A method and system for evaluating the ultimate bearing capacity of pipe segments based on numerical limit analysis

Abstract

The present invention belongs to the technical field of underground engineering structure bearing capacity research, and provides a method and system for evaluating the ultimate bearing capacity of a segment based on numerical limit analysis, comprising: S1: establishing a segment finite element analysis numerical model and setting initial load conditions and initial material parameters; S2: calculating the average stress value of each grid cell in the segment finite element analysis numerical model based on the initial load conditions and initial material parameters; S3: iteratively updating the initial material parameters; S4: iteratively updating the initial load conditions; S5: repeating steps S1-S4 until the initial load conditions do not allow the maximum average stress value among the average stress values ​​of all grid cells to be less than the corresponding yield stress value, thereby obtaining an evaluation result of the segment's ultimate bearing capacity. The present invention can achieve efficient evaluation of the segment's ultimate bearing capacity, is low-cost, short-time, and non-hazardous, and can improve the accuracy of numerical methods for evaluating the segment's ultimate bearing capacity.

Description

Technical Field

[0001] The present invention belongs to the technical field of underground engineering structure bearing capacity research, and particularly relates to a method and system for evaluating the ultimate bearing capacity of a pipe segment based on numerical limit analysis. Background Art

[0002] The ultimate bearing capacity of reinforced concrete structures, a topic of great interest in underground space engineering, has garnered widespread attention in recent years. Advances in underground space technology have placed higher demands on the ultimate bearing capacity of reinforced concrete structures relevant to practical projects. As the lining structure of shield tunnels, the ultimate bearing capacity of segments is crucial to the stability of shield tunnels and the safety of subway operations. Therefore, it is crucial to study the assessment methods for the ultimate bearing capacity of segments and to clarify the ultimate bearing capacity of segment structures.

[0003] Existing research methods for evaluating the ultimate bearing capacity of pipe segments primarily rely on experimental methods and numerical simulation. Full-scale load tests are often used in experimental methods, which are costly, time-consuming, and carry significant safety risks, as well as the tendency for unavoidable experimental errors to occur during testing. Numerical simulation methods offer poor accuracy in evaluating the ultimate bearing capacity of pipe segments, often relying on numerical calculations such as stress cloud maps and plastic zones to determine the ultimate bearing capacity, which is highly subjective. Currently, there is no method that can achieve high-precision evaluation of the ultimate bearing capacity of pipe segments under low-cost, low-time, and low-risk conditions. Summary of the Invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a method and system for evaluating the ultimate bearing capacity of pipe segments based on numerical limit analysis, which reduces evaluation costs, shortens evaluation time, avoids test risks, and improves the accuracy of numerical methods for evaluating the ultimate bearing capacity of pipe segments.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for evaluating the ultimate bearing capacity of a segment based on numerical limit analysis, the method comprising:

[0007] S1: Establish a finite element analysis numerical model for the segment and set the initial load conditions and initial material parameters;

[0008] S2: Calculating an average stress value of each grid cell in the segment finite element analysis numerical model based on the initial load condition and the initial material parameters;

[0009] S3: based on the compression cap closing the compression zone of the Menétrey-Willam type yield surface, when the relationship between the average stress value and the yield stress value on the closed Menétrey-Willam type yield surface corresponding to the average stress value satisfies a first preset stress condition, iteratively updating the initial material parameters;

[0010] S4: When the relationship between the maximum average stress value among the average stress values ​​of all grid cells and the corresponding yield stress value satisfies a second preset stress condition, determining whether to perform iterative update of the initial load condition;

[0011] S5: Repeat steps S1-S4 until the initial load condition does not allow the maximum average stress value among the average stress values ​​of all grid cells to be less than the corresponding yield stress value, thereby obtaining an evaluation result of the ultimate bearing capacity of the segment.

[0012] Preferably, in step S1,

[0013] The initial load condition is expressed as , is the load multiplier, s is the number of times the load value is iterated during the calculation process, is the reference load value;

[0014] The initial material parameters are expressed as ( , ), is the elastic modulus of the material, k is the number of iterations of the elastic modulus during the calculation process, and v is the Poisson's ratio of the material.

