Design method of metro tunnel reinforced with FRP multi-cavity structure and fiber composite

Abstract

The application discloses a subway tunnel FRP multi-cavity reinforcing structure design method and a fiber composite, relates to the field of reinforcing structure design, and through obtaining three-dimensional point cloud data of the inner surface of a shield segment and a theoretical design surface of the FRP multi-cavity profile, a global interface gap topology field is constructed, a discretization stiffness data matrix is constructed, forced displacement simulation of a simulated bolt fastening working condition is executed in a physical interference area, an initial bending stress field and a contact pressure distribution are calculated, a three-element logic discriminant interface mechanical defect set is executed, for the interface mechanical defect set, the grinding volume required for interference elimination and the medium volume required for filling the void are solved, an interface adaptability compensation strategy is generated, the interface adaptability compensation strategy is converted into segment pretreatment instructions and medium filling control instructions, and based on the effective section inertia moment, reinforcing efficiency checking is executed, safety warning is carried out, and the overall safety reserve coefficient of the reinforcing system under extreme working conditions is improved.

Description

Technical Field

[0001] This invention relates to the field of reinforced structure design, specifically to a design method for FRP multi-cavity reinforced structures for subway tunnels and fiber composite materials. Background Technology

[0002] As the service life of urban rail transit systems increases, structural reinforcement of tunnel segments becomes crucial for ensuring operational safety. Currently, the industry widely adopts a multi-cavity FRP reinforcement structure for subway tunnels (such as...). Figure 1 , Figure 2 and Figure 6 As shown), this structure uses FRP multi-cavity profiles prepared by bending pultrusion as the core component, and its cross-sectional structure includes multi-cavity forms such as closed box type or open slot type (e.g. Figure 3 As shown), the cavity is filled with high-strength self-compacting concrete or grout to suppress local buckling and increase the moment of inertia of the section. In terms of construction technology, this system typically employs a chemical bonding + mechanical anchoring connection mode (such as...). Figure 4 As shown in the diagram, this method utilizes an interfacial adhesive layer to transfer shear force, supplemented by high-strength bolts to forcibly fix the profile to the inner surface of the tunnel segment along the circumferential direction. Compared to traditional steel plate reinforcement, this fiber composite structure demonstrates advantages in the field of tunnel structure reinforcement due to its lightweight, high strength, corrosion resistance, and prefabrication capabilities.

[0003] However, in current engineering practice, the safety and effectiveness of the aforementioned reinforcement structures are constrained by the topological mapping deviation between "standardized manufactured components" and "randomly deformable base surfaces." Traditional reinforcement design methods ignore the microscopic three-dimensional morphological characteristics of the inner surface of the tunnel segment, simply assuming that the profile and the tunnel segment are ideally coaxially fitted. When rigid FRP profiles are forcibly installed on the surface of tunnel segments that undergo random deformation, geometric mismatches such as "curved ends and topped middle" or "partial voids" often occur, resulting in extremely uneven adhesive layer thickness between the FRP and the tunnel segment, for example, abruptly changing from 0 mm to more than 20 mm. This thickness fluctuation directly causes severe dispersion in interface coupling stiffness: in the misaligned hard contact area, the extremely thin adhesive layer will cause stress concentration leading to brittle cracking; in the deep pit void area, the excessively thick adhesive layer introduces flexible slippage, causing the FRP to be unable to effectively share the tunnel segment load, resulting in adhesive gaps, voids, or adhesive layer creep. More importantly, in order to eliminate physical gaps, the profiles are often forced to move by tightening bolts during construction to achieve a fit. This forced assembly introduces huge initial bending stress into the FRP profiles, causing the reinforced structure to consume part of the material's strength reserves before it bears load, thus significantly reducing the overall safety factor of the system.

[0004] To address the aforementioned shortcomings, a design method for a multi-cavity FRP reinforcement structure for subway tunnels and a fiber composite material are provided. Summary of the Invention

[0005] To address the technical problems mentioned in the background, a design method for FRP multi-cavity reinforcement structures for subway tunnels and fiber composite materials are proposed.

[0006] The design method for FRP multi-cavity reinforcement structures in subway tunnels includes the following steps:

[0007] The three-dimensional point cloud data of the inner surface of the shield tunnel segment and the theoretical design surface of the FRP multi-cavity profile are obtained, and the global interface gap topological field is constructed to divide the contact interface into various mechanical characteristic topological regions.

[0008] Based on the global interface gap topological field and the topological regions of various mechanical characteristics, a discretized stiffness data matrix is ​​constructed. Forced displacement simulation of bolt fastening condition is performed in the physical interference zone to calculate the initial bending stress field and contact pressure distribution. Ternary logic is used to identify the interface mechanical defect set.

[0009] For the set of interface mechanical defects, the grinding volume required to eliminate interference and the medium volume required to fill voids are calculated, an interface adaptive compensation strategy is generated, and the effective cross-sectional moment of inertia is calculated.

[0010] The interface adaptive compensation strategy is converted into segment pretreatment instructions and medium filling control instructions, and the reinforcement effectiveness is verified based on the effective cross-sectional moment of inertia to provide safety warnings.

[0011] Furthermore, the step of dividing the topological regions of each mechanical feature includes:

[0012] Based on the three-dimensional point cloud data of the inner surface of the shield tunnel segment and the theoretical design surface of the FRP multi-cavity profile, the elastic rebound mechanism of the pultrusion process and the chordal geometric physical constraints are introduced to perform reverse reconstruction based on the solid shape of the theoretical design surface to obtain the corrected theoretical design surface.

