Method and apparatus for analyzing chloride ion distribution in tunnel lining based on stress level
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- 山东高速工程检测有限公司
- Filing Date
- 2026-05-09
- Publication Date
- 2026-07-14
Smart Images
Figure CN122385457A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of tunnel engineering technology, and more specifically, to a method and equipment for analyzing chloride ion distribution in tunnel lining based on stress level. Background Technology
[0002] Tunnels are a type of cavity structure buried under (rock) soil layers. The external environment is affected by the surrounding rock (soil) and the water and ion media within the rock layers. The internal structure is open and subject to the relatively closed atmospheric environment. At the same time, in operation, it is also affected by the movement of pedestrians and vehicles.
[0003] Tunnels, as a special type of structure, differ significantly from ordinary concrete structures, primarily in that both the inner and outer surfaces of the lining concrete structure are subject to the effects of environmental media, resulting in severe damage and deterioration. The back of the lining structure is in direct contact with the soil, rock, and ambient water. It is affected by corrosive substances in the surrounding rock and soil layers, such as chloride ions, which, under the influence of pressure and concentration gradients, permeate and diffuse, causing water and corrosive ions in the soil to migrate into the concrete and undergo physical and chemical reactions.
[0004] Tunnel linings are mostly constructed using reinforced concrete. The diffusion of chloride ions in concrete is affected by many factors, but existing research mainly focuses on the effects of material mix proportions (such as water-cement ratio), environmental parameters (temperature and humidity), and time-varying effects on chloride ion diffusion. Summary of the Invention
[0005] The purpose of this application is to provide a method and equipment for analyzing chloride ion distribution in tunnel lining based on stress level, so as to analyze the influence of stress level on chloride ion diffusion.
[0006] In a first aspect, embodiments of this application provide a method for analyzing chloride ion distribution in tunnel lining based on stress levels, including: The stress distribution applied to the lining structure is determined based on the tunnel's burial depth and the surrounding rock grade. For the radial erosion path in the circumferential direction of a cross section in the tunnel, the diffusion coefficient of chloride ions is determined based on the stress corresponding to the erosion path. Based on the diffusion coefficient, boundary conditions, initial chloride ion concentration, and duration, the chloride ion erosion control equation is solved to obtain the chloride ion concentration distribution along the radial direction of the tunnel and its variation with time. The chloride ion distribution of the tunnel lining is obtained based on the chloride ion concentration distribution of all paths on all cross sections.
[0007] This application takes into account the fact that the diffusion coefficient of chemical ions in structural components is affected by the stress level of the components, and introduces a stress-dependent diffusion coefficient, which fully reflects the influence of the actual working state of the lining on the chloride ion transport process, and breaks through the limitation of the traditional model that regards concrete as a homogeneous medium.
[0008] In one possible implementation of the first aspect, the boundary conditions include: The chloride ion concentration at the outer boundary of the lining structure is constant and equal to the chloride ion concentration of the external chloride salt. The ion flux on the inner side of the lining structure and other boundaries is zero.
[0009] The embodiments of this application define the start and end points of chloride ion diffusion through boundary conditions, and obtain a unique correct solution that matches physical reality from an infinite number of mathematical solutions of the control function in combination with initial conditions.
[0010] In one possible implementation of the first aspect, the chloride ion erosion control equation is constructed by the following method: For any infinitesimal element along the erosion path, a function of the total amount of first chloride ions accumulated in the infinitesimal element per unit time is generated based on the cross-sectional area and volume of the infinitesimal element. The second total chloride ion function is determined by multiplying the increase in chloride ion concentration in the micro-element by the volume of the micro-element. The chloride ion diffusion control equation is generated based on the first chloride ion total amount function and the second chloride ion total amount function.
[0011] The embodiments of this application can calculate the distribution of chloride ions along the corrosion path using the chloride ion corrosion control equation, thereby determining the influence of stress on the chloride ion distribution.
[0012] In one possible implementation of the first aspect, the chloride ion erosion control equation is: ; in: Indicates chloride ion concentration; This represents the chloride ion diffusion coefficient that takes stress into account. Indicates time; Indicates the position of the infinitesimal element.
[0013] The embodiments of this application can calculate the distribution of chloride ions along the corrosion path using the chloride ion corrosion control equation, thereby determining the influence of stress on the chloride ion distribution.
[0014] In one possible implementation of the first aspect, obtaining the chloride ion distribution of the tunnel lining based on the chloride ion concentration distribution across all paths on all cross sections includes: The tunnel is discretized to obtain multiple cross-sections along the tunnel axis; The concentration transformation function for each cross section is determined based on the initial concentration of the lining and the additional concentration caused by external erosion. The concentration distribution function is generated by substituting the concentration transformation function into the finite element equation; the finite element equation is derived based on Fick's law and the law of conservation of mass. Based on the boundary and initial conditions, the concentration distribution function is solved by the time integration method to obtain the chloride ion concentration distribution along the radial direction of the tunnel for all erosion paths in the tunnel as a function of time.
[0015] The embodiments of this application use the finite element method for discretization, with each cross section represented by a node. The element shape function is introduced to calculate the concentration distribution. This method transforms the continuous problem into solving the nodal concentration, simplifying the calculation.
