Numerical simulation method and device for improving toughness of shield segment through AFRP

Abstract

The invention relates to a numerical simulation method and device for improving the toughness of a shield segment through AFRP. The numerical simulation method for improving the toughness of the shield segment through the AFRP comprises the steps that grid division is conducted on the three-dimensional shield segment according to reinforcement information, and an initialized concrete numerical model is obtained; thirdly, constructing an AFRP entity unit and a contact interface unit, and simultaneously embedding the combination of the AFRP entity unit and the contact interface unit and the calibrated slippage and stripping parameters into the initialized concrete numerical model to obtain an AFRP-concrete interface behavior numerical model with the bonding-slippage-stripping characteristic; performing incremental iteration on the numerical model according to a preset load to obtain simulation time history data; and finally, performing index calculation and evaluation on the simulation time history data to obtain performance evaluation data of the AFRP reinforced shield segment. According to the numerical simulation method for improving the toughness of the shield segment through the AFRP, the stability and modeling consistency of a numerical model under the complex bending working condition are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation of shield tunnel segment structures reinforced with aramid fiber reinforced polymer (AFRP) possessing bond-slip-peel properties, and particularly to a numerical simulation method, apparatus, electronic device, and computer storage medium for improving the toughness of shield tunnel segments using AFRP. Background Technology

[0002] In civil engineering structural design and safety assessment, numerical simulation is an indispensable analytical tool. Through numerical simulation, stress distribution, deformation response, crack propagation, and damage evolution of concrete structures can be predicted during the design phase, thus providing important basis for the toughness assessment of concrete structures. Common numerical simulation methods include the Finite Element Method (FEM) and the Finite Difference Method (FDM). Both belong to the solution techniques within the framework of continuum mechanics and are used to reproduce the actual stress behavior of concrete structures under external loads in a virtual environment or numerical simulation platform, including key responses such as stress distribution, deformation modes, crack propagation paths, and damage evolution trends.

[0003] In traditional or conventional concrete member analysis, the engineering community typically adopts the "fully bonded assumption" to simplify the calculation process and ensure the numerical stability of the FEM or FDM model. This assumption treats the steel reinforcement and concrete as a unified whole without relative slippage, allowing the stress transfer of the structure to rely solely on the material constitutive model. Therefore, under this assumption, by gradually applying external loads to the FEM or FDM model and iteratively calculating the response of the concrete structure in each loading step, the mechanical properties of the concrete member, such as stress-strain distribution, stiffness variation, and interfacial ultimate performance, can be obtained.

[0004] However, the "perfect bond assumption" in traditional or conventional concrete component analysis cannot be directly applied to shield tunnel segments, i.e., the segment structure of shield tunnels. This is because shield tunnel segments typically bear significant bending moments under operational conditions, and their overall mechanical behavior can be approximated as the stress mode of a curved beam under bending loading. In actual working conditions, the bond stress distribution between the internal steel reinforcement and the surrounding concrete of the shield tunnel segment often exhibits characteristics such as non-uniformity, stress concentration, and early degradation. Furthermore, as the external load gradually increases, the steel-concrete interface inevitably experiences bond-slip behavior, which leads to changes in the force transmission mechanism of the shield tunnel segment structure. This affects the evaluation indicators such as crack initiation location, stiffness degradation rate, and ultimate bearing capacity in the FEM or FDM model during the simulation process.

[0005] Based on this, in order to characterize the slip characteristics of the steel-concrete interface, existing technologies usually introduce interface elements, spring elements or contact models into the FEM or FDM model, and combine experimental data or standard parameters to describe or model the bond-slip behavior of the steel-concrete interface, so as to meet the bond-slip behavior generated between the internal steel bars and the surrounding concrete of the shield tunnel segment during the simulation process.

[0006] With the widespread application of aramid fiber reinforced polymer (AFRP) reinforcement technology in civil engineering, shield tunnel segments typically have AFRP surface-bonded to the tension zone. External loads are transferred from concrete to AFRP through the contact interface, leveraging the high strength and toughness of AFRP to effectively improve the ductility, load-bearing capacity, crack resistance, and overall toughness of the shield tunnel segments. However, when shield tunnel segments are subjected to significant bending moments, the interface with AFRP experiences bond degradation due to accumulated slip. Once the slip reaches a critical level, the AFRP enters the interface debonding stage, characterized by significant displacement of the AFRP relative to the concrete, or complete debonding where the AFRP detaches locally or even entirely from the concrete surface. Therefore, entering the AFRP interface debonding stage again alters the stress transfer mechanism and significantly affects the evolution path of damage variables in the Concrete Damage Plasticity (CDP) model.

[0007] Meanwhile, the interface peeling is a sudden mechanical process. The boundary between the transition from "slip" to "peeling" is extremely difficult to identify accurately in experiments or conventional models. This is because interface damage often first occurs locally in the weak area of ​​the interface and develops within a certain range. The overall load-displacement curve of the component does not show a prominent inflection point or stiffness loss during this stage. Therefore, experimental measurements cannot directly capture the true starting point of peeling. If the boundary identification is inaccurate, for example, if the critical slip point or the starting point of the residual segment is offset, the interface constitutive will be incorrectly segmented, which will further lead to systematic deviations in the force path, stiffness degradation curve and damage evolution process in numerical simulation.

[0008] Since the core mechanism by which AFRP enhances the toughness of tunnel boring machine (TBM) segments highly depends on interfacial stress transmission and damage evolution, the accuracy of stage boundary identification directly affects the evaluation of the toughness enhancement effect. Therefore, although existing technologies can describe the bond-slip behavior of TBM segments, they cannot accurately capture the stage boundaries of AFRP-reinforced TBM segments, thus failing to realistically reproduce the interfacial degradation process of AFRP-reinforced TBM segments, resulting in insufficient overall accuracy of numerical simulations. Summary of the Invention

[0009] Based on this, the purpose of the present invention is to provide a numerical simulation method for improving the toughness of shield tunnel segments using AFRP.

[0010] A numerical simulation method for improving the toughness of shield tunnel segments using AFRP includes the following steps: S1. Based on the reinforcement information, the three-dimensional AFRP-reinforced shield tunnel segment is meshed to obtain the initial concrete numerical model. S2. Construct AFRP solid elements and contact interface elements, and combine them with the calibrated slip-peeling parameters, and embed them into the initialized concrete numerical model to obtain a numerical model of AFRP-concrete interface behavior with bond-slip-peeling characteristics. The calibrated slip-off parameters are calibrated through the following steps: First, single shear tests and tensile tests were conducted on the AFRP-concrete interface, and mechanical data sets of the AFRP-concrete interface in the single shear tests and tensile tests were collected to form load-slip curves and stress-strain curves. Next, based on the initialization of the concrete numerical model, AFRP solid elements and contact interface elements are introduced, and a set of intermediate slip-stripping parameters that have not yet converged are assigned to them. Incremental iterative calculations are then performed on the working conditions corresponding to the single shear test and the positive tension test through the numerical simulation platform to obtain the simulated load-slip curves. Subsequently, a four-segment adaptive objective function is used to calculate the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset, so as to obtain the deviation value corresponding to the current intermediate slip stripping parameter. The four-stage adaptive objective function includes an objective function for the initial bonding stage, an objective function for the slip development stage, an objective function for the residual bonding stage, an objective function for the interface peeling stage, and a stage boundary penalty term. Finally, it is determined whether the deviation value corresponding to the current intermediate slip stripping parameter meets the iteration threshold: if not, it is considered that the current intermediate slip stripping parameter has not converged, and the current intermediate slip stripping parameter is updated and iterated using a multi-stage boundary-guided adaptive simulated annealing optimization algorithm to obtain the updated intermediate slip stripping parameter, and the incremental iteration calculation continues; if yes, it is considered that the current intermediate slip stripping parameter has been calibrated and is used as the calibrated slip stripping parameter. The multi-stage boundary-guided adaptive simulated annealing optimization algorithm is used to optimize the current intermediate slip stripping parameters while satisfying the physical value range constraints of the intermediate slip stripping parameters. Perform global optimization to cause the four-segment adaptive objective function value to converge to satisfy the iteration threshold; S3. Based on the preset load, the numerical model of the AFRP-concrete interface behavior with bond-slip-debond characteristics is incrementally iterated to obtain simulation time history data. S4. Calculate and evaluate the performance of the simulated time history data to obtain the performance evaluation data of the AFRP-reinforced shield tunnel segments.

[0011] The numerical simulation method for improving the toughness of shield tunnel segments using AFRP described in this invention, compared with the prior art, significantly improves the stability of the model and the controllability of the interface behavior by solidifying the AFRP coating area and explicitly embedding contact interface elements between the AFRP solid elements and the concrete elements. This allows the interface bonding, slippage and peeling behaviors to directly participate in the force transmission and damage evolution under three-dimensional stress conditions.