[0013] The modified theoretical design surface is imported into the coordinate system where the micro-morphology data is located, and the center axis vector of the preset bolt hole of the FRP profile and the center axis vector of the installed rebar hole on the inner surface of the segment are extracted.

[0014] Based on the preset bolt hole center axis vector and the constructed rebar hole center axis vector, a coaxiality deviation objective function is constructed, and a constrained least squares registration is performed to solve the optimal rigid body transformation matrix, driving the modified theoretical design surface to undergo pose transformation and locking the virtual pre-assembly pose.

[0015] Furthermore, the step of dividing the topological regions of each mechanical feature also includes:

[0016] Under the virtual pre-assembly pose, the directed Euclidean distance between the bottom surface of the corrected theoretical design surface and the inner surface of the segment is calculated, a global interface gap topological field is constructed, and the interface is divided into various mechanical feature topological regions based on a preset threshold. Each mechanical feature topological region includes a physical interference region, an effective bonding region, and a structural voiding region.

[0017] Furthermore, the steps for obtaining the modified theoretical design surface include:

[0018] Based on the local three-dimensional Cartesian coordinate system, the preset bolt hole positions of the FRP multi-cavity profile are retrieved as physical stiffness hard points. Using the physical stiffness hard points as the dividing line, the three-dimensional point cloud data is divided into multiple independent standard segment units along the longitudinal direction.

[0019] The three-dimensional point cloud data within each standard segment unit is projected onto a plane perpendicular to the profile axis to extract the true profile point set of the cross section.

[0020] Perform geometric center fitting based on the moment of inertia of the cross section on the set of true contour points of the cross section to generate the actual centroid trajectory line;

[0021] The theoretical neutral axis of the FRP multi-cavity profile is constructed, and the installation normal deviation value and the section torsion angle value are calculated by comparing the spatial position of the actual centroid trajectory line with the theoretical neutral axis.

[0022] Furthermore, the step of obtaining the modified theoretical design surface also includes:

[0023] Within the standard segment unit, an indeformable physical chord is constructed by connecting the anchor points at both ends, and the vertical distance from the arch of the actual centroid trajectory line to the physical chord is measured to obtain the actual sagitta.

[0024] By introducing the plane section assumption of mechanics of materials, and performing chord vector geometric inversion based on the physical chord length and the actual chord height, the true physical radius of curvature is derived.

[0025] The axial base curvature of the FRP multi-cavity profile is corrected using the actual physical radius of curvature, and the installation normal deviation value and the cross-sectional torsion angle value are superimposed on this basis to generate a variable-rate air-torsion reconstruction solid envelope, which is then used as the corrected theoretical design surface.

[0026] Furthermore, the step of performing ternary logic to determine the set of interface mechanical defects includes:

[0027] Based on the gap value distribution in the global interface gap topological field, the effective cementation zone and the structural voiding zone are given a rigid contact property with a maximum value by using the inverse proportional function relationship, and a discretized stiffness data matrix is ​​constructed.

[0028] Within the physical interference zone, a forced deformation vector is constructed to simulate the normal displacement load generated by bolt tightening. The initial bending stress field is calculated by combining the longitudinal bending elastic modulus and cross-sectional geometric coefficient of the FRP multi-cavity profile. The contact pressure distribution is calculated by combining the equivalent compressive stiffness of the vertical support wall panel of the FRP multi-cavity profile.

[0029] The initial bending stress field, contact pressure distribution, and discretized stiffness data matrix are subjected to ternary logic discrimination to identify the interface mechanical defect set. The interface mechanical defect set includes the stress concentration defect set and the substrate crushing defect set located in the physical interference zone, as well as the stiffness degradation defect set located in the structural voiding zone.

[0030] Furthermore, the step of calculating the effective cross-sectional moment of inertia includes:

[0031] For the physical interference zone corresponding to the set of stress concentration defects and the set of base material crushing defects, with the goal of eliminating contact interference, the volume of concrete to be removed from the surface of the segment is calculated to generate stress relief grinding volume data.

[0032] For the structural void zone corresponding to the stiffness degradation defect, the discrete infinitesimal integral algorithm is used to perform volume integration on the gap field, calculate the total cumulative grouting volume data of the whole domain and generate variable thickness filling volume data.

[0033] Stress-relieving grinding volume data, total grouting volume data accumulated across the entire domain, and variable-thickness filling volume data are used as interface adaptive compensation strategies.

[0034] Furthermore, the step of calculating the effective cross-sectional moment of inertia also includes:

[0035] Based on the distribution characteristics of the global interface shear stiffness, the global weighted average shear stiffness is calculated, and the composite structure synergistic stiffness correction coefficient is solved.

[0036] The effective moment of inertia of the FRP multi-cavity profile is obtained by reducing the theoretical moment of inertia of the composite structure by using the composite structure synergistic stiffness correction coefficient.

[0037] Furthermore, the step of calculating the effective cross-sectional moment of inertia includes:

[0038] The stress relief grinding volume data is converted into tool path code for CNC grinding equipment or contour line construction drawing for manual grinding, and used as pretreatment instructions for the tunnel segment surface.

[0039] The total cumulative grouting volume data of the entire domain is converted into the quantitative cutoff threshold of the grouting pump, and the variable thickness filling volume data is converted into the extrusion rate control sequence of the adhesive coating equipment as a medium filling control command.