[0016] In one possible implementation of the first aspect, the concentration transformation function is: ;in, This is the vector representing the total chloride ion content corresponding to all cross-sections; The chloride ion concentration vector at time t for each cross section caused by chloride ion diffusion; This is the vector representing the initial chloride ion content corresponding to all cross-sections.
[0017] The embodiments of this application simplify the initial conditions and reduce the computational load of subsequent calculations by constructing a concentration transformation function.
[0018] In one possible implementation of the first aspect, the finite element equation is: ; in, ; L is the tunnel length; The corresponding shape function matrix; The position of the infinitesimal element; The chloride ion diffusion coefficient under stress was taken into account. This is the vector representing the total chloride ion content corresponding to all cross-sections; Let be the boundary flux vector at time t; The concentration distribution function is generated by substituting the concentration transformation function into the finite element equation, including: Substituting the concentration transformation function into the finite element equation, the resulting concentration distribution function is: .
[0019] The embodiments of this application use the finite element method for discretization, with each cross section represented by a node. The concentration distribution is calculated by introducing element shape functions. This method transforms the continuous problem into solving the nodal concentration, simplifying the calculation.
[0020] In one possible implementation of the first aspect, the stress distribution applied to the lining structure is determined based on the tunnel's burial depth and the surrounding rock grade, including: The load distribution on the lining structure is determined based on the tunnel's burial depth and the surrounding rock grade. The tunnel lining structure is simplified into a beam model constructed using two-dimensional beam elements; The equivalent stiffness method is used to treat the stiffness of the tunnel as a single material property; Spring units that can only be compressed are installed at the outer edge of the lining to simulate the elastic support of the surrounding rock; the spring stiffness is determined according to the formation resistance coefficient. The surrounding rock load is applied to the beam model, and mechanical analysis is performed to obtain the stress of each cross section of the lining.
[0021] Secondly, embodiments of this application provide a device for analyzing chloride ion distribution in tunnel lining based on stress levels, comprising: The stress determination module is used to determine the stress distribution applied to the lining structure based on the tunnel's burial depth and surrounding rock grade. The diffusion coefficient determination module is used to determine the chloride ion diffusion coefficient based on the stress corresponding to the radial erosion path in the circumferential direction of a cross section in a tunnel. The concentration distribution determination module is used to solve the chloride ion erosion control equation based on the diffusion coefficient, boundary conditions, initial chloride ion concentration and duration, and obtain the chloride ion concentration distribution along the radial direction of the tunnel and its variation over time. The tunnel chloride ion distribution module is used to obtain the chloride ion distribution of the tunnel lining based on the chloride ion concentration distribution of all paths on all cross sections.
[0022] Thirdly, embodiments of this application provide an electronic device, including: a processor, a memory, and a bus, wherein: The processor and memory communicate with each other via a bus; The memory stores program instructions that can be executed by the processor, and the processor can execute the method of the first aspect by calling the program instructions.
[0023] Fourthly, embodiments of this application provide a non-transitory computer-readable storage medium, comprising: A non-transitory computer-readable storage medium stores computer instructions that cause the computer to perform the methods in the various possible implementations of the first aspect.
[0024] Fifthly, embodiments of this application provide a computer program product, including computer program instructions, which, when read and executed by a processor, perform the methods in various possible implementations of the first aspect.
[0025] Other features and advantages of this application will be set forth in the following description and will be apparent in part from the description or may be learned by practicing embodiments of this application. The objectives and other advantages of this application may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description
[0026] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0027] Figure 1 This is a schematic diagram of the one-dimensional corrosion direction of chloride ions provided in an embodiment of this application; Figure 2 This application provides a schematic diagram of one-dimensional diffusion of chloride ions in a concrete component; Figure 3 A finite element model diagram of a one-dimensional chloride ion corrosion problem; Figure 4 A schematic flowchart of a chloride ion distribution analysis method based on stress level is provided for an embodiment of this application; Figure 5 A schematic diagram illustrating a tunnel discrete along the axial direction, provided as an embodiment of this application; Figure 6 A schematic flowchart of another method for analyzing chloride ion distribution in tunnel lining based on the influence of stress level, provided in an embodiment of this application; Figure 7 A schematic diagram of a chloride ion distribution analysis device based on stress level is provided for an embodiment of this application; Figure 8 This is a schematic diagram of the physical structure of an electronic device provided in an embodiment of this application. Detailed Implementation
[0028] The embodiments of the technical solution of this application will now be described in detail with reference to the accompanying drawings. These embodiments are only used to more clearly illustrate the technical solution of this application and are therefore merely examples, and should not be used to limit the scope of protection of this application.
[0029] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.
[0030] In the description of the embodiments of this application, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.
[0031] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.
[0032] In the description of the embodiments in this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.
[0033] In the description of the embodiments of this application, the term "multiple" refers to two or more (including two), similarly, "multiple sets" refers to two or more (including two sets), and "multiple pieces" refers to two or more (including two pieces).
[0034] In the description of the embodiments of this application, the technical terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of this application and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this application.
[0035] In the description of the embodiments of this application, unless otherwise expressly specified and limited, technical terms such as "installation," "connection," "joining," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.