[0012] In addition, this invention uses load-slip curves and stress-strain curves obtained from single shear and tensile tests as calibration data, and employs a four-segment adaptive objective function and stage boundary penalty term to perform segmented fitting of the entire process of initial bonding, slip development, residual bonding and interface delamination. This effectively avoids stage boundary misalignment, improves the calibration accuracy of slip delamination parameters, and enables a more realistic numerical reproduction of the interface degradation process under the complex bending conditions of shield tunnel segments.

[0013] Furthermore, the intermediate slip stripping parameter set Specifically, it is expressed as:

[0014] In the formula, It is cohesive force; It is the internal friction angle; The ratio of shear stress to tensile stress; Residual cohesion; This is the residual internal friction angle; Interfacial tensile strength; Residual tensile strength; The specific representation of the four-segment adaptive objective function is as follows:

[0015] In the formula, Indicates the first The deviation value corresponding to the intermediate slip stripping parameter in the next iteration; The objective function for the initial bonding stage is expressed as follows:

[0016] In the formula, Indicates the first The iteration, and the intermediate slip stripping parameter is At that time, the numerical simulation yielded the first The load values ​​corresponding to each sampling point; Represents the first in the mechanics dataset Load values ​​at each sampling point; This represents the maximum load value in the load-slip curve of the mechanics dataset. This represents the total number of sampling points for the load-slip curve in the mechanics dataset; The total number of sampling points used to represent the initial bonding stage is calculated as follows:

[0017] in, Represents the first in the mechanics dataset The interface slip amount corresponding to each sampling point This represents the critical value of the slip development stage identified in the load-slip curve of the mechanics dataset; Indicates an indicator function; The objective function representing the slip development stage is expressed as follows:

[0018] In the formula, The total number of sampling points used to represent the slip development stage is calculated as follows:

[0019] in, This represents the critical value of the residual bond stage identified in the load-slip curve of the mechanical dataset; The objective function for the residual bonding stage is expressed as follows:

[0020] In the formula, The total number of sampling points used to represent the residual bonding stage is calculated as follows:

[0021] in, This represents the critical value of the interface peeling stage identified in the load-slip curve of the mechanical dataset; The objective function for the interface stripping phase is represented as follows:

[0022] In the formula, The total number of sampling points used to represent the interface stripping stage is specifically calculated as follows: ; This represents the stage boundary penalty term, used to constrain the current stage boundary penalty term. Intermediate slip stripping parameters of the next iteration The deviation between the stage critical values ​​identified in the obtained simulated load-slip curves and the corresponding stage critical values ​​of the tests in the mechanical dataset includes the penalty terms for the slip development stage, the penalty terms for the residual bonding stage, and the penalty terms for the interface peeling stage.

[0023] Accordingly, this invention employs sub-objective functions for the initial bonding stage, slip development stage, residual bonding stage, and interface peeling stage, enabling the mechanical response of each stage of the interface to be evaluated independently, thereby avoiding the problem of insufficient parameter sensitivity caused by the mixing of errors from different stages in traditional single objective functions.

[0024] In addition, by introducing a stage boundary penalty term, this invention imposes additional constraints on the correspondence between the simulated curve and the experimental curve at the critical slip point, the starting point of the residual segment, and the starting point of the peeling. This ensures that the calibration process not only pursues overall fitting accuracy but also ensures that the stage boundaries have physical consistency. This effectively overcomes the problems of fuzzy and easily misaligned interface slip and peeling stage boundaries, thereby significantly enhancing the identifiability of slip and peeling parameters and improving the fitting accuracy and model reliability of the entire process of interface damage evolution.

[0025] Furthermore, the specific representation of the stage boundary penalty term is as follows:

[0026] In the formula, Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the slip development stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient corresponding to the critical value of the slip development stage identified by the simulated load-slip curve is specifically expressed as follows:

[0027] Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the residual bond stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient for the critical value of the residual bond stage identified by the simulated load-slip curve is specifically expressed as follows:

[0028] Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the interface peeling stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient for the critical value of the interface peeling stage, identified by the simulated load-slip curve, is specifically expressed as follows:

[0029] In the formula, This is an offset constant.

[0030] Accordingly, this invention introduces a dynamic dimensionless penalty coefficient into the stage boundary penalty term, enabling the penalty intensity to automatically adjust according to the magnitude of the deviation between the simulation and experimental critical values: when there is only a small offset at the simulation stage boundary, the penalty coefficient is close to 1, which can avoid excessive amplification of experimental noise or natural dispersion; while when there is a significant misalignment at the stage boundary, the penalty coefficient will increase significantly with the increase of the deviation, thereby strengthening the constraint on key inflection points, thus avoiding false penalties while accurately capturing the critical values ​​of slip development, residual adhesion and interface peeling stages, significantly improving the physical consistency of mechanical stage division, the stability of parameter convergence and the predictability of the final model.

[0031] Furthermore, the multi-stage boundary-guided adaptive simulated annealing optimization algorithm adjusts the current intermediate slip-stripping parameters. The specific representation of global optimization is as follows:

[0032]

[0033]

[0034] In the formula, For the first The first of the intermediate slip-out parameters in the second iteration Uncorrected candidate parameter components after random perturbation of each parameter component; For the first In the nth iteration The adaptive perturbation step size coefficients of the intermediate slip stripping parameter components are specifically expressed as follows:

[0035] In the formula, The basic perturbation step size coefficient; among its intermediate slip stripping parameters Used to represent the main influencing factors in the initial bonding stage and the slip development stage, while The main influencing factors used to represent the residual bonding stage and the interface debonding stage; , , and They represent the first The relative contributions of the initial bonding stage, slip development stage, residual bonding stage, and interface peeling stage to the overall error in each iteration are specifically calculated as follows:

[0036]

[0037]

[0038]

[0039] In the formula, This is a constant offset representing the relative contribution of each stage to the overall error. For the first The random perturbation term of each parameter component is used to calculate the random perturbation term at a given step size. , for the Apply a random search to each parameter component; Indicates the first The candidate solution in the nth iteration One corrected candidate parameter component; Indicates the first The physical upper limit of each parameter component, Indicates the first The physical lower limit of each parameter component; Represents uniformly random numbers; For the first The acceptance probability of a candidate solution in the next iteration can be specifically expressed as:

[0040] In the formula, Indicates the first Annealing temperature parameters for the annealing criterion in the next iteration; Indicates the first The intermediate slip stripping parameter of the next iteration Each parameter component.

[0041] Accordingly, this invention utilizes a multi-stage boundary-guided adaptive simulated annealing optimization algorithm to dynamically adjust the perturbation step size of different parameter components in each iteration by leveraging the error contribution of each stage. This allows different proportions of parameter components, such as initial bonding, slip development, residual bonding, and interface peeling, to obtain differentiated search intensities.

[0042] Compared to traditional fixed-step or single-stage driven optimization methods, this invention can automatically concentrate search resources in regions with large stage errors and boundary deviations, improving the convergence speed and stability of parameter optimization in high-dimensional nonlinear and multi-peak objective functions. This results in a parameter set that simultaneously possesses high overall fitting accuracy, accurate stage boundary identification, and reasonable physical meaning, thereby significantly enhancing the robustness of interface constitutive calibration and the reliability of numerical simulation results for AFRP-reinforced shield tunnel segments.

[0043] A numerical simulation device for improving the toughness of shield tunnel segments using AFRP includes concrete mesh generation units, AFRP entity and contact interface embedding units, external load simulation units, and AFRP-reinforced shield tunnel segment performance evaluation units. The concrete mesh generation unit of the shield tunnel segment is used to perform mesh generation on the three-dimensional AFRP-reinforced shield tunnel segment according to the reinforcement information to obtain the initial concrete numerical model. The AFRP entity and contact interface embedding unit is used to construct AFRP entity unit and contact interface unit, and the combination of the two and the calibrated slip-peeling parameters are embedded into the initialized concrete numerical model to obtain a numerical model of AFRP-concrete interface behavior with bond-slip-peeling characteristics. The calibrated slip-off parameters are calibrated through the following steps: First, single shear tests and tensile tests were conducted on the AFRP-concrete interface, and mechanical data sets of the AFRP-concrete interface in the single shear tests and tensile tests were collected to form load-slip curves and stress-strain curves. Next, based on the initialization of the concrete numerical model, AFRP solid elements and contact interface elements are introduced, and a set of intermediate slip-stripping parameters that have not yet converged are assigned to them. Incremental iterative calculations are then performed on the working conditions corresponding to the single shear test and the positive tension test through the numerical simulation platform to obtain the simulated load-slip curves. Subsequently, a four-segment adaptive objective function is used to calculate the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset, so as to obtain the deviation value corresponding to the current intermediate slip stripping parameter. The four-stage adaptive objective function includes an objective function for the initial bonding stage, an objective function for the slip development stage, an objective function for the residual bonding stage, an objective function for the interface peeling stage, and a stage boundary penalty term. Finally, it is determined whether the deviation value corresponding to the current intermediate slip stripping parameter meets the iteration threshold: if not, it is considered that the current intermediate slip stripping parameter has not converged, and the current intermediate slip stripping parameter is updated and iterated using a multi-stage boundary-guided adaptive simulated annealing optimization algorithm to obtain the updated intermediate slip stripping parameter, and the incremental iteration calculation continues; if yes, it is considered that the current intermediate slip stripping parameter has been calibrated and is used as the calibrated slip stripping parameter. The multi-stage boundary-guided adaptive simulated annealing optimization algorithm is used to optimize the current intermediate slip stripping parameters while satisfying the physical value range constraints of the intermediate slip stripping parameters. Perform global optimization to cause the four-segment adaptive objective function value to converge to satisfy the iteration threshold; The external load simulation unit is used to incrementally iterate the numerical model of the AFRP-concrete interface behavior with bond-slip-debond characteristics according to the preset load, and obtain simulation time history data. The AFRP-reinforced shield tunnel segment performance evaluation unit is used to calculate and evaluate the indicators of the simulation time history data to obtain the performance evaluation data of the AFRP-reinforced shield tunnel segment. Attached Figure Description