[0040] Using the effective cross-sectional moment of inertia, the ultimate bearing capacity of the reinforced tunnel segment is recalculated. If it meets the specification requirements, the final construction plan is output; otherwise, a safety warning is issued.

[0041] Furthermore, a fiber composite material is a composite reinforcement system consisting of a bent pultruded FRP multi-cavity profile as the skeleton, filled with high-strength self-compacting concrete or grout, wrapped with a multi-directional fiber reinforcement layer and coated with a nano-protective layer, and connected with tunnel segments by adhesive bolts to form a synergistic force-bearing structure.

[0042] Compared with the prior art, the beneficial effects of the present invention are:

[0043] This invention acquires three-dimensional point cloud data of the inner surface of the tunnel lining segment and the theoretically designed curved surface of the FRP multi-cavity profile, constructs a global interface gap topological field, and precisely divides the contact interface into various mechanical characteristic topological regions. Based on the global interface gap topological field and each mechanical characteristic topological region, a discretized stiffness data matrix is ​​constructed. Forced displacement simulation of bolt tightening conditions is performed in the physical interference zone to calculate the initial bending stress field and contact pressure distribution. Ternary logic is used to identify the interface mechanical defect set. For the interface mechanical defect set, the grinding volume required to eliminate interference and the medium volume required to fill the voids are calculated, generating an interface adaptive compensation strategy and calculating the effective section moment of inertia. Existing technologies, when using bent pultruded FRP profiles for reinforcement, often ignore the geometric mismatch between the profile and the tunnel lining segment, relying on forced bolt tightening to eliminate gaps. This results in huge initial bending stress in the component before it bears load, consuming the material's strength reserves. This invention uses a chordal geometric inversion algorithm to restore the true natural shape of the profile after releasing residual stress and calculates the stress-relieving grinding volume required to eliminate physical interference in digital space. This proactive compensation strategy, which uses form to replace force, eliminates the additional internal forces caused by forced correction from a physical perspective, avoids early failure of FRP profiles due to excessive prestress, and improves the overall safety reserve coefficient of the reinforcement system under extreme working conditions.

[0044] This invention transforms the interface adaptive compensation strategy into segment pretreatment instructions and medium filling control instructions, and performs reinforcement performance verification based on the effective cross-sectional moment of inertia, providing safety early warning. Three-dimensional point cloud technology is used to reveal the topological mapping deviation of the micro-interface, and the interface is precisely divided into physical interference zones, effective bonding zones, and structural void zones. By generating variable-thickness filling volume data to guide differentiated construction—namely, variable instantaneous rate adhesive application for open sections and total volume control grouting for closed sections—the risk of stress concentration and brittle fracture in thin adhesive layers and stiffness degradation failure in thick adhesive layers are effectively avoided. A composite structure synergistic stiffness correction coefficient is introduced, transforming the complex nonlinear interface contact state into a quantifiable reduction of cross-sectional properties, providing a rigorous numerical verification basis for the load-bearing capacity of the reinforced structure, and ensuring the synergistic stress performance of FRP and concrete segments throughout their entire life cycle. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. The following drawings are not drawn to scale according to the actual size, but are intended to show the main idea of ​​the present invention.

[0046] Figure 1 Cross-sectional view of a flexurally pultruded multi-cavity composite;

[0047] Figure 2 Image of a bending pultruded multi-cavity composite material;

[0048] Figure 3 A compilation of cross-sectional structural diagrams for fiber-reinforced composite multi-cavity profiles;

[0049] Figure 4 Detailed front view of shield tunnel segments reinforced with fiber-reinforced composite multi-cavity profiles;

[0050] Figure 5 This is a schematic diagram illustrating the pultrusion process of FRP profiles.

[0051] Figure 6 Schematic diagram of a shield tunnel reinforced with flexurally pultruded multi-cavity composite material;

[0052] Figure 7 A flowchart illustrating the design method for FRP multi-cavity reinforcement structures in subway tunnels;

[0053] Figure 8 This is a schematic diagram of the geometric inversion of the chord vector and the generation of the envelope of the variable-rate void twist entity. Detailed Implementation

[0054] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are also within the scope of protection of the present invention.

[0055] like Figure 1 , Figure 2 , Figure 4 and Figure 6 As shown, the present invention employs a multi-cavity FRP reinforcement structure for subway tunnels;

[0056] Specifically, such as Figure 1 The diagram shows a cross-sectional view of a flexurally pultruded multi-cavity composite material. The core component of this invention is an FRP multi-cavity profile. From a microscopic perspective, it consists of a long-lasting nano-alloy polymer protective layer, a fiber-reinforced composite material layer (FRP shell), and cavity filler, arranged sequentially from the outside to the inside. The fiber-reinforced composite material layer employs a multi-directional fiber layup design, including circumferential fiber cloth and axial fiber bundles, to simultaneously meet the flexural strength and ductility requirements for tunnel reinforcement. The cavity filler is high-strength self-compacting concrete or high-strength grout. This combination of an outer FRP shell and an inner concrete filling utilizes the compressive strength of concrete to prevent local buckling of the FRP thin-walled cavity, while simultaneously using the high tensile strength of FRP to constrain the concrete, increasing the overall moment of inertia and flexural stiffness of the cross-section.