[0036] The diffusion of chloride ions in concrete is influenced by a variety of factors, but existing research mainly focuses on the effects of material proportions (such as water-cement ratio), environmental parameters (temperature and humidity), and time-varying effects on chloride ion diffusion. Although preliminary findings have revealed a significant impact of stress on chloride ion erosion diffusion, the underlying mechanisms have not yet been systematically understood. Especially under complex stress conditions, the quantitative relationship between stress level and chloride ion diffusion coefficient requires further investigation.
[0037] Based on this, this application provides a method for analyzing chloride ion distribution based on the influence of stress level. The core assumption of this method is that chloride ion erosion occurs in a one-dimensional diffusion along the radial direction of the tunnel. The tunnel structure is divided into multiple cross-sections in the axial direction, and each cross-section is further discretized into multiple radial erosion paths in the circumferential direction. The erosion paths are divided into a sufficient number of one-dimensional finite element erosion cells with very small lengths. The chloride ion erosion governing equation is used to solve for the chloride ion concentration distribution on each erosion path. Finally, the results of all paths are integrated to obtain the overall chloride ion distribution of the lining cross-section.
[0038] Figure 1 This illustration shows a one-dimensional erosion direction of chloride ions in an embodiment of this application. It is assumed that the erosion of the tunnel lining by chloride ions is a one-dimensional erosion along a cross-section. Since the chloride ions primarily originate from groundwater in the surrounding rock when the tunnel lining is eroded, the erosion direction is from the outer surrounding rock radially towards the inner side of the lining. Therefore, the tunnel structure is discretized into multiple cross-sections along the axial direction, and for each cross-section, chloride ions erode radially along the tunnel.
[0039] Based on Fick's first law, and introducing the diffusion coefficient that stress depends on, the one-dimensional diffusion equation of chloride ions in concrete structural members is as follows:
[0040] Where D(x) is the stress-dependent diffusion coefficient. Boundary conditions include: The outer boundary (x=x1, denoted as the ion concentration boundary) ): ; The inner boundary (x=x2, denoted as the ion flux boundary) ): .
[0041] Where C is the concentration of chloride ions; D is the chloride ion diffusion coefficient; This represents the concentration gradient of ions along the outward normal direction of the component surface; The "" sign indicates that the diffusion direction is in the opposite direction of the concentration gradient, meaning that ions always migrate from high concentration to low concentration. This represents the ion flux at the corresponding boundary, which satisfies the following relationship: And regarding the boundary of the problem under consideration ,have: .
[0042] like Figure 2 As shown, an arbitrary micro-element of a structural component is analyzed along the one-dimensional corrosion path of chloride ions. In the figure, chloride ions only diffuse along the positive x-axis of the micro-element. During the chloride ion corrosion diffusion process, the total amount of chloride ions accumulated in this micro-element per unit time can be written as:
[0043] in, Let be the cross-sectional area of the infinitesimal element perpendicular to the x-direction; Let be the volume of the infinitesimal element.
[0044] On the other hand, the total amount of chloride ions accumulated in a micro-element per unit time can be expressed as the product of the increase in chloride ion concentration in the micro-element and the volume of the micro-element, as shown in the following formula:
[0045] Substituting the equations simultaneously, we obtain the one-dimensional erosion control equation for chloride ions in concrete members:
[0046] According to the Galerkin method, the equivalent integral form of the above equation and the corresponding ion flux boundary equation can be expressed as:
[0047] in, Represents any virtual ion concentration distribution function for a concrete member that is allowed by boundary conditions; The boundary of ion flux for the concrete member is represented by ν; the volume of the concrete member is represented by ν. and These represent the volume element and area element of the corresponding integration domain, respectively.
[0048] Integrate the above equation by parts, apply Gauss's divergence theorem, and substitute the conditions. , , The simplified formula can be obtained as follows: .
[0049] Where L represents the length of the concrete component along the direction of chloride ion erosion.
[0050] like Figure 3 As shown, for a one-dimensional erosion problem, the ion concentration at any cross-sectional position of a concrete member perpendicular to the erosion direction is the same at any time. Therefore, in finite element analysis, a node can be used to replace a cross-section perpendicular to the ion erosion direction.
[0051] Based on the above theoretical foundation Figure 4 This is a schematic flowchart of a method for analyzing chloride ion distribution based on stress level, provided as an embodiment of this application. The method includes: Step 401: Determine the stress distribution applied to the lining structure based on the tunnel depth and surrounding rock grade.
[0052] Based on tunnel design data, the burial depth and surrounding rock grade are determined. According to relevant design specifications, the distribution of loosening pressure loads acting on the lining by the surrounding rock is calculated. For shallow-buried tunnels or tunnels in special geological conditions, the total soil column pressure or other special loads must also be considered.
[0053] In finite element method (FEM) software, a load-structure model is established to calculate the internal forces of the tunnel lining. Specifically, the tunnel lining is simplified into a two-dimensional planar beam model, with its axis being the centerline of the lining. The equivalent stiffness method is employed. The reinforced concrete lining is considered as a homogeneous material, and its equivalent elastic modulus E is calculated using the formula... calculate.
[0054] in, This refers to the elastic modulus of concrete. This represents the cross-sectional area of the concrete. This refers to the elastic modulus of the reinforcing steel. This represents the cross-sectional area of the reinforcing steel. This method can reasonably reflect the overall axial and flexural stiffness of composite materials.
[0055] The elastic resistance of the surrounding rock is often considered by setting spring units that are only subjected to compression around the lining.