[0015] Preferably, in step S2, the method for calculating the average stress value of each grid cell in the segment finite element analysis numerical model includes:

[0016] Calculating a linear elastic solution for each grid cell in the segment finite element analysis numerical model based on the initial load condition and the initial material parameters;

[0017] Based on the stress value of the linear elastic solution of each grid cell, the average stress value of the principal stress at all Gaussian nodes on each grid cell is obtained; wherein the average stress value is expressed in the principal stress space using the Haigh-Westgaard coordinate system, which includes the hydrostatic stress invariant , deviatoric stress invariant and the polar Lode Point , point O is the origin of the Haigh-Westgaard coordinate system.

[0018] Preferably, in step S3, the Menétrey-Willam type yield surface is a yield surface applied to concrete materials. The intersection of the ray in the direction and the Menétrey-Willam type yield surface is the mean stress value The corresponding yield point is expressed as .

[0019] Preferably, in step S3, the expression for the shape of the closed Menétrey-Willam type yield surface is as follows:

[0020] ,

[0021] ,

[0022] ,

[0023] ,

[0024] Where, is the explicit equation of the compression cap when it is expressed in the principal stress space using the Haigh-Westgaard coordinate system. The position is determined by the concrete material parameters obtained from two experiments. and Decide, is the explicit equation for the Menétrey-Willam type yield surface when expressed in the principal stress space using the Haigh-Westgaard coordinate system; is the uniaxial compressive strength of concrete; is the uniaxial tensile strength of concrete; e is the eccentricity parameter of the yield surface, and m represents the friction parameter of the material. Represents the elliptic function corresponding to the shape of the yield surface.

[0025] The present invention also provides a segment ultimate bearing capacity evaluation system based on numerical limit analysis, for implementing the method, the system comprising:

[0026] Finite element model building module, used to establish the segment finite element analysis numerical model and set the initial load conditions and initial material parameters;

[0027] A stress value calculation module, configured to calculate an average stress value of each grid cell in a segment finite element analysis numerical model based on the initial load condition and the initial material parameters;

[0028] a material parameter updating module, configured to iteratively update the initial material parameters based on a compression cap closing a compression zone of a Menétrey-Willam type yield surface, when a relationship between the average stress value and a yield stress value on the closed Menétrey-Willam type yield surface corresponding to the average stress value satisfies a first preset stress condition;

[0029] a load condition updating module, configured to determine whether to perform iterative update of the initial load condition when a relationship between a maximum average stress value among the average stress values ​​of all grid cells and a corresponding yield stress value satisfies a second preset stress condition;

[0030] The evaluation result acquisition module is used to repeat the operations from the finite element model construction module to the load condition update module until the initial load condition does not allow the maximum average stress value among the average stress values ​​of all grid cells to be less than the corresponding yield stress value, thereby obtaining the evaluation result of the ultimate bearing capacity of the pipe segment.

[0031] Preferably, in the finite element model building module,

[0032] The initial load condition is expressed as , is the load multiplier, s is the number of times the load value is iterated during the calculation process, is the reference load value;

[0033] The initial material parameters are expressed as ( , ), is the elastic modulus of the material, k is the number of iterations of the elastic modulus during the calculation process, and v is the Poisson's ratio of the material.

[0034] Preferably, the stress value calculation module includes:

[0035] a linear elastic solution calculation unit, configured to calculate a linear elastic solution for each grid cell in the segment finite element analysis numerical model based on the initial load condition and the initial material parameters;

[0036] The average stress value calculation unit is used to obtain the average stress value of the principal stress at all Gaussian nodes on each grid unit based on the stress value of the linear elastic solution of each grid unit; wherein the average stress value is expressed in the principal stress space using the Haigh-Westgaard coordinate system, and the Haigh-Westgaard coordinate system includes the hydrostatic stress invariant , deviatoric stress invariant and the polar Lode Point , point O is the origin of the Haigh-Westgaard coordinate system.

[0037] Compared with existing technologies, the present invention has the following advantages: It uses a numerical limit analysis method to evaluate the ultimate bearing capacity of segments. By utilizing computer programming languages ​​to redevelop finite element analysis software, this method enables efficient evaluation of the ultimate bearing capacity of segments. This method is low-cost, time-efficient, and non-hazardous. It improves the accuracy of numerical methods for evaluating the ultimate bearing capacity of segments, identifies the failure mechanism of segments, and predicts the location of damage, providing a reference for studying the ultimate bearing capacity of segments. Furthermore, the size and material properties of segments can be arbitrarily varied to analyze the ultimate bearing capacity of different segments. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0039] Figure 1 This is a flow chart of a method for evaluating the ultimate bearing capacity of a segment based on numerical limit analysis according to an embodiment of the present invention;