[0057] like Figure 2 The image shown is a physical picture of a bent pultruded multi-cavity composite material. This FRP multi-cavity profile is not a traditional straight profile that is bent later, but a fixed curvature component integrally manufactured using a bent pultrusion molding process. It possesses a standard axial curvature that matches the inner surface of subway tunnel segments when it leaves the factory. This prefabricated physical form not only eliminates the enormous rebound stress generated when traditional straight plates are forcibly bent and installed, but also ensures the continuity and integrity of the fibers in the bent state, solving the defects of fiber wrinkling or breakage due to bending in traditional processes.

[0058] like Figure 3 As shown, the cross-sectional structure of the FRP multi-cavity profile includes, but is not limited to, two-cavity, three-cavity, four-cavity, or single-cavity structures. Based on adaptability to construction processes, the profile cross-section is divided into closed box-type cross-sections (such as...). Figure 3 The rectangular tube structure shown in the upper middle row) and the open slotted section (such as...) Figure 3 (The C-shaped or I-shaped structure shown in the middle row). The closed box-shaped cross-section is suitable for the prefabrication and post-grouting process, with its bottom plate closed; the open groove-shaped cross-section is suitable for automated adhesive application and bonding processes, with its bottom surface open, facilitating direct application and testing of the adhesive layer.

[0059] like Figure 4 The image shows a detailed front view of a shield tunnel segment reinforced with a fiber-reinforced composite multi-cavity profile, illustrating the connection details between the FRP profile and the segment. This reinforcement system employs a dual connection method: chemical bonding and mechanical anchoring. On one hand, continuous bonding between surfaces is achieved through an interfacial structural adhesive layer, transferring shear force. On the other hand, several sets of high-strength bolts or chemical anchors are spaced along the profile's axial direction, with the bolts penetrating pre-drilled holes into the segment matrix. These bolt locations are the physical stiffness hard points defined in the aforementioned design method; they not only serve to fix and prevent detachment but are also the main force points forcing the FRP profile to conform to the segment's deformation.

[0060] like Figure 5 The diagram illustrates the principle of the FRP profile pultrusion process, revealing the manufacturing principle of the core component of this invention. Unlike conventional linear pultrusion, this process introduces a variable curvature heating system and a specific guiding and conveying device. After impregnation with resin, the multi-strand fiber yarn does not pass through a straight mold, but rather follows a specific bending and curing path under dynamic traction. This process ensures that the FRP profile locks in the preset axial curvature during the resin cross-linking and curing stage, thus giving the profile an initial bending shape without internal stress after demolding, laying the geometric foundation for subsequent bonding with tunnel segments.

[0061] like Figure 6 The diagram illustrates a shield tunnel reinforced with bent pultruded multi-cavity composite material, showcasing the macroscopic application of this reinforcement structure on a complete tunnel segment ring. Multiple bent pultruded FRP multi-cavity profiles are arranged parallel to each other along the tunnel circumference, tightly fitting the inner arc surface of the segment to form a rib-type reinforcement system. In the application scenario of a closed box girder section, the diagram also shows grouting ports located at the ends or sides of the profiles, used to inject filling media into the structural voids at the interface after installation, thereby forming a complete composite structural system where the FRP profile, adhesive / grout layer, and existing concrete segment work together to bear the load.

[0062] Example 1

[0063] like Figure 7 As shown, for the aforementioned FRP multi-cavity reinforcement structure for subway tunnels, the design method for FRP multi-cavity reinforcement structures for subway tunnels includes the following steps:

[0064] Step S100: Obtain the three-dimensional point cloud data of the inner surface of the shield tunnel segment and the theoretical design surface of the FRP multi-cavity profile, construct the global interface gap topology field, and accurately divide the contact interface into various mechanical characteristic topology regions.

[0065] The process of constructing the discretized variable cross-section flow channel model in step S100 specifically includes the following steps:

[0066] Step S101: Based on the three-dimensional point cloud data of the inner surface of the shield tunnel segment and the theoretical design surface of the FRP multi-cavity profile, the elastic rebound mechanism of the pultrusion process and the chordal geometric physical constraints are introduced to perform reverse reconstruction based on the solid shape on the theoretical design surface to obtain the corrected theoretical design surface.

[0067] A high-precision 3D laser scanner was used to perform a panoramic scan of the inner surface of the shield tunnel segments, obtaining 3D point cloud data of the inner surface of the shield tunnel segments that reflects the actual assembly misalignment and convergence deformation state of the segments. ; Constructing the theoretical design surface for FRP multi-cavity profiles The theoretically designed surface This refers to the process of extracting the cross-sectional geometric features, including the combination of the inner and outer contours of the FRP multi-cavity profile, from the design drawings and generating a three-dimensional solid envelope surface along the axial design trajectory. Specifically, for example... Figure 6 As shown, this curved surface represents the process of FRP profiles undergoing... Figure 5 After preparation, the standard geometric shape, in an ideal manufacturing state and without taking into account the effects of process springback and installation deformation, will be used to... and This serves as the foundational input data for subsequent reverse reconstruction of the entity's shape based on chordal geometric constraints.

[0068] Step S1011: Based on the theoretical design of the surface, establish a local three-dimensional Cartesian coordinate system;

[0069] Based on the local three-dimensional Cartesian coordinate system, the preset bolt hole positions of the FRP multi-cavity profile are retrieved as physical stiffness hard points. Using the physical stiffness hard points as the dividing line, the three-dimensional point cloud data is divided into several independent standard segment units along the longitudinal direction.

[0070] The three-dimensional point cloud data within each standard segment unit is projected onto a plane perpendicular to the profile axis to extract the true profile point set of the cross section.