[0056] The calculated surrounding rock pressure (usually reduced according to specifications) is applied to the outer edge of the beam model for static calculation. After solving, the internal force results (axial force N, bending moment M) at each point along the circumference of the lining are output, and the stress distribution at each point section can then be calculated.
[0057] Step 402: For the radial erosion path in the circumferential direction of a cross section in the tunnel, determine the chloride ion diffusion coefficient based on the stress corresponding to the erosion path.
[0058] For any cross-section of the tunnel, several key points are selected circumferentially along the inner wall of the lining (i.e., the side in contact with the corrosive environment). Starting from each key point, a radial straight line is defined along the lining thickness towards the surrounding rock, which is a erosion path. See [link to relevant documentation] for details. Figure 1 .
[0059] From the stress field obtained in step 401, extract the concrete stress values corresponding to different depths along the erosion path.
[0060] By substituting the stress value corresponding to each point on the erosion path into the predetermined stress-diffusion coefficient relationship, the chloride ion diffusion coefficient D at that point can be calculated. Therefore, the diffusion coefficient D(x) corresponding to the erosion path as a function of depth (radial position) can be obtained.
[0061] It is understandable that the stress-diffusion coefficient relationship can be interpreted as stress function .
[0062] Step 403: Based on the diffusion coefficient, boundary conditions, initial chloride ion concentration and duration, solve the chloride ion erosion control equation to obtain the chloride ion concentration distribution along the radial direction of the tunnel and its variation with time.
[0063] For a specific erosion path, a one-dimensional chloride ion erosion control equation is established, which is as follows: ; in: Indicates chloride ion concentration; This represents the chloride ion diffusion coefficient that takes stress into account. Indicates time; This indicates the position of the micro-element.
[0064] It should be noted that this equation needs to be solved under boundary conditions, which can be found in the above embodiments and will not be repeated here.
[0065] Since D(x) is a function of position, the above equation is usually difficult to solve analytically and requires numerical methods, such as the finite element method. The erosion path is discretized in space (depth direction) and time to form a grid system. Combined with boundary and initial conditions, the discretized equation is iteratively solved in a computer to obtain the chloride ion concentration value of each grid point at each discrete time point.
[0066] Step 404: Obtain the chloride ion distribution of the tunnel lining based on the chloride ion concentration distribution of all paths on all cross sections. After obtaining the chloride ion concentration distribution of all paths on each cross section, the chloride ion distribution of the tunnel lining can be obtained by summing all the cross sections.
[0067] This application takes into account the fact that the diffusion coefficient of chemical ions in structural components is affected by the stress level of the components, and introduces a stress-dependent diffusion coefficient, which fully reflects the influence of the actual working state of the lining on the chloride ion transport process, and breaks through the limitation of the traditional model that regards concrete as a homogeneous medium.
[0068] Based on the above embodiments, the chloride ion erosion control equation is constructed using the following method: For any infinitesimal element along the erosion path, a function of the total amount of first chloride ions accumulated in the infinitesimal element per unit time is generated based on the cross-sectional area and volume of the infinitesimal element. The second total chloride ion function is determined by multiplying the increase in chloride ion concentration in the micro-element by the volume of the micro-element. The chloride ion diffusion control equation is generated based on the first chloride ion total amount function and the second chloride ion total amount function.
[0069] In the specific implementation process, for a certain erosion path, a micro-element with a thickness of dx can be cut out, and its cross-sectional area is A. Therefore, the volume of the micro-element is dV=A*dx.
[0070] J(x,t) is defined as the chloride ion flux at position x and time t, and its physical meaning is the mass of chloride ions passing through a unit area per unit time, with units of mol / (m²). 2 s) or kg / (m 2 The flux is described by Fick's first law: J = -D * (s). C / x). The negative sign indicates that the diffusion direction is opposite to the direction of the concentration gradient increase.
[0071] The net inflow at point x is the amount of chloride ions flowing in from the left side of the infinitesimal element during time dt, and its formula is: J(x,t)*A*dt. The outflow at point x+dx is the amount of chloride ions flowing out from the right side of the infinitesimal element during time dt, and its formula is: J(x+dx,t) *A*dt. Therefore, the net inflow of the infinitesimal element per unit time can be calculated. The specific calculation method is: divide the net inflow at point x and the outflow at point x+dx by dt, and calculate the difference to obtain the amount of chloride ions stored in the infinitesimal element per unit time, which is the first total chloride ion function. This function is specifically: .
[0072] The following calculates the increase in chloride ion storage within a micro-element per unit time: First, calculate the current storage capacity. Specifically, at time t, the chloride ion concentration within the infinitesimal element is: Therefore, the total chloride ion storage within the micro-element is: After a tiny time interval dt, the concentration becomes At this point, the total chloride ion storage within the microelement is: During time dt, the increase in storage is... .
[0073] Dividing the increase in the above storage by dt yields the increase in chloride ion storage per unit time within the infinitesimal element, which is the second total chloride ion function, specifically expressed as: .
[0074] According to the law of conservation of mass, the net inflow equals the internal storage increment. Therefore, the first total chloride ion function and the second total chloride ion function can be combined to obtain the chloride ion erosion control equation. The chloride ion erosion control equation can be expressed as: .in: Indicates chloride ion concentration; This represents the chloride ion diffusion coefficient that takes stress into account. Indicates time; This indicates the position of the micro-element.