[0044] Figure 1 This is a simplified structural diagram of the numerical simulation device for improving the toughness of shield tunnel segments using AFRP, as described in this invention. Figure 2 This is a simplified flowchart illustrating the numerical simulation method for improving the toughness of tunnel lining segments using AFRP as described in this invention. Figure 3 This is a schematic diagram comparing the load-displacement curves obtained from the numerical model of the AFRP-concrete interface behavior with bond-slip-peel characteristics constructed in this invention under damage loading conditions with experimental results. Figure 4 The load-displacement curves are obtained by the concrete numerical model with slip characteristics constructed in this invention under the condition of pre-reinforced and intact tunnel segments. Detailed Implementation

[0045] To address the problem that existing technologies cannot accurately capture the stage boundaries of AFRP-reinforced shield tunnel segments, resulting in insufficient overall accuracy of numerical simulation parameters, this invention meshes the three-dimensional shield tunnel segments based on reinforcement information and assigns basic physical parameters of concrete to the meshed 3D shield tunnel segments, forming a computable initial concrete numerical model. Next, AFRP solid elements and contact interface elements are constructed, and their combination, along with calibrated slip-peeling parameters, are embedded into the initial concrete numerical model to obtain a numerical model of AFRP-concrete interface behavior exhibiting bond-slip-peeling characteristics. Based on this, the numerical model of AFRP-concrete interface behavior exhibiting bond-slip-peeling characteristics is incrementally iterated according to preset loads to obtain simulation time history data. Finally, the simulation time history data is used to calculate and evaluate indicators, yielding performance evaluation data for the AFRP-reinforced shield tunnel segments.

[0046] Accordingly, by explicitly introducing contact interface elements to simulate the bond-slip between AFRP and concrete, the overestimation of stiffness and bearing capacity caused by the assumption of complete bond is avoided, making the evaluation results closer to reality. At the same time, solid elements combined with parametric interfaces are used instead of the traditional combination of special springs and contact algorithms, reducing the risk of non-convergence caused by contact tolerance and parameter coupling, and effectively improving the controllability of modeling and calculation.

[0047] Based on the above design, this invention proposes a numerical simulation method for improving the toughness of shield tunnel segments using AFRP, and based on this method, proposes a numerical simulation device for improving the toughness of shield tunnel segments using AFRP.

[0048] Please also refer to Figure 1 and Figure 2 , Figure 1 This is a simplified structural diagram of the numerical simulation device for improving the toughness of shield tunnel segments using AFRP, as described in this invention. Figure 2 This is a simplified flowchart illustrating the numerical simulation method for improving the toughness of tunnel segments using AFRP, as described in this invention.

[0049] The numerical simulation device for improving the toughness of shield tunnel segments using AFRP includes a concrete mesh generation unit 1 for the shield tunnel segments, an embedding unit 2 for the AFRP entity and the contact interface, an external load simulation unit 3, and an AFRP-reinforced shield tunnel segment performance evaluation unit 4.

[0050] The concrete mesh division unit 1 of the shield tunnel segment is used to perform step S1: to divide the three-dimensional AFRP-reinforced shield tunnel segment into meshes according to the reinforcement information, and obtain the initial concrete numerical model.

[0051] Specifically, the reinforcement information is a dataset used to describe the layout and mechanical properties of the internal steel reinforcement of the AFRP-reinforced shield tunnel segment in the actual design. It typically includes the material type, strength grade, elastic modulus, density, yield stress, geometric characteristics, layout path, protective layer thickness, and layout deviation of the steel reinforcement, thus serving as descriptive information on the distribution and configuration of the internal steel reinforcement structure of the AFRP-reinforced shield tunnel segment. It is usually obtained from design drawings, reinforcement details, or construction BIM models.

[0052] The three-dimensional AFRP-reinforced shield tunnel segment is a concrete three-dimensional solid geometric model established based on the AFRP-covered area in the actual AFRP-reinforced shield tunnel segment design. It is usually modeled in three dimensions using CAD or finite element preprocessing platforms to characterize the volume domain and boundary domain of the AFRP-reinforced shield tunnel segment.

[0053] The mesh generation is used to discretize the continuous domain of the three-dimensional AFRP-reinforced shield tunnel segment into a computationally capable numerical model, resulting in an initialized concrete numerical model. This model is capable of supporting the embedding of reinforcing steel elements, as well as subsequent AFRP elements and contact interface elements. Specifically, it includes the following sub-steps: First, the three-dimensional AFRP-reinforced shield tunnel segments are meshed according to the preset feature dimensions to form an original numerical model with multiple concrete mesh nodes.

[0054] It should be noted that during the meshing process, the corresponding outer surface can be locally meshed according to the subsequent AFRP bonding location and the area where interface delamination may occur. This ensures a good correspondence between the interface geometry and the mesh nodes when embedding AFRP solid elements and contact interface elements. Furthermore, the original numerical model only geometrically includes the area to be bonded with AFRP; that is, this area is explicitly identified as a potential interface region in the mesh. However, in this step, the material properties of AFRP have not yet been assigned to this area, nor have AFRP elements or contact interface elements been generated.

[0055] Next, the steel reinforcement layout path in the reinforcement information is imported into the original numerical model according to a unified coordinate system; at the same time, steel reinforcement elements are generated on the corresponding layout path according to the geometric and mechanical parameters in the reinforcement information, thereby forming a concrete numerical model with steel reinforcement.

[0056] Finally, based on the basic physical parameters of concrete, the corresponding concrete constitutive model is assigned to the concrete elements in the concrete numerical model with reinforcement, and boundary or monitoring sets are constructed to extract time history responses such as displacement, stress or strain, thus forming an initial concrete numerical model.

[0057] The basic physical parameters of the concrete are assumed to be elastic modulus, Poisson's ratio, compressive strength and fracture energy. The concrete constitutive model of the present invention is assumed to be the concrete plastic damage model. Meanwhile, the boundary or monitoring set includes fixed support surface, loading surface and key response monitoring points by default.

[0058] It should be noted that the concrete constitutive model described in this invention is not limited to the concrete plastic damage model, and other equivalent elastoplastic or damage models can be selected according to actual engineering needs. At the same time, the size of the mesh division, the dense area or the distribution of mesh nodes can be adaptively adjusted according to the overlapping requirements of subsequent AFRP elements and contact interface elements. In addition, the reinforcement information can also be extended according to different engineering designs (such as double-layer reinforcement, spiral reinforcement). Those skilled in the art can flexibly determine it according to the specific engineering object and analysis objectives. This invention does not limit the specific geometric modeling or parameter settings.

[0059] The AFRP entity and the contact interface embedding unit 2 is used to perform step S2: construct AFRP entity units and contact interface units, and combine the two and the calibrated slip-peel parameters, and embed them into the initialized concrete numerical model to obtain a numerical model of AFRP-concrete interface behavior with bond-slip-peel characteristics.

[0060] Generally speaking, when performing numerical simulations of AFRP reinforcement on concrete structures, existing technologies typically employ a combination of "shell elements + special spring elements" or "shell elements + contact algorithm" to characterize the interfacial bonding behavior between AFRP and concrete.

[0061] Among them, shell elements are used to characterize the out-of-plane thinness of AFRP sheets, while special spring elements or contact algorithms are used to simulate the relative displacement, frictional slip and local cracking generated at the AFRP-concrete interface under stress, thereby realizing a basic description of the interface mechanical behavior.