[0071] Surface Design Based on Theory A local three-dimensional Cartesian coordinate system is established, and the length extension direction of the FRP multi-cavity profile is defined as the axial direction. The cross-sectional width direction perpendicular to the axial direction is defined as the transverse direction. The height direction is defined as the normal direction. Retrieve the pre-set bolt hole positions used for fixing the FRP multi-cavity profile design in the axial direction. The design coordinate positions, due to the extremely high constraint characteristics of bolted connections after installation, are stress concentration sources leading to the forced assembly effect. These discretely distributed coordinate positions are defined as physical stiffness hard points with high bending stiffness. This segmentation method conforms to the analysis logic of beam elements in mechanics of materials, with supports as the boundaries. It uses two adjacent physical stiffness hard points as the basis for segmentation. The coordinates of (i.e., two adjacent rows of bolt holes) are the longitudinal boundary, and the three-dimensional point cloud data is used as the boundary. Along the axial direction Physical cutting An independent standard segment unit Each standard segment unit This represents the physical range where independent suspension or bulging deformation may occur under the forced constraint of bolts.

[0072] For each standard segment unit The cross-section at the geometric center of the unit is selected as the projection reference plane. ; Traverse all discrete point data within this unit, denoted as ,in Indicates the first [unit] in this unit Each data point retains its horizontal coordinate. with normal coordinates Keep it unchanged, and change its axial coordinates. Unified mapping to the projection reference plane By adjusting the axial coordinates, the axial position differences are eliminated, and the three-dimensional spatial point set is reduced and compressed into a two-dimensional planar point set. A point cloud slicing algorithm is used to denoise and extract boundaries from the two-dimensional planar point set. Specifically, a statistical filtering algorithm is used to calculate the boundary values ​​for each point. The average distance to its neighborhood points is used to remove outliers with an average distance greater than the standard deviation threshold; Alpha-Shape (Alpha-Shape) is employed. The shape-based algorithm extracts edge features. The principle of this algorithm is to set a rolling circle radius. The rolling circle is made to roll outside the point set. When two points of the rolling circle touch and there are no other data points inside the circle, the line segment connecting these two points is determined to be the boundary line segment. By traversing all point sets, this algorithm can automatically identify the topological structure of the point sets, thereby separating dense solid regions from sparse background regions. It accurately reconstructs a closed geometric curve that reflects the true cross-sectional shape of the standard segment unit after stress release, including the outer contour and the shape of the preset bolt hole positions. This closed geometric curve is defined as the true cross-sectional contour point set. .

[0073] In step S1011, establishing physical stiffness hard points based on preset bolt hole positions and dividing the 3D point cloud into independent standard segment units is to accurately align the digital analysis model with the actual physical force transmission path of the structure. This process is indispensable in the entire method because the bolt connection physically forms a high-strength constraint boundary, causing the deformation behavior of the profile to be not continuous along its entire length, but rather exhibiting local beam element characteristics bounded by the anchor points. This analysis is based on the beam element analysis theory in mechanics of materials, namely, that support constraints determine the deformation mode and internal force distribution of the component. Only through segmentation can the subsequent analysis of the deformation of the suspended or bulging structure be ensured to conform to the actual mechanical behavior of the precast component under strong constraint conditions, thereby avoiding the obscuring of key local geometric features due to overall averaging.

[0074] Step S1012: Perform geometric center fitting based on the moment of inertia of the cross section on the set of true contour points of the cross section to generate the actual centroid trajectory line;

[0075] The theoretical neutral axis of the FRP multi-cavity profile is constructed, and the installation normal deviation value and the section torsion angle value are calculated by comparing the spatial position of the actual centroid trajectory line with the theoretical neutral axis.

[0076] For each standard segment unit The corresponding true profile point set of the cross section Perform geometric property analysis. This is based on the true contour point set of the cross-section. The spatial morphology objectively reflects the initial manufacturing defects inherent in FRP multi-cavity profiles after demolding, necessitating the calculation of their geometric centroid. The specific process is as follows: using the polygon vertex summation method, the discrete points constituting the closed contour are arranged in a counter-clockwise order. A directed trapezoid or triangle is constructed using the coordinates of adjacent contour points. The total area of ​​the closed region is calculated by accumulating the cross product of the coordinates of adjacent points. Simultaneously, the product of the coordinates of adjacent contour points and their differences is accumulated and integrated to obtain the area of ​​the closed region relative to the coordinates of the adjacent contour points. shaft and The static moment of the axis; by dividing the calculated static moment value by the total area of ​​the closed region, the geometric centroid coordinates of the cross section under the current real-world condition can be accurately determined. , This indicates the geometric center position of the true profile point set of the cross-section along the width direction. This indicates the geometric center position of the set of points representing the true profile of the cross-section along the height / normal direction. All... The geometric centroid coordinates obtained from the standard segment elements are connected in axial order, and a continuous spatial curve is generated through spline interpolation, which is defined as the actual centroid trajectory line. Retrieve the theoretically designed surface The line connecting the geometric centers of the cross-section under ideal design conditions is extracted as the theoretical neutral axis. And extract the axis parallel to the width direction of the cross section in its local coordinate system as the horizontal axis of the theoretical cross section. That is, the horizontal main axis direction. In each standard segment unit... Axial direction (i.e., the direction of profile length extension) The position of the geometric midpoint is determined on the [structure / structure], and this position is the location of the constraint points at both ends of the element. The intermediate coordinates on the axis typically correspond to the extreme region of springback deformation; on the actual centroid trajectory line... Extract the feature point corresponding to the axial coordinate of the midpoint position, and calculate the distance from the feature point to the theoretical neutral axis. The vertical Euclidean distance, which is the installation normal deviation value. This parameter quantifies the degree of deviation of the profile from the design position in the normal direction and is the main geometric factor causing fluctuations in the adhesive layer thickness. Principal component analysis (PCA) is used to analyze the true profile point set of the cross-section. The spatial distribution covariance matrix is ​​subjected to eigenvalue decomposition, and the direction of the maximum variance is extracted as the actual principal axis of inertia. This direction mathematically corresponds to the direction of the first principal component of the point set. Since calculating the direction of the first principal component of the point set using PCA is a mature existing technique, the specific algorithm process will not be elaborated here. Instead, we will compare it with the horizontal axis of the theoretical cross-section. The included angle between the two sides is the cross-sectional torsion angle value that characterizes the profile's torsion around its axis during transportation or installation. This parameter reveals the torsional misalignment between the profile and the segment, which is a potential cause of interfacial shear stress concentration after installation.