[0075] Based on the above embodiments, after obtaining the chloride ion concentration distribution along the radial direction of the tunnel and changing over time along a certain erosion path, it is possible to obtain the chloride ion concentration distribution along the radial direction of the tunnel and changing over time along all erosion paths on the complete tunnel. The specific method is as follows: The tunnel is discretized using the finite element method to obtain multiple cross-sections along the tunnel axis; The concentration transformation function for each cross section is determined based on the initial concentration of the lining and the additional concentration caused by external erosion. The concentration distribution function is generated by substituting the concentration transformation function into the finite element equation; wherein the finite element equation is derived based on Fick's law and the law of conservation of mass. Based on the boundary and initial conditions, the concentration distribution function is solved using the time integration method to obtain the chloride ion concentration distribution along the radial direction of the tunnel for all erosion paths in the tunnel, which varies with time.
[0076] In the specific implementation process, based on the principle of differentiation, the tunnel structure can be divided into multiple cross-sections along the axial direction, such as... Figure 5 As shown. Each cross-section is further discretized circumferentially into multiple radial erosion paths. Based on the fundamental principles of the finite element method, the formulas obtained from the above calculations are... Discretization is performed, and element shape functions are introduced to represent the ion concentration at any cross-sectional position using nodal ion concentrations: .
[0077] in, The corresponding shape function matrix; This is the column vector of ion concentrations at all node locations in the erosion finite element model. Therefore, and It can be written as: .
[0078] ; .
[0079] .
[0080] Meanwhile, the virtual ion concentration at any location within the lining component can be expressed as: .
[0081] Substituting into the simplified formula, we get: .
[0082] In the formula, and Let L be the shape function, and L be the length of the concrete member along the direction of ion erosion.
[0083] because The arbitrariness of the component, and the presence of ion flux on all boundaries except the outer boundary of the component (x=x1). The above formula can be further written as: .
[0084] In the formula: ; The ion flux entering the concrete member from the outer boundary (x=x1) of the member.
[0085] Obviously, in actual structures, the stress varies at different locations, and the ion diffusion coefficient at the corresponding locations also differs. However, in the finite element method, the stress within a single element is uniform, and the stress within the element... To facilitate practical operation, this embodiment of the application accurately describes the influence of different stress levels at different locations on the ion diffusion coefficient by dividing the structural finite element model elements into sufficiently small units. Therefore, a one-dimensional finite element equation for the chloride corrosion development of concrete components considering the stress dependence of the chloride ion diffusion coefficient can be obtained: .
[0086] in, ; .
[0087] In the specific solution of the matrix and In this case, the corresponding matrices for all elements can be solved first. and Then, following the "matching" rule of the finite element method, the matrix is obtained by lumping. and Specifically, for a general Lagrange linear interpolation shape function, the i-th erosion finite element... and It can be represented as: .
[0088] .
[0089] In the formula, and and represent the length of the i-th unit along the erosion direction and the chloride ion diffusion coefficient, respectively.
[0090] To solve the finite element equations, let the concentration transformation function be: .
[0091] In the formula: Let the initial chloride ion content vector of the concrete member be (assuming that the chloride ion concentration at each node is equal to the initial chloride ion content vector). ); Let be the ion concentration vector at each node of the concrete member at time t, induced by ion diffusion.
[0092] Substituting the above equation into the finite element equation, we obtain the concentration distribution function: .
[0093] At this point, the corresponding boundary conditions and initial conditions are as follows: .
[0094] .
[0095] .
[0096] In the formula: Initial chloride ion content of structural components; For structure The ion concentration specified at the boundary (external erosion concentration, assumed to remain constant during ion erosion).
[0097] Meanwhile, the ion concentration boundary on the outer side of the component The concentration of chloride ions in the external environment at (x=x1) remains constant. The invariant boundary conditions are: .
[0098] .
[0099] Furthermore, at the initial time t=0, the initial ion concentration of the component at any position except the outer boundary (x=x1) is... The initial conditions are: .
[0100] Dividing the governing equations into blocks based on the external boundary nodes and other nodes of the concrete member, we have: .
[0101] In the formula: and It is a column vector with all elements equal to 1, and the dots on the sign represent the derivative of the corresponding physical quantity with respect to time.
[0102] Expanding the above equation and substituting the boundary and initial conditions, we get: .
[0103] .
[0104] From the above equation, we can solve for: .
[0105] Furthermore, the one-dimensional ion erosion process can be solved in Matlab software using the following step-by-step integration method: (1) Discretize the time intervals into 0, ... , , ...; (2) For the initial time t=0, according to The ion growth rate at t=0 can be obtained by the following formula. : .
[0106] (3) Based on the initial concentration and the corresponding ion concentration erosion rate, calculate using the following formula. Ion concentration at non-eroded outer boundary nodes caused by ion erosion at any given time: .
[0107] (4) Based on the obtained Further calculations Ion acceleration caused by ion erosion at non-erosion outer boundary nodes at any given time As shown in the following formula: .
[0108] (5) Repeat this cycle, pressing " Following the order of "", we obtain the ion growth rate and ion concentration caused by ion erosion at all discrete time-time non-erosion boundary nodes, and further obtain the ion concentration at any point inside the structure at each time-time.