[0040] Figure 2 Schematic diagram of the finite element analysis numerical model of the pipe segment according to the embodiment of the present invention

[0041] Figure 3 This is a schematic diagram of the iterative calculation principle of numerical limit analysis according to an embodiment of the present invention;

[0042] Figure 4 Schematic diagram of comparison between the model results and the test results of an embodiment of the present invention;

[0043] Figure 5 Schematic diagram of the results obtained by numerical calculation of an embodiment of the present invention, wherein (a) is the stress cloud diagram of the finite element analysis numerical model under the ultimate load state, (b) is the displacement cloud diagram of the finite element analysis numerical model under the ultimate load state, and (c) is the velocity field of the finite element analysis numerical model under the ultimate load state. DETAILED DESCRIPTION

[0044] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0045] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] Example 1

[0047] like Figure 1 A segment ultimate bearing capacity evaluation method based on numerical limit analysis is shown. This method, based on numerical limit analysis theory and using Python for secondary development of ABAQUS, enables efficient evaluation of the segment ultimate bearing capacity. The accuracy of the numerical limit analysis method is verified by comparison with full-scale segment ultimate bearing capacity test results.

[0048] The method comprises:

[0049] S1: Establish a finite element analysis numerical model for the segment and set the initial load conditions and initial material parameters. Specifically, establish a finite element analysis numerical model for the segment. In this embodiment, Figure 2 As shown, the segment has an inner diameter of 7500 mm, an outer diameter of 8300 mm, a width of 1800 mm, and a concrete cover thickness of approximately 60 mm. The numerical model includes concrete and embedded reinforcement. The concrete material is C50 high-strength concrete, and the reinforcement is HRB400E. Only longitudinal reinforcement and stirrups are considered. The longitudinal tension reinforcement consists of 18 steel bars with a diameter of 20 mm, and the longitudinal compression reinforcement consists of 8 steel bars with a diameter of 18 mm and 10 steel bars with a diameter of 20 mm. The stirrup diameter is 12 mm. Bond slip between the concrete and the steel bars is not considered. The model boundary conditions are based on the constraints applied to the actual segment being evaluated, which is consistent with the constraints applied to the segment in the test. The bottom support of the segment numerical model is fixed in the vertical direction, but can move and rotate in other directions.

[0050] A further embodiment is that in step S1, the initial load applied to the finite element analysis numerical model of the segment is applied in accordance with the load application method applied to the segment in the test, that is, two linear loads are applied to the outer surface of the segment with a distance of 1200 mm between them; the initial load condition is expressed as , is the load multiplier, which will be iteratively updated during the numerical calculation process. The initial value is set to 1 and is a dimensionless number. s is the number of times the load value is iterated during the calculation process. The initial value is set to 1. is the reference load value. The initial value is user-defined and is set to 100 kN in this embodiment. It remains unchanged during the iterative update process.

[0051] The initial material parameters are expressed as ( , ), It is the elastic modulus of the material, which will be updated iteratively during the numerical calculation process. The initial value is set to the elastic modulus of the material used for the segment. In this example, the initial value is set to 3.45 10 4 MPa; k is the number of iterations of the elastic modulus during the calculation process, and its initial value is set to 1; v is the Poisson's ratio of the material, which is set to 0.2 in this embodiment and remains unchanged during the iteration process.

[0052] S2: Calculating the average stress value of each mesh unit in the segment finite element analysis numerical model based on the initial load conditions and the initial material parameters; A further embodiment is that in step S2, the method for calculating the average stress value of each mesh unit in the segment finite element analysis numerical model includes:

[0053] Based on the initial load conditions and initial material parameters, the linear elastic solution of each mesh element in the segment finite element analysis numerical model is calculated;

[0054] Based on the stress value of the linear elastic solution of each mesh element, the average stress value of the principal stress at all Gaussian nodes on each mesh element is obtained. ; The mean stress value is expressed in the principal stress space using the Haigh-Westgaard coordinate system, which includes the hydrostatic stress invariant , deviatoric stress invariant and the polar Lode Point , point O is the origin of the Haigh-Westgaard coordinate system.