[0077] Step S1012, which involves fitting the actual centroid trajectory and calculating the installation normal deviation and cross-sectional torsion angle, aims to quantify the initial geometric defects objectively generated during the manufacturing and transportation of FRP multi-cavity profiles. This step is crucial because ignoring these initial deviations would lead to the system incorrectly assuming the profile is in an ideally straight state, thus significantly underestimating the degree of geometric mismatch during actual installation. The analysis is primarily based on the static moment principle in cross-sectional geometry to accurately pinpoint the centroid position. Principal component analysis is used to perform eigenvalue decomposition on the covariance matrix of the cross-sectional point cloud. By calculating the angle between the principal axis of inertia and the theoretical axis, the spatial torsion posture of the profile relative to the design reference is mathematically revealed precisely, providing quantitative data for subsequent physical correction.

[0078] like Figure 8 The diagram shown illustrates the geometric inversion of the chord vector and the generation of the envelope of the variable-rate void twist entity.

[0079] Reference Figure 8 In the chordal geometric inversion process of step S1013, the figure shows... The physical stiffness of the hard point is shown in the figure. The diagram shows the physical chord length connecting the two hard points. The actual centroid trajectory line is shown in the diagram. The diagram shows the actual measured sagittal height. The actual physical radius of curvature is derived. During the solid envelope generation process in step S1014, the diagram shows... The corrected axis is shown in the diagram. The diagram shows the normal deviation. The cross-sectional torsion angle is shown in the figure. Reconstruct the entity envelope for the final generated variable-rate void twist.

[0080] Reference Figure 8 In the upper part, for each standard segment element, the physical stiffness hard points at both ends of the element along the axial direction are extracted. The three-dimensional spatial coordinates. Because the bolted connection physically restricts the relative displacement of the ends, it forces both ends of the profile to be in contact with the tube segment; therefore, connecting these two... Construct a physical chord with a fixed and indeformable geometric length. In the actual centroid trajectory line Above, search for distance from the physical chord length The geometric vertex with the largest vertical distance is used to measure this distance as the actual sag. Introducing the plane section assumption from the mechanics of materials, based on the chord shown in the diagram... With Arrow Based on the geometric relationships, the true physical radius of curvature of the standard segment element under the released pultrusion residual stress state after demolding is derived. This parameter quantitatively characterizes the natural bending morphology of FRP multi-cavity profiles without external force constraints.

[0081] Step S1013: Within the standard segment unit, connect the anchor points at both ends to construct an indeformable physical chord length, and measure the vertical distance from the arch top of the actual centroid trajectory line to the physical chord length to obtain the actual sagittal height;

[0082] By introducing the plane section assumption of mechanics of materials, and performing chord vector geometric inversion based on the physical chord length and the actual chord height, the true physical radius of curvature is derived.

[0083] For each standard segment unit Extract the unit along the axial direction Physical stiffness hard points at both ends The three-dimensional spatial coordinates are the preset bolt hole coordinates determined in the previous steps. Based on the geometric principle that two points determine a straight line, a straight line segment connecting the physical stiffness hard points at both ends of the unit is generated in the local three-dimensional Cartesian coordinate system. Since the bolt connection physically restricts the relative displacement of the ends, it forces the two ends of the profile to be in contact with the tube segment. This straight line segment is defined as a physical chord with a fixed geometric length and no deformation. In the actual centroid trajectory line Above, search for locations located within the standard segment unit and at a distance from the physical chord length. The geometric vertex with the greatest vertical distance, i.e., the location of the springback dome, is measured to the physical chord length from that geometric vertex. The vertical Euclidean distance is defined as the actual sag that characterizes the maximum springback amplitude of the profile within that local unit. Introducing the plane section assumption from mechanics of materials, and based on the chord-vector geometric relationship theorem, using the formula... By performing chordal geometric inversion calculations, the true physical radius of curvature of the standard segment element under the condition of releasing pultrusion residual stress after demolding can be derived. This parameter quantitatively characterizes the natural bending shape of FRP multi-cavity profiles without external force constraints. By comparing this value with the actual curvature radius of the shield tunnel segment, it can accurately reproduce the geometric mismatch phenomena commonly seen in engineering, such as upturned ends, topped middle, or partially suspended sections. This provides accurate geometric input for subsequent calculation of the initial bending stress caused by forcibly eliminating this mismatch.