[0109] Finally, by integrating the chloride ion distributions along each erosion path inside the lining, the chloride ion distribution at a specific time at each location inside the tunnel lining can be obtained.
[0110] Based on the above embodiments, Figure 6 This is a schematic flowchart of another method for analyzing chloride ion distribution in tunnel lining based on stress level, provided in an embodiment of this application. A beam model corresponding to the tunnel can be pre-constructed, and the stress distribution on the lining structure can be determined based on the beam model. The specific method is as follows: The load distribution on the lining structure is determined based on the tunnel's burial depth and the surrounding rock grade. The method for determining the load distribution on the lining structure is described in the above embodiment and will not be repeated here.
[0111] A beam model was created using the finite element software Abaqus. The load-structure method was employed, and the calculated surrounding rock pressure was proportionally reduced before being applied to the lining structure. Specifically, the tunnel lining was simulated using two-dimensional beam elements, and the combined action of the secondary lining concrete and reinforcing steel was simulated using the equivalent stiffness method, as shown in the following formula: .
[0112] In the formula: E1 and E2 represent the elastic modulus of concrete and steel reinforcement, respectively; A1 and A2 represent the cross-sectional area of concrete and steel reinforcement, respectively.
[0113] Simultaneously, connector elements are used as foundation springs to simulate the interaction between the tunnel structure and the surrounding rock. The connector elements are controlled to only translate and not rotate. The spring's force-displacement relationship (i.e., spring stiffness) is set according to the stratum resistance coefficient to control the tensile and compressive properties of the connector elements, ensuring they only bear compressive stress and automatically fail under tension, exerting no effect on the structure. The spring stiffness is calculated as the product of the stratum resistance coefficient and half the sum of the lengths of the two lining elements connected to the connector element.
[0114] Based on the established beam model, the distribution of internal forces in the lining was calculated and analyzed.
[0115] The calculation program for this model was developed using programming software. The inputs include the external environment of the tunnel lining (i.e., the chloride ion concentration Cs in the surrounding rock), the chloride ion content C0 of the lining itself, the chloride ion erosion time t, and the chloride ion diffusion coefficient D. The chloride ion concentration Cs in the surrounding rock and the chloride ion content C0 of the lining itself are assumed to remain constant during the analysis. This allows the determination of chloride ion erosion at different cross-sections of the tunnel lining. After comprehensively ranking the chloride ion erosion conditions of all cross-sectional sections of the lining, the model calculation is complete.
[0116] In summary, the core assumption of this application's embodiments is that chloride ion erosion occurs in a one-dimensional diffusion along the tunnel's radial direction. The tunnel structure is divided into multiple cross-sections axially, and each cross-section is further discretized into multiple radial erosion paths circumferentially. These erosion paths are divided into a sufficient number of one-dimensional erosion finite elements of very short length. Finally, the results of all paths are integrated to obtain the overall chloride ion distribution across the lining cross-section. Based on diffusion theory, the migration of chloride ions from high-concentration areas (such as groundwater in the surrounding rock) to low-concentration areas (the inner side of the lining) is emphasized. The influence of lining stress level on the chloride ion diffusion coefficient is considered: the diffusion rate changes at different stress levels. Boundary conditions include a constant chloride ion concentration at the outer boundary (equivalent to the external chloride salt concentration), and zero ion flux at the inner and other boundaries, ensuring the simulation conforms to physical reality. The finite element method is used for discretization, with each cross-section represented by a node, and element shape functions are introduced to calculate the concentration distribution. This method transforms a continuous problem into a nodal concentration solution, simplifying the calculation. The solution process uses a step-by-step integration method, discretizing time at equal intervals, dividing the total time into small steps, and iteratively calculating the ion concentration step by step. Initially, the concentration inside the lining is set to an initial value. In each step, the rate of change of ion concentration is calculated first, then the concentration value is updated, and this process is repeated until the target time is reached. Boundary conditions are handled in blocks to ensure that the concentration on the outside is constant and the flux on the inside is zero, thus efficiently simulating the erosion process. Based on the tunnel depth and surrounding rock grade, the load distribution of the lining is calculated to determine the stress state. The equilibrium arch theory is used for deep-buried tunnels, while the rock mass holding effect is considered for shallow-buried tunnels. A beam model is built using finite element software to simulate the lining structure. The lining is represented by beam elements, and the interaction with the surrounding rock is simulated by spring elements, bearing only pressure. The internal force distribution is extracted from the model and converted into stress data to determine the diffusion coefficient. Through programming, parameters such as external concentration, initial concentration, and time are input, and the one-dimensional erosion equation is solved in combination with the stress data, outputting the chloride ion distribution.
[0117] Figure 7 This is a schematic diagram of a chloride ion distribution analysis device based on stress level, provided as an embodiment of this application. This device can be a module, program segment, or code on an electronic device. It should be understood that this device is similar to the one described above. Figure 4 The method implementation corresponds to this and can be executed. Figure 4The specific functions of the device involved in the various steps of the method embodiment can be found in the description above; to avoid repetition, detailed descriptions are omitted here. The device includes: a stress determination module 701, a diffusion coefficient determination module 702, a concentration distribution determination module 703, and a tunnel chloride ion distribution module 704, wherein: The stress determination module 701 is used to determine the stress distribution applied to the lining structure based on the tunnel's burial depth and surrounding rock grade; The diffusion coefficient determination module 702 is used to determine the diffusion coefficient of chloride ions based on the stress corresponding to the radial erosion path in the circumferential direction of a cross section in the tunnel. The concentration distribution determination module 703 is used to solve the chloride ion erosion control equation based on the diffusion coefficient, boundary conditions, initial chloride ion concentration and duration, to obtain the chloride ion concentration distribution along the radial direction of the tunnel and over time. The tunnel chloride ion distribution module 704 is used to obtain the chloride ion distribution of the tunnel lining based on the chloride ion concentration distribution of all paths on all cross sections.