[0062] However, existing technologies have significant limitations in AFRP-reinforced shield tunnel segments, which are subjected to significant bending and substantial interface slip accumulation. First, there is a lack of unified standards for parameter selection in special spring elements and contact algorithms. Parameters such as interface bonding, friction, and pull-out failure often rely on empirical selection, resulting in insufficient repeatability of parameters. Second, when the structure simultaneously exhibits significant curvature, complex reinforcement, strong bending, and a tendency for local interface delamination, the coupling between shell elements and special spring elements is weak, easily leading to non-convergence or iterative oscillation problems under cyclic loading or nonlinear large deformation conditions. At the same time, shell elements are difficult to deeply couple with the concrete plastic damage model (CDP), which will cause the microscopic processes such as interface damage evolution, stiffness degradation, and crack propagation to be inconsistent with the concrete damage evolution process, resulting in underestimation or overestimation of the overall structural stiffness and bearing capacity.

[0063] Therefore, existing technologies are insufficient to accurately simulate the entire bonding-slippage-peeling process after AFRP reinforcement in complex structural systems such as tunnel segments.

[0064] Based on this, the present invention constructs solid elements as the modeling method for AFRP to explicitly characterize the anisotropic stress and bond-slip-delamination effect. At the same time, the slip process does not depend on the geometric integrity of the solid elements, but is directly realized through parametric control. That is, by using calibrated slip-delamination parameters, the entire process of bond, slip and delamination of the AFRP-concrete interface is numerically realized, thereby effectively improving the simulation accuracy of the entire process of interface degradation of AFRP-reinforced shield tunnel segments.

[0065] Specifically, the AFRP bonding position in the initial concrete numerical model is converted into a computable AFRP solid element to bear the forces in all directions and characterize the local tensile, shear and in-plane slip response of AFRP during loading, thus obtaining a concrete numerical model with AFRP solid elements.

[0066] The AFRP solid element is used to solidify the AFRP bonding position in the initialized concrete numerical model in three dimensions, so that it can participate in stress transmission, interface relative displacement calculation and damage evolution description in subsequent simulation calculations.

[0067] Next, in the concrete numerical model with AFRP solid elements, contact interface elements are embedded between the outer surface mesh nodes of the AFRP bonding position and the corresponding outer surface mesh nodes of the concrete elements to obtain a concrete numerical model with interface relative displacement and interface separation properties.

[0068] The contact interface unit is used to establish an independently solvable interface layer between the AFRP solid element and the concrete element, thereby characterizing the normal cracking, tangential slip, residual slip and local separation behavior of the two during the loading process, so that the AFRP can undergo a full process response of bond-slip-peeling relative to the concrete.

[0069] Finally, based on the calibrated slip-peeling parameters, parameter values ​​are assigned to the AFRP solid elements and contact interface elements in the concrete numerical model that possesses interface relative displacement and interface separation properties, thereby obtaining a numerical model of the AFRP-concrete interface behavior with bond-slip-peeling characteristics.

[0070] The parameter assignment is used to write parameters such as cohesion, residual cohesion, internal friction angle, residual internal friction angle, tensile strength, residual tensile strength, and interface method / tangential stiffness into the corresponding contact interface element. At the same time, the basic physical parameters of AFRP (including AFRP length, width, thickness, density, and contact area) are written into the AFRP solid element, so that it can participate in the nonlinear solution together with the concrete constitutive and steel reinforcement elements during the calculation process.

[0071] It should be noted that in the process of constructing the AFRP solid unit and the contact interface unit, the present invention comprehensively considers several known major failure modes in AFRP-reinforced shield tunnel segments, including tensile failure of the AFRP material itself, interface peeling failure between concrete and AFRP and the bonding adhesive layer, and cracking failure of the concrete body.

[0072] Among these, interfacial debonding failure between concrete and the adhesive layer and cracking failure of the concrete matrix are the most common failure modes in engineering and have the most significant impact on overall load-bearing performance. Therefore, this invention embeds AFRP solid elements and contact interface elements into the initial concrete numerical model, enabling the model to explicitly simulate tensile failure of AFRP, slip-debonding evolution of the interface, and damage propagation of concrete under three-dimensional stress conditions, thereby covering the failure modes of interfacial debonding failure between concrete and the adhesive layer and cracking failure of the concrete matrix.

[0073] Furthermore, since the solid element is a three-dimensional continuous element, it can simultaneously bear normal, tangential and bending forces. This invention reproduces the bond, slip and peel relationship between AFRP and concrete through calibrated slip-peel parameters without the need to introduce special spring elements or complex contact algorithms, thereby reflecting the interface degradation process and directly affecting the overall structural stiffness, internal force redistribution and final failure mode.

[0074] To obtain calibrated slip-peel parameters with high fitting accuracy, so that they can accurately reflect the entire process of bonding, slip, and peeling at the AFRP-concrete interface, this invention performs calibration through the following steps: First, single shear tests and tensile tests were conducted on the AFRP-concrete interface, and mechanical data sets of the AFRP-concrete interface in the single shear tests and tensile tests were collected to form load-slip curves and stress-strain curves.

[0075] The mechanical dataset includes interface slip, loads generated by shear or pull-out, local strain and local stress of the interface or adhesive layer; the load-slip curve is formed by combining the loads generated by shear or pull-out with the interface slip; the stress-strain curve is formed by combining the local strain and local stress of the interface or adhesive layer.

[0076] Furthermore, the load-slip curve contains complete mechanical data for the initial bonding stage, slip development stage, residual bonding stage, and interface debonding stage, and can serve as the basis for the a priori range of values ​​for slip debonding parameters (e.g., including but not limited to cohesion, internal friction angle, tensile strength, interface / tangential stiffness, and their residual parameters); the stress-strain curve is used to assist in identifying the local failure initiation point and damage evolution rate at the interface, and can serve as the initial input basis for the optimization iteration of slip debonding parameters.

[0077] It should be noted that the single shear test and the positive tension test can adopt the central pull-out test arrangement. The test methods, specimen preparation and loading system can refer to the relevant provisions in the "Code for Design of Strengthening Concrete Structures" (GB 50367—2013). Multiple sets of repeated tests are used to ensure the stability, effectiveness and repeatability of the mechanical data set, so as to provide a reliable test basis for the calibration of slip-peeling parameters. This invention is not specifically limited.

[0078] Next, based on the initialization of the concrete numerical model, AFRP solid elements and contact interface elements are introduced, and a set of intermediate slip-stripping parameters that have not yet converged are assigned to them. Incremental iterative calculations are then performed on the working conditions corresponding to the single shear test and the positive tension test through the numerical simulation platform to obtain the simulated load-slip curves.

[0079] Among them, the intermediate slip stripping parameter set This is used to describe the mechanical properties of the AFRP-concrete interface throughout the entire process of bond, slip, residue, and debonding, and is specifically expressed as follows:

[0080] In the formula, Cohesion is the peak intensity used to characterize interfacial bonding properties. The internal friction angle is used to characterize the tangential friction slip behavior; The shear-tensile stress ratio is the ratio of shear stress to tensile stress. Residual cohesion is a residual value used to characterize the bonding properties after interfacial slippage. The residual internal friction angle is used to characterize the frictional slip behavior in the residual stage. Interfacial tensile strength is used to characterize normal bonding ability; Residual tensile strength is a parameter used to characterize the tensile properties of the interface in the residual stage after the interface has been peeled off.

[0081] The initial value of the intermediate slip-peeling parameter can be set based on the characteristic range of the load-slip curve and stress-strain curve in the aforementioned mechanical dataset, and gradually updated in subsequent calculation iterations to approximate the actual slip-peeling parameter.

[0082] The incremental iterative calculation means that the numerical simulation platform constructs a numerical model of the AFRP-concrete interface corresponding to the single shear test and the positive tension test based on the current intermediate slip-stripping parameters, and applies displacement loads to it step by step, and solves the response of the AFRP-concrete interface at each loading step, thereby obtaining the simulated load-slip curve.

[0083] Subsequently, the objective function is used to calculate the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset, so as to obtain the deviation value corresponding to the current intermediate slip-slip parameter.