[0084] In step S1013, the derivation of the true physical radius of curvature through chord-vector geometric inversion is to restore the natural stress-free form of the FRP multi-cavity profile after demolding, when the residual pultrusion stress is released. This step is crucial in the methodology because the curvature difference between the natural form of the profile and the tunnel segment form is the physical source of the forced assembly stress. Directly using the designed curvature will fail to capture the prestress state caused by process springback. The analysis is based on the circular arc geometry theorem, that is, a fixed chord length and a measured vector height can uniquely determine the radius of a circular arc. Combined with the plane section assumption, the profile is treated as an elastic body, thus accurately obtaining its true physical parameters in the free state through geometric inversion, ensuring that subsequent stress calculations are based on the true physical benchmark.

[0085] Reference Figure 8 The lower half utilizes the actual physical radius of curvature. Correcting the axial base curvature, a corrected axis is generated by fitting and generating a model that reflects the natural springback camber. Based on this, Based on this, a local coordinate system is constructed. Homogeneous transformation matrix for pose reconstruction of cross section: using cross section torsion angle The driving section generates rigid body torsion about the axial direction, utilizing the normal deviation. The driving section generates a rigid body displacement along the normal direction. This displacement occurs along the corrected axis. Perform a solid sweep operation to generate a variable-rate torsion reconstructed solid envelope that possesses both axial curvature characteristics and axial torsion and normal offset characteristics. This enables the precise digital reconstruction of the free initial shape of FRP profiles before they are subjected to bolt force.

[0086] Step S1014: Correct the axial base curvature of the FRP multi-cavity profile using the real physical radius of curvature, and superimpose the installation normal deviation value and the cross-sectional torsion angle value on this basis to generate a variable rate void torsion reconstruction solid envelope, and use the variable rate void torsion reconstruction solid envelope as the corrected theoretical design surface.

[0087] Using the true physical radius of curvature The axial foundation curvature of the FRP multi-cavity profile is physically corrected by means of: based on the local three-dimensional Cartesian coordinate system established in step S1011, maintaining each standard segment unit. Physical stiffness hard points at both ends The three-dimensional coordinate position remains unchanged, with the actual physical radius of curvature. Using geometric constraint parameters, a unique circular arc curve connecting the two hard points of the unit is fitted in three-dimensional space. This circular arc curve is defined as the corrected axis reflecting the natural springback camber state of the FRP multi-cavity profile after stress release. Based on this, using the corrected axis... As a reference for the spatial scanning path, construct a 4×4 homogeneous transformation matrix for the local coordinate system. The pose of the cross section is reconstructed. The matrix... The specific construction form is as follows:

[0088]

[0089] Among them, the upper left corner of the matrix Submatrix using cross-sectional torsion angle values Construct around the axis The rotational transformation drives the cross-section to generate rigid body torsion to reproduce torsional deformation; the translation vector in the fourth column of the matrix utilizes the installation normal deviation value. filling The component drives the cross section to generate rigid body displacement along the normal direction to compensate for the installation clearance. This is achieved through the corrected axis. Apply the homogeneous transformation matrix sequentially to all cross sections. A coordinate transformation is performed, and the transformed discrete sections are used as control sections. Solid lofting or sweeping operations are then performed to generate a new three-dimensional solid model that retains the cross-sectional geometric features, including the combination of the inner and outer contours of the FRP multi-cavity profile in the design drawing, and also possesses the curvature features that vary along the axial direction and the spatial features of torsion around the axial direction. This model is defined as the variable-rate torsion reconstruction solid envelope. Since generating a 3D envelope surface using multi-section control points for solid lofting or sweeping is a mature existing technique in computer graphics, the specific surface interpolation algorithm process will not be elaborated here. The variable-rate torsion reconstructs the solid envelope. As the modified theoretical design surface This enables the digital and precise reconstruction of the free initial shape of the FRP profile before it is subjected to bolt force, laying the geometric foundation for the subsequent step S202 to calculate the energy and internal force required to force this free shape onto the surface of the segment.

[0090] In step S1014, generating the variable-rate torsion reconstruction entity envelope using modified parameters is to construct a digital twin model of the profile that explicitly includes all geometric deviations, curvature variations, and torsional characteristics. This step is indispensable because it provides accurate geometric boundary conditions for calculating the energy required to forcibly compress the profile from a free state onto the segment surface. Without this reconstruction model, the forced assembly process cannot be realistically reproduced. Its analytical basis lies in the homogeneous transformation matrix theory of spatial kinematics. By constructing a transformation matrix containing rotational and translational components, the cross-sectional point set is mapped to rigid body motion along the modified axis, thereby reconstructing a three-dimensional spatial form in digital space that is completely consistent with the physical entity, laying the geometric foundation for subsequent mechanical simulations.

[0091] Step S102: Import the corrected theoretical design surface into the coordinate system where the micro-morphology data is located, and extract the center axis vector of the preset bolt hole of the FRP profile and the center axis vector of the constructed rebar hole on the inner surface of the segment.

[0092] Based on the preset bolt hole center axis vector and the constructed rebar hole center axis vector, a coaxiality deviation objective function is constructed, and a constrained least squares registration is performed to solve the optimal rigid body transformation matrix, driving the modified theoretical design surface to undergo pose transformation and locking the virtual pre-assembly pose.