[0118] Based on the above embodiments, the boundary conditions include: The chloride ion concentration at the outer boundary of the lining structure is constant and equal to the chloride ion concentration of the external chloride salt. The ion flux on the inner side and other boundaries of the lining structure is zero.
[0119] Based on the above embodiments, the chloride ion erosion control equation is constructed by the following method: For any micro-element on the erosion path, a first total chloride ion accumulation function per unit time is generated based on the cross-sectional area and volume of the micro-element. The second total chloride ion function is determined by multiplying the increase in chloride ion concentration in the micro-element by the volume of the micro-element. The chloride ion erosion control equation is generated based on the first chloride ion total amount function and the second chloride ion total amount function.
[0120] Based on the above embodiments, the chloride ion erosion control equation is as follows: ; in: Indicates chloride ion concentration; This represents the chloride ion diffusion coefficient that takes stress into account. Indicates time; This indicates the position of the micro-element.
[0121] Based on the above embodiments, the tunnel chloride ion distribution module 704 is specifically used for: The tunnel is discretized to obtain multiple cross-sections along the tunnel axis; The concentration transformation function for each cross section is determined based on the initial concentration of the lining and the additional concentration caused by external erosion. The concentration distribution function is generated by substituting the concentration transformation function into the finite element equation; wherein the finite element equation is derived based on Fick's law and the law of conservation of mass. Based on the boundary and initial conditions, the concentration distribution function is solved using the time integration method to obtain the chloride ion concentration distribution along the radial direction of the tunnel for all erosion paths in the tunnel, which varies with time.
[0122] Based on the above embodiments, the root concentration transformation function is: ;in, This is the vector representing the total chloride ion content corresponding to all cross-sections; The chloride ion concentration vector at time t for each cross section caused by chloride ion expansion; This is the vector representing the initial chloride ion content corresponding to all cross-sections.
[0123] Based on the above embodiments, the finite element equation is: ; in, ; L is the tunnel length; The corresponding shape function matrix; The position of the infinitesimal element; The chloride ion diffusion coefficient under stress was taken into account. This is the vector representing the total chloride ion content corresponding to all cross-sections; Let be the boundary flux vector at time t; The step of generating a concentration distribution function by substituting the concentration transformation function into the finite element equation includes: The concentration transformation function is then substituted into the finite element equation to generate the concentration distribution function as follows: .
[0124] Based on the above embodiments, the stress determination module 701 is specifically used for: The load distribution on the lining structure is determined based on the tunnel's burial depth and the surrounding rock grade. The tunnel lining structure is simplified into a two-dimensional beam element to construct an initial beam model; The equivalent stiffness method was used to simulate the combined action of the secondary lining concrete and steel reinforcement to obtain the simulated elastic modulus. Connecting elements are used as foundation springs to simulate the interaction between surrounding rock components in the lining structure domain; The spring stiffness of the foundation spring is set according to the soil resistance coefficient to obtain the final beam model; The surrounding rock load is applied to the beam model, and mechanical analysis is performed to obtain the stress of each cross section of the lining.
[0125] Figure 8 This is a schematic diagram of the physical structure of the electronic device provided in the embodiments of this application, such as... Figure 8 As shown, the electronic device includes: a processor 801, a memory 802, and a bus 803; wherein: The processor 801 and the memory 802 communicate with each other through the bus 803; The processor 801 is used to call program instructions in the memory 802 to execute the methods provided in the above-described method embodiments, including, for example: determining the stress distribution applied to the lining structure based on the tunnel's burial depth and surrounding rock grade; determining the chloride ion diffusion coefficient based on the stress corresponding to the radial erosion path in the circumferential direction of a cross section in the tunnel; solving the chloride ion erosion control equation based on the diffusion coefficient, boundary conditions, initial chloride ion concentration, and duration to obtain the chloride ion concentration distribution along the radial direction of the tunnel and changing with time; and obtaining the chloride ion distribution of the tunnel lining based on the chloride ion concentration distribution of all paths on all cross sections.
[0126] The processor 801 can be an integrated circuit chip with signal processing capabilities. The processor 801 can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor.
[0127] The memory 802 may include, but is not limited to, random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.
[0128] This embodiment discloses a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, and when the program instructions are executed by the computer, the computer can perform the methods provided in the above-described method embodiments, such as: determining the stress distribution applied to the lining structure based on the tunnel's burial depth and surrounding rock grade; determining the chloride ion diffusion coefficient based on the stress corresponding to the radial erosion path in the circumferential direction of a cross section in the tunnel; solving the chloride ion erosion control equation based on the diffusion coefficient, boundary conditions, initial chloride ion concentration, and duration to obtain the chloride ion concentration distribution along the radial direction of the tunnel and changing with time; and obtaining the chloride ion distribution of the tunnel lining based on the chloride ion concentration distribution of all paths on all cross sections.