[0084] Since the slip behavior between AFRP and concrete has an initial bond stage, a slip development stage, a residual bond stage, and an interface peeling stage, the objective function described in this invention uses a four-segment adaptive objective function to calculate the deviation value corresponding to the current intermediate slip peeling parameter. The four-segment adaptive objective function , indicating the first The deviation values ​​corresponding to the intermediate slip-peeling parameters in each iteration include the objective function for the initial bonding stage, the objective function for the slip development stage, the objective function for the residual bonding stage, the objective function for the interface peeling stage, and the stage boundary penalty term, which are specifically represented as follows:

[0085] In the formula, The objective function for the initial bonding stage measures the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset during the initial bonding stage. Its specific representation is as follows:

[0086] In the formula, Indicates the first The iteration, and the intermediate slip stripping parameter is At that time, the numerical simulation yielded the first The load values ​​corresponding to each sampling point; Represents the first in the mechanics dataset The load value at each sampling point, i.e., the load generated by shear or pull-out; This represents the maximum load value in the load-slip curve of the mechanics dataset, i.e., the peak value of the load-slip curve in the mechanics dataset, and is used to perform dimensionless normalization of the error. This represents the total number of sampling points for the load-slip curve in the mechanics dataset; The total number of sampling points used to represent the initial bonding stage is calculated as follows:

[0087] in, Represents the first in the mechanics dataset The interface slip amount corresponding to each sampling point The critical value representing the slip development stage identified in the load-slip curve of the mechanical dataset is used to characterize the threshold at which the initial bonding stage ends and the slip development stage begins. This indicates an indicator function that outputs 1 if the condition is met, and 0 otherwise.

[0088] The objective function representing the slip development stage measures the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset during the slip development stage. Its specific representation is as follows:

[0089] In the formula, The total number of sampling points used to represent the slip development stage is calculated as follows:

[0090] in, The critical value representing the residual bond stage identified in the load-slip curve of the mechanical dataset is used to represent the slip threshold at which the load-slip curve in the mechanical dataset transitions from peak softening to the residual plateau. The objective function for the residual bond stage is used to measure the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset during the residual bond stage. Its specific representation is as follows:

[0091] In the formula, The total number of sampling points used to represent the residual bonding stage is calculated as follows:

[0092] in, This represents the critical value of the interface peeling stage identified in the load-slip curve of the mechanical dataset, and is used to represent the slip threshold at the end of the residual bonding stage and the beginning of the interface peeling stage in the load-slip curve of the mechanical dataset. The objective function for the interface stripping stage is denoted as follows: It measures the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset during the interface stripping stage.

[0093] In the formula, The total number of sampling points used to represent the interface stripping stage is specifically calculated as follows: ; This represents the stage boundary penalty term, used to constrain the current stage boundary penalty term. Intermediate slip stripping parameters of the next iteration The deviation between the stage critical values ​​identified in the obtained simulated load-slip curve and the corresponding stage critical values ​​in the mechanical data set ensures that the stage boundaries of the initial bonding stage, slip development stage, residual bonding stage, and interface peeling stage are as consistent as possible in the simulated curve and the experimental curve. The stage boundary penalty terms include penalty terms for the slip development stage, penalty terms for the residual adhesion stage, and penalty terms for the interface peeling stage, which are specifically represented as follows:

[0094] In the formula, Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the slip development stage identified by the simulated load-slip curve is used to characterize the slip position at the end of the initial bonding stage and the beginning of the slip development stage in the numerical simulation process. Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the residual bond stage identified by the simulated load-slip curve is used to characterize the slip position at the end of the simulated slip development stage and the beginning of the residual bond stage in the numerical simulation process. Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the interface peeling stage identified by the simulated load-slip curve is used to characterize the slip position at the end of the simulated residual bonding stage and the beginning of the interface peeling stage. For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient corresponding to the critical value of the slip development stage identified by the simulated load-slip curve is used for adaptive weight adjustment based on the boundary error of the current stage, and its specific representation is as follows:

[0095] In the formula, This is an offset constant used to prevent the denominator from being zero; the present invention does not limit its specific value.

[0096] For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient for the critical value of the residual bond stage, identified by the simulated load-slip curve, is used for adaptive weight adjustment based on the current stage boundary error. Its specific representation is as follows:

[0097] For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient for the critical value of the interface peeling stage, identified by the simulated load-slip curve, is used for adaptive weight adjustment based on the current stage boundary error. Its specific representation is as follows:

[0098] In this study, a stage boundary penalty term is introduced into the objective function to avoid the "misfitting" problem caused by relying solely on overall curve fitting. This means that while the simulated load-slip curve is close to the experimental curve in overall shape, significant misfitting occurs at the critical stage boundaries, such as the critical values ​​of the slip development stage, the residual bonding stage, and the interface peeling stage. This effectively improves the physical rationality of the intermediate slip peeling parameter calibration results and the fitting accuracy of all stages.

[0099] It should be noted that, due to the stage critical value measured in the experiment, i.e. , and The present invention inherently possesses a certain degree of discreteness and experimental error, while the dynamic dimensionless penalty coefficient used in this invention... , and It does not impose excessive penalties on small-range stage boundary deviations because when the simulated stage boundary deviations are within a small range relative to the critical values ​​of each stage in the corresponding experiment, due to... The penalty term contributes less to the overall objective function. In this case, the optimization process is mainly dominated by the objective function of each stage, thus ensuring that the model will not undergo unnecessary parameter adjustments due to small fluctuations in the experiment.

[0100] Only when the stage boundary deviates significantly from the test behavior will the dynamic dimensionless penalty coefficient increase significantly due to the increase in deviation, so that the stage boundary penalty term occupies a higher weight in the objective function, thereby strengthening the suppression of "severe misfit". This allows the calibration process to effectively ensure the physical consistency between the simulated load-slip curve and the test curve at the key stage boundary position without amplifying the test noise, and thus accurately capture the stage boundary of the AFRP reinforced shield tunnel segment.

[0101] In addition, to further improve the physical reliability of the stage boundaries, during the collection of mechanical data, multiple sets of single shear and tensile test mechanical data can be collected by increasing the test budget, and the statistical average or confidence interval of the critical values ​​of each stage can be taken, thereby reducing the uncertainty caused by the fluctuation of a single test. This allows the dynamic penalty mechanism to operate under more stable and statistically representative benchmark conditions, thereby further improving the calibration accuracy and physical rationality of the slip stripping parameters. Thus, the physical consistency is effectively guaranteed through the dynamic penalty mechanism of stage boundary deviation. Furthermore, this invention does not limit the number of mechanical data collection sets or the statistical method.

[0102] Finally, it is determined whether the deviation value corresponding to the current intermediate slip stripping parameter meets the iteration threshold: if not, it is considered that the current intermediate slip stripping parameter has not converged, and the current intermediate slip stripping parameter is updated and iterated using a multi-stage boundary-guided adaptive simulated annealing optimization algorithm to obtain the updated intermediate slip stripping parameter, and the incremental iteration calculation continues; if yes, it is considered that the current intermediate slip stripping parameter has been calibrated and is used as the calibrated slip stripping parameter.

[0103] The iteration threshold can be specifically defined by the following judgment expression:

[0104] In the formula, The convergence threshold representing the relative change in the value of the four-segment adaptive objective function is used to measure the relative error of the deviation value corresponding to the intermediate slip stripping parameter in two consecutive iterations. This indicates the total dimension of the intermediate slip stripping parameters, which defaults to 7. Indicates the first The intermediate slip stripping parameter of the next iteration Each parameter component; Indicates the first The physical upper limit of each parameter component, Indicates the first The physical lower limit of each parameter component is a known constant, used to ensure that the intermediate slip stripping parameter is always within a reasonable physical value range. This is the convergence threshold for the relative change of the slip stripping parameter, used to measure the average change of the intermediate slip stripping parameter in the normalized parameter space over two consecutive iterations. Therefore, when both conditions in the iteration threshold are met simultaneously, or when the number of iterations reaches the preset maximum number of iterations, the current intermediate slip-off parameters are considered to have converged, and the updated intermediate slip-off parameters are then applied. As a calibration slip stripping parameter, its preset maximum number of iterations can be set according to the required accuracy or hardware computing power.

