprehensive stress field of the finite element mesh model.

[0129] Steps S100-S400 above obtain the initial stress field G0 of the finite element mesh model under the initial unfrozen conditions. Based on this initial stress field G0, the frost heave stress field G1 during the freezing process is simulated. Superimposing the two yields the comprehensive stress field of the finite element mesh model, i.e., the final stress field distribution of the frozen soil curtain. At this point, the final stress field distribution is obtained. This approach avoids the situation in traditional schemes where all finite element models are assumed to be isothermal, resulting in an unrealistic stress field and effectively improving the accuracy of the determined comprehensive stress field.

[0130] Furthermore, the method also includes: based on the comprehensive stress field of the finite element mesh model obtained above, determining whether the stress distribution of each element mesh in the finite element mesh model meets the actual requirements.

[0131] In a specific example, the discrete stresses in the composite stress field of the finite element mesh model are interpolated to make them continuous, resulting in a continuous stress field that is then visualized. Subsequently, the continuous stress field is assessed manually or using stress thresholds to determine whether it meets the requirements for construction freezing.

[0132] Based on the same inventive concept, embodiments of the present invention also provide a numerical system for analyzing the stress field of frozen soil curtains in tunnels based on the finite element method, such as... Figure 3As shown, the system includes: a memory, a processor, and computer program code stored in the memory and running on the processor, wherein when the processor executes the computer program code, the system can execute any of the aforementioned numerical methods for analyzing the stress field of tunnel frozen soil curtain based on the finite element method.

[0133] In this embodiment of the invention, the system can be divided into functional modules according to the above method example. For example, each module can correspond to a separate functional module, or two or more functions can be integrated into one processing module. The integrated module can be implemented in hardware. It should be noted that the module division in this embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.

[0134] Based on the same inventive concept, embodiments of the present invention also provide a numerical device for analyzing the stress field of frozen soil curtains in tunnels based on the finite element method, such as... Figure 4 As shown, the device includes:

[0135] The data acquisition module is used to acquire a three-dimensional model of the tunnel construction site and geological material property data;

[0136] The model acquisition module is used to perform mesh generation on the three-dimensional model and obtain the finite element mesh model of the three-dimensional model.

[0137] The initial stress field acquisition module is used to perform stress simulation on the finite element mesh model based on the geological material property data, and to acquire the initial stress field of the finite element mesh model before freezing.

[0138] The frost heave stress field acquisition module is used to analyze the trend of soil density change during freezing based on the stress distribution of each element mesh in the initial stress field of the finite element mesh model, and to determine the frost heave stress field of the finite element mesh model.

[0139] The integrated stress field acquisition module is used to superimpose the initial stress field and the frost heave stress field to determine the integrated stress field of the finite element mesh model.

[0140] It should be noted that the apparatus provided in the above embodiments is only an example of the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the computer device can be divided into different functional modules to complete all or part of the functions described above. In addition, the numerical method embodiment for stress field analysis of frozen soil curtain tunnel based on finite element method provided in the above embodiments belongs to the same concept, and its specific implementation process is detailed in the method embodiment, which will not be repeated here.

[0141] Based on the same inventive concept, embodiments of the present invention also provide a computer program product, which includes: computer program code, which, when run on a computer, causes the computer to execute any of the aforementioned numerical methods for analyzing the stress field of tunnel frozen soil curtain based on the finite element method.

[0142] Based on the same inventive concept, embodiments of the present invention also provide a computer-readable storage medium storing computer program code, which, when run on a computer, causes the computer to execute any of the aforementioned numerical methods for analyzing the stress field of tunnel frozen soil curtain based on the finite element method.

[0143] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A numerical method for stress field analysis of frozen soil curtain tunnels based on the finite element method, characterized in that, Includes the following steps: Obtain a 3D model of the tunnel construction site and geological material property data; The three-dimensional model is meshed to obtain the finite element mesh model of the three-dimensional model; Based on the geological material property data, the finite element mesh model is subjected to stress simulation to obtain the initial stress field of the finite element mesh model before freezing. Based on the stress distribution of each element in the finite element mesh model in the initial stress field, the trend of soil density change during freezing is analyzed, and the frost heave stress field of the finite element mesh model is determined. The initial stress field and the frost heave stress field are superimposed to determine the comprehensive stress field of the finite element mesh model; Determine the frost heave stress field of the finite element mesh model, including: Based on the stress distribution of each element mesh in the initial stress field in the finite element mesh model, the probability of density increase of each element mesh during freezing is determined. Based on the probability of density increase, the soil density of each cell grid after freezing is determined; Based on the soil density after freezing and the relationship between the thermal conductivity coefficient and the soil density, the thermal conductivity coefficient of each unit grid after freezing is determined. Based on the thermal conductivity coefficient and the distance of each unit grid to the nearest freezing tube, the frost heave stress of each unit grid is determined; By integrating the frost heave stresses of all element meshes in the finite element mesh model, the frost heave stress field of the finite element mesh model is obtained. Determining the probability of an increase in density for each cell grid upon freezing includes: Obtain the compression vector of each element mesh in the finite element mesh model, which is compressed by its neighboring element meshes. Determine the angle of difference between the extrusion vector and the stress vector of each adjacent cell grid in the initial stress field; Based on the difference angle and the magnitude of the stress vector of each adjacent cell grid in the initial stress field, the probability of density increase of each cell grid during freezing is determined. Determining the probability of an increase in density for each cell grid upon freezing includes: The stress components are obtained by multiplying the magnitude of the stress vector in the initial stress field of each adjacent cell grid with the cosine of the difference angle. The stress components are summed to obtain the sum, and the sum is normalized to obtain the probability of density increase of each unit grid during freezing. Determining the soil density of each cell after freezing includes: The product of the density increase probability and the preset maximum probability density increment is used to obtain the soil density increment of each cell after freezing. The soil density increment is superimposed with the initial global assumption of frozen soil density to obtain the soil density of each cell grid after freezing. Determining the thermal conductivity of each cell after freezing includes: Obtain the thermal conductivity coefficient of the tunnel construction site under different soil densities; The least squares function was used to fit the thermal conductivity coefficient under different soil densities to obtain the fitting curve of thermal conductivity coefficient as a function of soil density. The soil density after freezing is substituted into the fitting curve, and the thermal conductivity coefficient of each cell grid after freezing is determined by the fitting curve. Determining the frost heave stress of each unit grid includes: Determine the thermal conductivity coefficient and the ratio of the distance from each cell grid to the nearest frozen tube; The ratio is normalized to obtain the degree of frost heave stress for each unit grid. The product of the degree of frost heave stress and the set maximum frost heave force is determined to obtain the frost heave stress of each unit grid.

2. The numerical method for stress field analysis of frozen soil curtain tunnels based on finite element method according to claim 1, characterized in that, Obtaining the initial stress field of the finite element mesh model before freezing includes: Based on the geological material property data, the parameters of the finite element mesh model are set; Pressure is applied to the finite element mesh model to simulate the actual stress on the frozen wall, and the initial stress field of the finite element mesh model is obtained.

3. The numerical method for stress field analysis of frozen soil curtain tunnels based on finite element method according to claim 1, characterized in that, The method further includes: Based on the comprehensive stress field, determine whether the stress distribution of each element mesh in the finite element mesh model meets the actual requirements.

4. A numerical system for analyzing the stress field of a tunnel frozen soil curtain based on the finite element method, characterized in that, It includes a memory, a processor, and executable computer program code stored in the memory and executable on the processor. When the processor executes the computer program code, it performs the numerical method for stress field analysis of tunnel frozen soil curtain based on any one of claims 1 to 3.

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