[0055] S3: Based on the compression cap closing the compression zone of the Menétrey-Willam type yield surface, when the relationship between the average stress value and the yield stress value on the closed Menétrey-Willam type yield surface corresponding to the average stress value satisfies the first preset stress condition, iteratively updating the initial material parameters; a further embodiment is that in step S3, the Menétrey-Willam type yield surface is a yield surface applied to concrete material, The intersection of the ray in the direction and the Menétrey-Willam type yield surface is the mean stress value The corresponding yield point is expressed as .like Figure 3 shown.

[0056] A further implementation method is that in step S3, the Menétrey-Willam type yield surface is improved, and a "compression cap" is used to close the compressive area of ​​the yield surface so that it can express the mechanical behavior of the concrete material near the hydrostatic stress axis. The expression of the closed Menétrey-Willam type yield surface shape is as follows:

[0057] ,

[0058] ,

[0059] ,

[0060] ,

[0061] Where, is the explicit equation of the compression cap when it is expressed in the principal stress space using the Haigh-Westgaard coordinate system. The position is determined by the concrete material parameters obtained from two experiments. and Decide, , ; is the explicit equation for the Menétrey-Willam type yield surface when expressed in the principal stress space using the Haigh-Westgaard coordinate system; is the uniaxial compressive strength of concrete, which is 32.4 MPa in this embodiment; is the uniaxial tensile strength of concrete, which is 2.64 MPa in this embodiment; e is the eccentricity parameter of the yield surface, which determines the ellipticity of the yield surface and satisfies the equation . m represents the friction parameter of the material, Represents the elliptic function corresponding to the shape of the yield surface.

[0062] Regarding the first preset stress condition, that is, when the stress obtained by the linear elastic finite element analysis of some grid cells meets , the elastic modulus of the grid unit will be reduced, and the calculation formula is:

[0063] ,

[0064] Where, is the updated elastic modulus of the mesh element, is the initial elastic modulus of the mesh element.

[0065] S4: When the relationship between the maximum average stress value among the average stress values ​​of all grid cells and the corresponding yield stress value satisfies the second preset stress condition, it is determined whether to perform iterative update of the initial load condition. Regarding the second preset stress condition, the maximum average stress value among the average stress values ​​of all grid cells is defined as , the point corresponding to this stress value in the principal stress space is the point farthest from the yield surface, that is, The maximum point, and the stress value of the corresponding yield point is expressed as When the maximum stress value in the linear elastic solution of all mesh elements satisfies When maintaining the load unchanged, using the updated elastic modulus of all mesh elements , and enter a new round of linear elastic finite element analysis until the maximum stress value is met , the elastic modulus stops updating, and the load multiplier is updated and increased to obtain , used for the next iterative calculation. Figure 3 As shown in the figure (i=1,2,...n) is the average stress point of the mesh element obtained from the linear elastic analysis; For The corresponding yield point on the modified Menétrey-Willam type yield surface; The average stress point of the mesh element farthest from the yield surface in the principal stress space; For The corresponding yield point on the modified Menétrey-Willam type yield surface. The average stress point of the mesh element obtained by linear elastic analysis when the value of i is n; For The corresponding yield point on the modified Menétrey-Willam type yield surface.

[0066] S5: Repeat steps S1-S4 until the initial load condition does not allow the maximum average stress value of the average stress values ​​of all grid cells to be less than the corresponding yield stress value, and obtain the evaluation result of the ultimate bearing capacity of the segment. The evaluation result includes the ultimate bearing capacity data of the segment and the prediction of the location where the segment failure occurs, that is, the weak point that is prone to failure. Specifically, after the updated elastic modulus and updated loads Linear elastic calculation is performed under the conditions, that is, steps S1-S4 are repeated until the maximum average stress value of the grid unit obtained by the new round of calculation meets , which means that the maximum average stress value under this load value is not allowed to be less than the corresponding yield stress value. The cycle ends and the calculation is completed.

[0067] The present invention is further illustrated below by comparing the evaluation method of the present invention with a full-scale segment loading test for the same segment loading condition. In the full-scale segment loading test, the segment design parameters are exactly the same as those in the numerical limit analysis method. Figure 4 This is a comparison chart of the numerical calculation results of the constructed segment numerical model and the full-scale test results. Figure 4It can be seen that the numerical method of the present invention is very close to the results of the full-scale test. Compared with the full-scale test results, the results of the numerical method are more conservative. This is because the boundary conditions of the numerical simulation are idealized boundary conditions. Unlike the full-scale test, the material in the numerical model is an ideal isotropic uniform material, which deviates from the actual situation. Moreover, the concrete and steel cage in the actual segment are cast together during the production process, and the relative positions of the steel bars and concrete in the numerical model are not necessarily exactly the same, which causes the error between the results of the numerical method and the results of the full-scale test. In addition, the numerical calculation method provides a schematic diagram of the failure mechanism of the segment, Figure 5 (a) Figure 5 (b) Figure 5 (c) The stress contours, displacement contours, and velocity fields of the finite element analysis model under the ultimate load condition are shown. The numerical method provides the locations of weak areas in the segment under the ultimate load condition. In summary, the numerical results obtained by this method are highly consistent with the experimental results, and the model can be considered sufficiently accurate.