[0105] The multi-stage boundary-guided adaptive simulated annealing optimization algorithm is used to optimize the current intermediate slip stripping parameters while satisfying the physical value range constraints of the intermediate slip stripping parameters. Perform global optimization to cause the four-segment adaptive objective function value to converge to satisfy the iterative threshold. For the first... The intermediate slip stripping parameter of the next iteration Component of parameters This refers to the final updated value of the parameter components after being filtered by the simulated annealing acceptance criteria. The specific update can be found in the following expression:

[0106]

[0107]

[0108] In the formula, For the first The first of the intermediate slip stripping parameters in the second iteration The uncorrected candidate parameter components after random perturbation of the parameter components are used to perform random search in the neighborhood of the current solution to expand the exploration domain for parameter component updates. For the first In the nth iteration An adaptive perturbation step size coefficient for the intermediate sliding stripping parameter components is used to adaptively adjust the parameter components according to the importance of errors at different stages, so that the parameter components in stages with large errors receive larger perturbation step sizes, thereby enhancing the optimization algorithm's ability to correct for the corresponding stages. Its specific representation is as follows:

[0109] In the formula, The basic perturbation step size coefficient is used to control the overall perturbation scale; among its intermediate slip stripping parameters... Used to represent the main influencing factors in the initial bonding stage and the slip development stage, while The main influencing factors used to represent the residual bonding stage and the interface debonding stage; , , and They represent the first The relative contributions of the initial bonding stage, slip development stage, residual bonding stage, and interface peeling stage in each iteration to the overall error are used to assign different perturbation weights to parameter components sensitive to different stages during parameter updates, enabling the optimization process to prioritize correcting stages with larger errors. The specific calculation is as follows:

[0110]

[0111]

[0112]

[0113] In the formula, This is an offset constant representing the relative contribution of each stage to the overall error, used to ensure that the denominator in the calculation of the relative contribution is not zero; For the first The random perturbation term of each parameter component is used to calculate the random perturbation term at a given step size. , for the Each parameter component is subjected to a random search, and its value range is: The present invention preferably uses random variables that satisfy a zero-mean distribution, because using a zero-mean distribution can avoid systematic shifts in parameter updates, thereby maintaining the unbiased search characteristics of the disturbance within the physical value range; Indicates the first The candidate solution in the nth iteration Each candidate parameter component is used to represent a candidate solution after correction of the physical value range. This represents a uniformly random number, used to simulate the acceptance criterion random sampling in the annealing algorithm, i.e., to randomly decide whether to accept a candidate solution. Its value range is ; For the first The acceptance probability of a candidate solution in the next iteration can be specifically expressed as:

[0114] In the formula, Indicates the first The annealing temperature parameter of the annealing criterion in the next iteration is used to control the probability that the optimization algorithm accepts a poor solution, thereby improving its ability to escape local minima and enhancing its global search capability. Exponential cooling or other equivalent cooling strategies can be employed. This invention is not specifically limited to certain aspects and is subject to updates. The acceptance probability adopts the Boltzmann simulated annealing criterion, which enables the algorithm to accept poor solutions at high temperatures to escape local minima, and gradually enhances convergence during the cooling process.

[0115] Accordingly, the multi-stage boundary-guided adaptive simulated annealing optimization algorithm can achieve global optimization of intermediate slip-peeling parameters while ensuring physical constraints and parameter stability. This enables the four-stage adaptive objective function to converge reliably and ultimately obtains calibrated slip-peeling parameters that accurately reflect the entire process of AFRP-concrete interface bonding-slip-residue-peeling.

[0116] The external load simulation unit 3 is used to perform step S3: according to the preset load, incrementally iterate the numerical model of the AFRP-concrete interface behavior with bond-slip-delamination characteristics to obtain simulation time history data.

[0117] Specifically, the preset load is set according to the engineering conditions of the AFRP-reinforced shield tunnel segment, and can be a displacement control load, a force control load, or a combination of the two. For example, for the stress conditions dominated by bending, a loading surface can be set on the inner and outer sides of the segment or in the mid-span area, and vertical displacement, radial displacement, or equivalent water and soil pressure can be applied on the loading surface to drive the numerical model of the AFRP-concrete interface behavior with bond-slip-strip characteristics from the elastic stage to the entire process of damage, cracking and finally bearing capacity limit.

[0118] The incremental iteration is used to represent that during the loading process, the numerical simulation platform divides the total load into several loading steps, applies them to the numerical model of the AFRP-concrete interface behavior with bond-slip-strip characteristics one by one with a small step size, and solves the nonlinear response of the structure in each loading step. Meanwhile, during each solution step, the numerical simulation platform will synchronously update the concrete constitutive model, namely the tensile and compressive damage variables and stiffness degradation state in the concrete plastic damage model (CDP), as well as update the contact interface element response of the AFRP-concrete interface.

[0119] The contact interface unit response includes interface slip, interface tangential / normal stress, damage evolution parameters, and peeling determination variables. The peeling determination variables are used to represent the interface normal constraint failure state. They are automatically calculated from the normal stress-slip relationship of the contact interface unit. This invention does not specifically limit the calculation method. The numerical simulation platform can extract the interface peeling start time, peeling development range, and complete debonding area based on the evolution process of the peeling determination variables. This can be used to quantitatively analyze the spatial distribution and evolution process of AFRP-concrete interface degradation in subsequent performance evaluation. The simulation time history data is used to record the mechanical response results of AFRP-reinforced shield tunnel segments throughout the numerical simulation process. It includes load-displacement curves, interface slip curves, AFRP stress-strain distribution, concrete damage factor field, and displacement time history response of each key point during loading.

[0120] The load-displacement curve is used to measure the overall stiffness change and ultimate bearing capacity of the AFRP-reinforced shield tunnel segment, thereby depicting the entire process from the elastic stage to damage, cracking and failure. The interface slip curve is used to describe the relative displacement evolution of the AFRP unit and the concrete interface in the AFRP reinforced shield tunnel segment during the loading process, thereby reflecting the whole process of interface bonding degradation and friction slip, and can be combined with the spatial distribution of the peeling judgment variable to characterize the whole process of slip evolving into peeling. The stress-strain distribution of AFRP is used to reveal the force transmission of AFRP reinforcement units along the path in AFRP-reinforced shield segments, thereby determining the stress concentration and yield development of AFRP units in different regions of the concrete numerical model. The concrete damage factor field is used to reflect the cracking area and failure mode of concrete in AFRP-reinforced shield tunnel segments, thereby simulating the process of damage propagation caused by cracking in AFRP-reinforced shield tunnel segments. The displacement time history response is used to record the evolution of the displacement of key monitoring points of the AFRP-reinforced shield tunnel segment over time or loading step during the entire loading process, in order to evaluate the deformation mode and limit state determination of the structure.

[0121] It should be emphasized that this invention does not limit the type of numerical solution platform or the specific iterative algorithm. The numerical solution platform can be selected from the Newton-Raphson method, the arc-length method, the adaptive step size strategy, or other nonlinear iterative strategies according to different working conditions and computational requirements to ensure the convergence and stability of the solution process. The incremental iteration can be implemented in the framework of the finite element method (FEM) or the finite difference method (FDM).

[0122] The AFRP-reinforced shield tunnel segment performance evaluation unit 4 is used to perform step S4: calculate and evaluate the indicators of the simulation time history data to obtain the performance evaluation data of the AFRP-reinforced shield tunnel segment.

[0123] Specifically, the calculation and evaluation of the indicators include the following sub-steps: First, based on the response of the contact interface elements in the simulation time history data, a response sequence of the AFRP interface and the concrete interface is constructed to characterize the bonding, slippage and delamination behavior of the contact interface throughout the loading process.

[0124] Next, the response sequence of the AFRP interface and the concrete interface was divided into stages according to the calibrated slip-debonding parameters, resulting in the stage division results of the initial bond stage, slip development stage, residual bond stage, and interface debonding stage.

[0125] After completing the stage division, all stage division results are gradually aligned with the load-displacement curves, AFRP stress-strain distribution, concrete damage factor field, and key point displacement time history response in the simulation time history data to identify the structural stress mode, stiffness degradation process, crack propagation characteristics, and interface damage evolution law corresponding to each stage, thereby obtaining the aligned response data.

[0126] Finally, based on the mechanical characteristics of different stages, performance indicators are extracted from the aligned response data to obtain a set of performance indicators for the initial bonding stage, slip development stage, residual bonding stage, and interface peeling stage. This yields the performance evaluation data for AFRP-reinforced shield tunnel segments, which is used to evaluate the overall load-bearing capacity, stiffness degradation law, interface reliability, and peeling resistance of AFRP-reinforced shield tunnel segments.

[0127] It should be noted that this invention does not limit the specific calculation formula, evaluation threshold or weighting method of performance indicators. Those skilled in the art can make adjustments based on engineering specifications, test results or actual working conditions, as long as the stage division is completed based on the simulation time history data and the multi-field response is evaluated in segments.

[0128] Compared to existing technologies, this invention replaces the traditional combination of special springs and contact algorithms with solid units and parameterized interfaces. This allows the interface mechanical behavior to be fully expressed through controllable slip-peeling parameters, avoiding iterative oscillations and non-convergence problems caused by contact tolerance, friction algorithm coupling, and improper selection of spring stiffness. This significantly improves the stability and modeling consistency of the numerical model under complex bending conditions, thereby improving the accuracy of the toughness enhancement effect assessment.

[0129] Secondly, this invention introduces a four-stage piecewise error term and a stage boundary penalty mechanism with dynamic dimensionless coefficients into the objective function. This mechanism can adaptively adjust the penalty intensity based on the magnitude of the deviation between the simulated curve and the experimental curve at the critical slip point and the peeling start point. This avoids amplifying experimental noise and enhances the boundary calibration capability when stages are misaligned, ensuring the physical consistency of the entire process of interface bonding, slippage, residue, and peeling.