[0129] This embodiment provides a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the methods provided in the above-described method embodiments. These instructions include, for example: determining the stress distribution applied to the lining structure based on the tunnel's burial depth and surrounding rock grade; determining the chloride ion diffusion coefficient based on the stress corresponding to the radial erosion path along the circumferential direction of a cross-section in the tunnel; solving the chloride ion erosion control equation based on the diffusion coefficient, boundary conditions, initial chloride ion concentration, and duration to obtain the chloride ion concentration distribution along the radial direction of the tunnel along the erosion path, varying with time; and obtaining the chloride ion distribution of the tunnel lining based on the chloride ion concentration distribution of all paths on all cross-sections.
[0130] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.
[0131] Furthermore, the units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[0132] Furthermore, the functional modules in the various embodiments of this application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.
[0133] In this document, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, without necessarily requiring or implying any such actual relationship or order between these entities or operations.
[0134] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.
Claims
1. A method for analyzing chloride ion distribution in tunnel lining based on stress level, characterized in that, include: The stress distribution applied to the lining structure is determined based on the tunnel's burial depth and the surrounding rock grade. For the radial erosion path in the circumferential direction of a cross section in the tunnel, the diffusion coefficient of chloride ions is determined based on the stress corresponding to the erosion path. Based on the diffusion coefficient, boundary conditions, initial chloride ion concentration, and duration, the chloride ion erosion control equation is solved to obtain the chloride ion concentration distribution along the radial direction of the tunnel and its variation over time. The chloride ion distribution of the tunnel lining is obtained based on the chloride ion concentration distribution of all paths on all cross sections.
2. The method according to claim 1, characterized in that, The boundary conditions include: The chloride ion concentration at the outer boundary of the lining structure is constant and equal to the chloride ion concentration of the external chloride salt. The ion flux on the inner side and other boundaries of the lining structure is zero.
3. The method according to claim 1, characterized in that, The chloride ion erosion control equation was constructed using the following method: For any micro-element on the erosion path, a first total chloride ion accumulation function per unit time is generated based on the cross-sectional area and volume of the micro-element. The second total chloride ion function is determined by multiplying the increase in chloride ion concentration in the micro-element by the volume of the micro-element. The chloride ion erosion control equation is generated based on the first chloride ion total amount function and the second chloride ion total amount function.
4. The method according to claim 3, characterized in that, The chloride ion erosion control equation is as follows: ; in: Indicates chloride ion concentration; This represents the chloride ion diffusion coefficient that takes stress into account. Indicates time; This indicates the position of the micro-element.
5. The method according to claim 1, characterized in that, The method of obtaining the chloride ion distribution of the tunnel lining based on the chloride ion concentration distribution of all paths across all cross sections includes: The tunnel is discretized to obtain multiple cross-sections along the tunnel axis; The concentration transformation function for each cross section is determined based on the initial concentration of the lining and the additional concentration caused by external erosion. The concentration distribution function is generated by substituting the concentration transformation function into the finite element equation; wherein the finite element equation is derived based on Fick's law and the law of conservation of mass. Based on the boundary and initial conditions, the concentration distribution function is solved using the time integration method to obtain the chloride ion concentration distribution along the radial direction of the tunnel for all erosion paths in the tunnel, which varies with time.
6. The method according to claim 5, characterized in that, The concentration transformation function is: ;in, This is the vector representing the total chloride ion content corresponding to all cross-sections; The chloride ion concentration vector at time t is generated for each cross section for all chloride ion expansions; This is the vector representing the initial chloride ion content corresponding to all cross-sections.
7. The method according to claim 5, characterized in that, The finite element equation is: ; in, ; L represents the tunnel length. For the corresponding shape function matrix; The position of the infinitesimal element; The chloride ion diffusion coefficient under stress was taken into account. This is the vector representing the total chloride ion content corresponding to all cross-sections; Let be the boundary flux vector at time t; The step of generating a concentration distribution function by substituting the concentration transformation function into the finite element equation includes: Substituting the concentration transformation function into the finite element equation, the resulting concentration distribution function is: .
8. The method according to any one of claims 1-7, characterized in that, The determination of stress distribution applied to the lining structure based on tunnel burial depth and surrounding rock grade includes: The load distribution on the lining structure is determined based on the tunnel's burial depth and the surrounding rock grade. The tunnel lining structure is simplified into a two-dimensional beam element to construct an initial beam model; The equivalent stiffness method was used to simulate the combined action of the secondary lining concrete and steel reinforcement to obtain the simulated elastic modulus. Connecting elements are used as foundation springs to simulate the interaction between surrounding rock components in the lining structure domain; The spring stiffness of the foundation spring is set according to the soil resistance coefficient to obtain the final beam model; The surrounding rock load is applied to the beam model, and mechanical analysis is performed to obtain the stress of each cross section of the lining.
9. An electronic device, characterized in that, include: Processor, memory, and bus, among which: The processor and the memory communicate with each other via the bus; The memory stores program instructions that can be executed by the processor, and the processor can execute the method as described in any one of claims 1-8 by calling the program instructions.
10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that, when executed by a computer, cause the computer to perform the method as described in any one of claims 1-8.