[0068] Example 2

[0069] The present invention also provides a segment ultimate bearing capacity evaluation system based on numerical limit analysis, which is used to implement the method. The system includes:

[0070] Finite element model building module, used to establish the segment finite element analysis numerical model and set the initial load conditions and initial material parameters;

[0071] The stress value calculation module is used to calculate the average stress value of each grid element in the segment finite element analysis numerical model based on the initial load conditions and initial material parameters;

[0072] a material parameter updating module, configured to iteratively update initial material parameters based on closing a compression zone of a Menétrey-Willam type yield surface with a compression cap, when a relationship between a mean stress value and a yield stress value on the closed Menétrey-Willam type yield surface corresponding to the mean stress value satisfies a first preset stress condition;

[0073] a load condition updating module, configured to determine whether to perform iterative update of the initial load condition when the relationship between the maximum average stress value among the average stress values ​​of all grid cells and the corresponding yield stress value satisfies a second preset stress condition;

[0074] The evaluation result acquisition module is used to repeat the operations from the finite element model construction module to the load condition update module until the initial load condition does not allow the maximum average stress value among the average stress values ​​of all grid cells to be less than the corresponding yield stress value, thereby obtaining the evaluation result of the ultimate bearing capacity of the pipe segment.

[0075] A further embodiment is that, in the finite element model building module,

[0076] The initial load condition is expressed as , is the load multiplier, s is the number of times the load value is iterated during the calculation process, is the reference load value;

[0077] The initial material parameters are expressed as ( , ), is the elastic modulus of the material, k is the number of iterations of the elastic modulus during the calculation process, and v is the Poisson's ratio of the material.

[0078] In a further embodiment, the stress value calculation module includes:

[0079] The linear elastic solution calculation unit is used to calculate the linear elastic solution of each grid element in the segment finite element analysis numerical model based on the initial load conditions and initial material parameters;

[0080] The average stress value calculation unit is used to obtain the average stress value of the principal stress at all Gaussian nodes on each grid element based on the stress value of the linear elastic solution of each grid element; the average stress value is expressed in the Haigh-Westgaard coordinate system in the principal stress space, and the Haigh-Westgaard coordinate system includes the hydrostatic stress invariant , deviatoric stress invariant and the polar Lode Point , point O is the origin of the Haigh-Westgaard coordinate system.

[0081] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for evaluating the ultimate bearing capacity of a segment based on numerical limit analysis, characterized in that: The method comprises: S1: Establish a finite element analysis numerical model for the segment and set the initial load conditions and initial material parameters; S2: Calculating an average stress value of each grid cell in the segment finite element analysis numerical model based on the initial load condition and the initial material parameters; S3: based on the compression cap closing the compression zone of the Menétrey-Willam type yield surface, when the relationship between the average stress value and the yield stress value on the closed Menétrey-Willam type yield surface corresponding to the average stress value satisfies a first preset stress condition, iteratively updating the initial material parameters; S4: When the relationship between the maximum average stress value among the average stress values ​​of all grid cells and the corresponding yield stress value satisfies a second preset stress condition, determining whether to perform iterative update of the initial load condition; S5: Repeat steps S1-S4 until the initial load condition does not allow the maximum average stress value among the average stress values ​​of all grid cells to be less than the corresponding yield stress value, thereby obtaining an evaluation result of the ultimate bearing capacity of the segment; In step S3, the expression for the closed Menétrey-Willam type yield surface shape is as follows: ， ， ， ， Where, is the explicit equation of the compression cap when it is expressed in the principal stress space using the Haigh-Westgaard coordinate system. The position is determined by the concrete material parameters obtained from two experiments. and Decide, is the explicit equation for the Menétrey-Willam type yield surface when expressed in the principal stress space using the Haigh-Westgaard coordinate system; is the uniaxial compressive strength of concrete; is the uniaxial tensile strength of concrete; e is the eccentricity parameter of the yield surface, and m represents the friction parameter of the material. Represents the elliptic function corresponding to the shape of the yield surface.