[0130] Finally, the multi-stage boundary-guided adaptive simulated annealing optimization algorithm constructed in this invention combines the adaptive perturbation step size driven by the stage error contribution with the annealing acceptance criterion. It can automatically concentrate search resources in regions with large stage errors and boundary deviations, and enable parameter search to have global optimization capabilities under the premise of satisfying physical constraints, which significantly improves the convergence speed and reliability of slip stripping parameter calibration.

[0131] In addition, please see Figure 3 , Figure 3 This is a schematic diagram comparing the load-displacement curves obtained from the numerical model of the AFRP-concrete interface behavior with bond-slip-delamination characteristics constructed in this invention under damage loading conditions with experimental results. Figure 3 It is evident that the numerical simulation results are highly consistent with the experimental results, with a high degree of matching in the elastic stage. As loading continues, the slope of the curve gradually decreases, and further damage begins to appear on the inner surface of the segment. The structure re-enters the plastic stage, and the numerical simulation can accurately reproduce the nonlinear evolution law exhibited in the experiment, verifying the authenticity and effectiveness of the model after introducing the bond-slip effect through solid elements and interface elements.

[0132] Please see Figure 4 , Figure 4 This is the load-displacement curve obtained by the concrete numerical model with slip characteristics constructed in this invention under the condition of pre-reinforced tunnel segments. Figure 4As can be seen, in the initial stage of loading, the slope of the load-displacement curve gradually decreases, corresponding to the development process of the reinforced segment from the elastic stage to the plastic stage. However, as loading continues, when the slope of the curve approaches zero, a sharp drop in bearing capacity occurs. According to the damage cloud map of the model, the reason for the sharp drop in bearing capacity is the local peeling phenomenon between AFRP and the reinforced segment. This phenomenon is consistent with that observed in full-scale tests. Therefore, by employing concrete plastic damage constitutive models, interface elements, and calibrated bond parameters, this invention can not only realistically reflect the bond-slip effect of the AFRP-concrete interface but also accurately reproduce the entire process of AFRP-concrete interface peeling, ensuring the reliability of the simulation results.

[0133] Based on the same inventive concept, this application also provides an electronic device, which can be a server, desktop computing device, or mobile computing device (e.g., laptop computing device, handheld computing device, tablet computer, netbook, etc.). The device includes one or more processors and a memory, wherein the processor is used to execute a program to implement the numerical simulation method for improving the toughness of AFRP shield tunnel segments according to embodiments of the present invention; the memory is used to store computer programs executable by the processor.

[0134] Based on the same inventive concept, this application also provides a computer-readable storage medium corresponding to the aforementioned embodiment of a numerical simulation method for improving the toughness of AFRP shield tunnel segments. The computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the steps of the numerical simulation method for improving the toughness of AFRP shield tunnel segments described in any of the above embodiments.

[0135] This application may take the form of a computer program product implemented on one or more storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing program code. Computer storage media include permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information may be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to: phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0136] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and the present invention also intends to include these modifications and variations.

Claims

1. A numerical simulation method for improving the toughness of shield tunnel segments using AFRP, characterized in that, Includes the following steps: S1. Based on the reinforcement information, the three-dimensional AFRP-reinforced shield tunnel segment is meshed to obtain the initial concrete numerical model. S2. Construct AFRP solid elements and contact interface elements, and combine them with the calibrated slip-peeling parameters, and embed them into the initialized concrete numerical model to obtain a numerical model of AFRP-concrete interface behavior with bond-slip-peeling characteristics. The calibrated slip-off parameters are calibrated through the following steps: First, single shear tests and tensile tests were conducted on the AFRP-concrete interface, and mechanical data sets of the AFRP-concrete interface in the single shear tests and tensile tests were collected to form load-slip curves and stress-strain curves. Next, based on the initialization of the concrete numerical model, AFRP solid elements and contact interface elements are introduced, and a set of intermediate slip-stripping parameters that have not yet converged are assigned to them. Incremental iterative calculations are then performed on the working conditions corresponding to the single shear test and the positive tension test through the numerical simulation platform to obtain the simulated load-slip curves. Subsequently, a four-segment adaptive objective function is used to calculate the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset, so as to obtain the deviation value corresponding to the current intermediate slip stripping parameter. The four-stage adaptive objective function includes an objective function for the initial bonding stage, an objective function for the slip development stage, an objective function for the residual bonding stage, an objective function for the interface peeling stage, and a stage boundary penalty term. Finally, it is determined whether the deviation value corresponding to the current intermediate slip stripping parameter meets the iteration threshold: if not, it is considered that the current intermediate slip stripping parameter has not converged, and the current intermediate slip stripping parameter is updated and iterated using a multi-stage boundary-guided adaptive simulated annealing optimization algorithm to obtain the updated intermediate slip stripping parameter, and the incremental iteration calculation continues; if yes, it is considered that the current intermediate slip stripping parameter has been calibrated and is used as the calibrated slip stripping parameter. The multi-stage boundary-guided adaptive simulated annealing optimization algorithm is used to optimize the current intermediate slip stripping parameters while satisfying the physical value range constraints of the intermediate slip stripping parameters. Perform global optimization to cause the four-segment adaptive objective function value to converge to satisfy the iteration threshold; S3. Based on the preset load, the numerical model of the AFRP-concrete interface behavior with bond-slip-debond characteristics is incrementally iterated to obtain simulation time history data. S4. Calculate and evaluate the performance of the simulated time history data to obtain the performance evaluation data of the AFRP-reinforced shield tunnel segments.

2. The numerical simulation method for improving the toughness of shield tunnel segments using AFRP as described in claim 1, characterized in that, The intermediate slip stripping parameter set Specifically, it is expressed as: In the formula, It is cohesive force; It is the internal friction angle; The ratio of shear stress to tensile stress; Residual cohesion; This is the residual internal friction angle; Interfacial tensile strength; Residual tensile strength; The specific representation of the four-segment adaptive objective function is as follows: In the formula, Indicates the first The deviation value corresponding to the intermediate slip stripping parameter in the next iteration; The objective function for the initial bonding stage is expressed as follows: In the formula, Indicates the first The iteration, and the intermediate slip stripping parameter is At that time, the numerical simulation yielded the first The load values ​​corresponding to each sampling point; Represents the first in the mechanics dataset Load values ​​at each sampling point; This represents the maximum load value in the load-slip curve of the mechanics dataset. This represents the total number of sampling points for the load-slip curve in the mechanics dataset; The total number of sampling points used to represent the initial bonding stage is calculated as follows: in, Represents the first in the mechanics dataset The interface slip amount corresponding to each sampling point This represents the critical value of the slip development stage identified in the load-slip curve of the mechanics dataset; Indicates an indicator function; The objective function representing the slip development stage is expressed as follows: In the formula, The total number of sampling points used to represent the slip development stage is calculated as follows: in, This represents the critical value of the residual bond stage identified in the load-slip curve of the mechanical dataset; The objective function for the residual bonding stage is expressed as follows: In the formula, The total number of sampling points used to represent the residual bonding stage is calculated as follows: in, This represents the critical value of the interface peeling stage identified in the load-slip curve of the mechanical dataset; The objective function for the interface stripping phase is represented as follows: In the formula, The total number of sampling points used to represent the interface stripping stage is specifically calculated as follows: ; This represents the stage boundary penalty term, used to constrain the current stage boundary penalty term. Intermediate slip stripping parameters of the next iteration The deviation between the stage critical values ​​identified in the obtained simulated load-slip curves and the corresponding stage critical values ​​of the tests in the mechanical dataset includes the penalty terms for the slip development stage, the penalty terms for the residual bonding stage, and the penalty terms for the interface peeling stage.

3. The numerical simulation method for improving the toughness of shield tunnel segments using AFRP according to claim 2, characterized in that, The specific representation of the stage boundary penalty term is as follows: In the formula, Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the slip development stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient corresponding to the critical value of the slip development stage identified by the simulated load-slip curve is specifically expressed as follows: Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the residual bond stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient for the critical value of the residual bond stage identified by the simulated load-slip curve is specifically expressed as follows: Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the interface peeling stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient for the critical value of the interface peeling stage, identified by the simulated load-slip curve, is specifically expressed as follows: In the formula, This is an offset constant.

4. The numerical simulation method for improving the toughness of shield tunnel segments using AFRP according to claim 3, characterized in that, The multi-stage boundary-guided adaptive simulated annealing optimization algorithm optimizes the current intermediate slip-stripping parameters. The specific representation of global optimization is as follows: In the formula, For the first The first of the intermediate slip stripping parameters in the second iteration Uncorrected candidate parameter components after random perturbation of each parameter component; For the first In the nth iteration The adaptive perturbation step size coefficients of the intermediate slip stripping parameter components are specifically expressed as follows: In the formula, The basic perturbation step size coefficient; Among the intermediate slip peeling parameters Used to represent the main influencing factors in the initial bonding stage and the slip development stage, while The main influencing factors used to represent the residual bonding stage and the interface debonding stage; , , and They represent the first The relative contributions of the initial bonding stage, slip development stage, residual bonding stage, and interface peeling stage to the overall error in each iteration are specifically calculated as follows: In the formula, This is a constant offset representing the relative contribution of each stage to the overall error. For the first The random perturbation term of each parameter component is used to calculate the random perturbation term at a given step size. , for the Apply a random search to each parameter component; Indicates the first The candidate solution in the nth iteration One corrected candidate parameter component; Indicates the first The physical upper limit of each parameter component, Indicates the first The physical lower limit of each parameter component; Represents uniformly random numbers; For the first The acceptance probability of a candidate solution in the next iteration can be specifically expressed as: In the formula, Indicates the first Annealing temperature parameters for the annealing criterion in the next iteration; Indicates the first The intermediate slip stripping parameter of the next iteration Each parameter component.

5. A numerical simulation device for improving the toughness of AFRP shield tunnel segments, characterized in that, This includes concrete mesh generation units for tunnel segments, embedded units for AFRP entities and contact interfaces, external load simulation units, and performance evaluation units for AFRP-reinforced tunnel segments. The concrete mesh generation unit of the shield tunnel segment is used to perform mesh generation on the three-dimensional AFRP-reinforced shield tunnel segment according to the reinforcement information to obtain the initial concrete numerical model. The AFRP entity and contact interface embedding unit is used to construct AFRP entity unit and contact interface unit, and the combination of the two and the calibrated slip-peeling parameters are embedded into the initialized concrete numerical model to obtain a numerical model of AFRP-concrete interface behavior with bond-slip-peeling characteristics. The calibrated slip-off parameters are calibrated through the following steps: First, single shear tests and tensile tests were conducted on the AFRP-concrete interface, and mechanical data sets of the AFRP-concrete interface in the single shear tests and tensile tests were collected to form load-slip curves and stress-strain curves. Next, based on the initialization of the concrete numerical model, AFRP solid elements and contact interface elements are introduced, and a set of intermediate slip-stripping parameters that have not yet converged are assigned to them. Incremental iterative calculations are then performed on the working conditions corresponding to the single shear test and the positive tension test through the numerical simulation platform to obtain the simulated load-slip curves. Subsequently, a four-segment adaptive objective function is used to calculate the deviation between the simulated load-slip curve and the corresponding load-slip curve in the mechanical dataset, so as to obtain the deviation value corresponding to the current intermediate slip stripping parameter. The four-stage adaptive objective function includes an objective function for the initial bonding stage, an objective function for the slip development stage, an objective function for the residual bonding stage, an objective function for the interface peeling stage, and a stage boundary penalty term. Finally, it is determined whether the deviation value corresponding to the current intermediate slip stripping parameter meets the iteration threshold: if not, it is considered that the current intermediate slip stripping parameter has not converged, and the current intermediate slip stripping parameter is updated and iterated using a multi-stage boundary-guided adaptive simulated annealing optimization algorithm to obtain the updated intermediate slip stripping parameter, and the incremental iteration calculation continues; if yes, it is considered that the current intermediate slip stripping parameter has been calibrated and is used as the calibrated slip stripping parameter. The multi-stage boundary-guided adaptive simulated annealing optimization algorithm is used to optimize the current intermediate slip stripping parameters while satisfying the physical value range constraints of the intermediate slip stripping parameters. Perform global optimization to cause the four-segment adaptive objective function value to converge to satisfy the iteration threshold; The external load simulation unit is used to incrementally iterate the numerical model of the AFRP-concrete interface behavior with bond-slip-debond characteristics according to the preset load, and obtain simulation time history data. The AFRP-reinforced shield tunnel segment performance evaluation unit is used to calculate and evaluate the indicators of the simulation time history data to obtain the performance evaluation data of the AFRP-reinforced shield tunnel segment.

6. The numerical simulation device for improving the toughness of shield tunnel segments using AFRP according to claim 5, characterized in that, The intermediate slip stripping parameter set Specifically, it is expressed as: In the formula, It is cohesive force; It is the internal friction angle; The ratio of shear stress to tensile stress; Residual cohesion; This is the residual internal friction angle; Interfacial tensile strength; Residual tensile strength; The specific representation of the four-segment adaptive objective function is as follows: In the formula, Indicates the first The deviation value corresponding to the intermediate slip stripping parameter in the next iteration; The objective function for the initial bonding stage is expressed as follows: In the formula, Indicates the first The iteration, and the intermediate slip stripping parameter is At that time, the numerical simulation yielded the first The load values ​​corresponding to each sampling point; Represents the first in the mechanics dataset Load values ​​at each sampling point; This represents the maximum load value in the load-slip curve of the mechanics dataset. This represents the total number of sampling points for the load-slip curve in the mechanics dataset; The total number of sampling points used to represent the initial bonding stage is calculated as follows: in, Represents the first in the mechanics dataset The interface slip amount corresponding to each sampling point This represents the critical value of the slip development stage identified in the load-slip curve of the mechanics dataset; Indicates an indicator function; The objective function representing the slip development stage is expressed as follows: In the formula, The total number of sampling points used to represent the slip development stage is calculated as follows: in, This represents the critical value of the residual bond stage identified in the load-slip curve of the mechanical dataset; The objective function for the residual bonding stage is expressed as follows: In the formula, The total number of sampling points used to represent the residual bonding stage is calculated as follows: in, This represents the critical value of the interface peeling stage identified in the load-slip curve of the mechanical dataset; The objective function for the interface stripping phase is represented as follows: In the formula, The total number of sampling points used to represent the interface stripping stage is specifically calculated as follows: ; This represents the stage boundary penalty term, used to constrain the current stage boundary penalty term. Intermediate slip stripping parameters of the next iteration The deviation between the stage critical values ​​identified in the obtained simulated load-slip curves and the corresponding stage critical values ​​of the tests in the mechanical dataset includes the penalty terms for the slip development stage, the penalty terms for the residual bonding stage, and the penalty terms for the interface peeling stage.

7. The numerical simulation device for improving the toughness of AFRP shield tunnel segments according to claim 6, characterized in that, The specific representation of the stage boundary penalty term is as follows: In the formula, Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the slip development stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient corresponding to the critical value of the slip development stage identified by the simulated load-slip curve is specifically expressed as follows: Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the residual bond stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient for the critical value of the residual bond stage identified by the simulated load-slip curve is specifically expressed as follows: Indicates based on the first Intermediate slip stripping parameters of the next iteration The critical value of the interface peeling stage identified by the simulated load-slip curve; For the first Intermediate slip stripping parameters of the next iteration The dynamic dimensionless penalty coefficient for the critical value of the interface peeling stage, identified by the simulated load-slip curve, is specifically expressed as follows: In the formula, This is an offset constant.

8. The numerical simulation device for improving the toughness of shield tunnel segments using AFRP according to claim 7, characterized in that, The multi-stage boundary-guided adaptive simulated annealing optimization algorithm optimizes the current intermediate slip-stripping parameters. The specific representation of global optimization is as follows: In the formula, For the first The first of the intermediate slip-out parameters in the second iteration Uncorrected candidate parameter components after random perturbation of each parameter component; For the first In the nth iteration The adaptive perturbation step size coefficients of the intermediate slip stripping parameter components are specifically expressed as follows: In the formula, The basic perturbation step size coefficient; Among the intermediate slip peeling parameters Used to represent the main influencing factors in the initial bonding stage and the slip development stage, while The main influencing factors used to represent the residual bonding stage and the interface debonding stage; , , and They represent the first The relative contributions of the initial bonding stage, slip development stage, residual bonding stage, and interface peeling stage to the overall error in each iteration are specifically calculated as follows: In the formula, This is a constant offset representing the relative contribution of each stage to the overall error. For the first The random perturbation term of each parameter component is used to calculate the random perturbation term at a given step size. , for the Apply a random search to each parameter component; Indicates the first The candidate solution in the nth iteration One corrected candidate parameter component; Indicates the first The physical upper limit of each parameter component, Indicates the first The physical lower limit of each parameter component; Represents uniformly random numbers; For the first The acceptance probability of a candidate solution in the next iteration can be specifically expressed as: In the formula, Indicates the first Annealing temperature parameters for the annealing criterion in the next iteration; Indicates the first The intermediate slip stripping parameter of the next iteration Each parameter component.

9. An electronic device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the processor executes the computer program, it implements a numerical simulation method for improving the toughness of AFRP shield tunnel segments as described in any one of claims 1-4.

10. A computer-readable storage medium storing computer-executable instructions, characterized in that, When the computer-executable instructions are executed by the processor, they implement a numerical simulation method for improving the toughness of shield tunnel segments using AFRP, as described in any one of claims 1-4.

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