2. The method according to claim 1, characterized in that In step S1, The initial load condition is expressed as , is the load multiplier, s is the number of times the load value is iterated during the calculation process, is the reference load value; The initial material parameters are expressed as ( , ), is the elastic modulus of the material, k is the number of iterations of the elastic modulus during the calculation process, and v is the Poisson's ratio of the material.

3. The method according to claim 1, characterized in that In step S2, the method for calculating the average stress value of each grid cell in the segment finite element analysis numerical model includes: Calculating a linear elastic solution for each grid cell in the segment finite element analysis numerical model based on the initial load condition and the initial material parameters; Based on the stress value of the linear elastic solution of each grid cell, the average stress value of the principal stress at all Gaussian nodes on each grid cell is obtained; wherein the average stress value is expressed in the principal stress space using the Haigh-Westgaard coordinate system, which includes the hydrostatic stress invariant , deviatoric stress invariant and the polar Lode Point , point O is the origin of the Haigh-Westgaard coordinate system.

4. The method according to claim 3, characterized in that In step S3, the Menétrey-Willam type yield surface is applied to the concrete material. The intersection of the ray in the direction and the Menétrey-Willam type yield surface is the mean stress value The corresponding yield point is expressed as .

5. A system for evaluating the ultimate bearing capacity of a segment based on numerical limit analysis, for implementing the method according to any one of claims 1 to 4, characterized in that: The system comprises: Finite element model building module, used to establish the segment finite element analysis numerical model and set the initial load conditions and initial material parameters; A stress value calculation module, configured to calculate an average stress value of each grid cell in a segment finite element analysis numerical model based on the initial load condition and the initial material parameters; a material parameter updating module, configured to iteratively update the initial material parameters based on a compression cap closing a compression zone of a Menétrey-Willam type yield surface, when a relationship between the average stress value and a yield stress value on the closed Menétrey-Willam type yield surface corresponding to the average stress value satisfies a first preset stress condition; a load condition updating module, configured to determine whether to perform iterative update of the initial load condition when a relationship between a maximum average stress value among the average stress values ​​of all grid cells and a corresponding yield stress value satisfies a second preset stress condition; an evaluation result acquisition module, configured to repeat operations from the finite element model construction module to the load condition update module until the initial load condition does not allow the maximum average stress value among the average stress values ​​of all mesh elements to be less than the corresponding yield stress value, thereby obtaining an evaluation result of the ultimate bearing capacity of the segment; In the material parameter update module, the expression for the closed Menétrey-Willam yield surface shape is as follows: ， ， ， ， Where, is the explicit equation of the compression cap when it is expressed in the principal stress space using the Haigh-Westgaard coordinate system. The position is determined by the concrete material parameters obtained from two experiments. and Decide, is the explicit equation for the Menétrey-Willam type yield surface when expressed in the principal stress space using the Haigh-Westgaard coordinate system; is the uniaxial compressive strength of concrete; is the uniaxial tensile strength of concrete; e is the eccentricity parameter of the yield surface, and m represents the friction parameter of the material. Represents the elliptic function corresponding to the shape of the yield surface.

6. The system according to claim 5, characterized in that In the finite element model building module, The initial load condition is expressed as , is the load multiplier, s is the number of times the load value is iterated during the calculation process, is the reference load value; The initial material parameters are expressed as ( , ), is the elastic modulus of the material, k is the number of iterations of the elastic modulus during the calculation process, and v is the Poisson's ratio of the material.

7. The system according to claim 5, characterized in that The stress value calculation module includes: a linear elastic solution calculation unit, configured to calculate a linear elastic solution for each grid cell in the segment finite element analysis numerical model based on the initial load condition and the initial material parameters; The average stress value calculation unit is used to obtain the average stress value of the principal stress at all Gaussian nodes on each grid unit based on the stress value of the linear elastic solution of each grid unit; wherein the average stress value is expressed in the principal stress space using the Haigh-Westgaard coordinate system, and the Haigh-Westgaard coordinate system includes the hydrostatic stress invariant , deviatoric stress invariant and the polar Lode Point , point O is the origin of the Haigh-Westgaard coordinate system.

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