[0093] The modified theoretical design surface Import the 3D point cloud data of the inner surface of the shield tunnel segment obtained in step S101. In the local three-dimensional Cartesian coordinate system, based on The digital model data identifies the geometric features of all bolt holes pre-set in the profile flange or base plate during the design phase. The geometric center line of each hole is extracted and defined as the vector of the pre-set bolt hole center axis, forming a set of profile axes. This vector represents the installation reference of the FRP profile under ideal processing conditions. The three-dimensional point cloud data... A cylinder fitting algorithm based on random sampling consistency is executed to identify cylindrical point cloud clusters on the inner surface of the tunnel segment where drilling or chemical anchoring has been completed. The central axis direction of each fitted cylinder is calculated and defined as the vector of the central axis of the drilled rebar holes, forming a set of tunnel segment axes. This vector represents the actual anchoring path affected by on-site construction errors. Based on this, a mathematical model of the rigid body transformation matrix is ​​constructed: in three-dimensional space, any movement or rotation of the FRP profile relative to the segment can be represented by a... rigid body transformation matrix Unique representation; the matrix consists of a Rotation submatrix and Translation vector Composed of, where the rotation submatrix Includes rotational degrees of freedom around the three axes of the global coordinate system, and translation vectors. Includes along the global coordinate system , , The three translational degrees of freedom of the axis, here , , The axis system refers to the three-dimensional point cloud data. The global spatial reference frame in which it is located is distinct from the profile local coordinate system defined in step S1011. To solve for these six unknown parameters, a least-squares objective function based on physical hard points is constructed: from... Extract the first The center point coordinates of each hole With axial unit vector , constitute a subset of the source vector ;from Extract the corresponding first Coordinates of the center point of each anchor hole With axial unit vector , constitute a subset of the target vector Construct the coaxiality deviation objective function. This function is defined as the weighted sum of squares of the deviations in axial distance and the axial angle between all corresponding hole pairs, and its mathematical expression is: ,in, This indicates the serial number of the hole pair involved in registration, with a value ranging from 1 to... , This represents the total number of pairs of pre-set bolt holes on the FRP profile that can form a valid correspondence with the rebar holes on the segment. Indicates the first FRP profile The geometric center coordinates of a preset bolt hole in the local coordinate system Indicates the first FRP profile The axial unit direction vector of a preset bolt hole, Indicates the first segment on the tube Fitted center coordinates of each rebar hole in the global coordinate system Indicates the first segment on the tube The axial unit direction vector of each anchor hole, and These are the weighting coefficients for the distance and angle deviation terms, respectively. A constrained least-squares registration operation is performed to lock the unique pose: a singular value decomposition algorithm or a Levenberg-Marquardt iterative algorithm is used to apply the above objective function. Nonlinear optimization is performed to find the solution. The solver continuously fine-tunes the matrix. The six degrees of freedom parameters in the objective function It converges to a local minimum. The final matrix obtained at this point... This is the optimal rigid body transformation matrix. This optimal rigid body transformation matrix is ​​then applied to the modified theoretically designed surface. At all geometric nodes, the overall pose transformation is driven in virtual space. At this point, the FRP profile is in a mathematical equilibrium state where all bolt holes are aligned as much as possible and relative sliding is no longer possible. This state physically corresponds precisely to the final static state of the profile after the worker fastens it onto the pipe segment and tightens all bolts, forcibly constraining it to the surface of the pipe segment. This mathematically calculated and locked spatial state is defined as the unique physical spatial state of the FRP multi-cavity profile under actual installation conditions, i.e., the virtual pre-assembled pose. .

[0094] Step S103: Under the virtual pre-assembly pose, calculate the directed Euclidean distance between the bottom surface of the corrected theoretical design surface and the inner surface of the tube segment, construct the global interface gap topological field, and divide the interface into various mechanical feature topological regions based on a preset threshold. Each mechanical feature topological region includes a physical interference region, an effective bonding region, and a structural void region.

[0095] Based on virtual pre-assembly pose Freeze the modified theoretical design surface With the three-dimensional point cloud data The relative spatial position, specifically the optimal rigid body transformation matrix. Acting on the modified theoretical design surface Update the 3D spatial coordinates of all geometric vertices relative to the 3D point cloud data. The positional relationships remain constant, forming a static computational baseline scene, upon which subsequent analysis is based. Extraction The bottom surface region used for bonding with the tunnel lining segments is discretized using a finite element mesh generation algorithm. A set of triangular facets composed of n nodes; extract the nth node. Spatial coordinates of discrete grid nodes And read the normal direction of the face where the node is located as the local surface normal vector. For each discrete grid node As the emission source, along its corresponding local surface normal vector Virtual detection rays are projected onto the point cloud model of the tunnel segment. A spatial bounding box tree algorithm is used to accelerate the calculation of the ray and its corresponding data. Geometric intersections of a discrete point cloud fitted surface Solution point With point The Euclidean distance between them. If the ray vector and the normal vector are in opposite directions, that is, the intersection point is inside the FRP solid, the distance is defined as negative; otherwise, it is positive. Thus, the _____ is obtained. Discrete gap values ​​of each node To transform discrete data on a three-dimensional curved surface into a two-dimensional continuous field, a parametric mapping plane is constructed on the bottom surface of the FRP profile. , This represents the horizontal and vertical parameter coordinates; specifically, it involves discretizing the mesh nodes. The geodesic arc length relative to a preset zero point on the profile cross-section outline is defined as the transverse parametric coordinate. This represents the unfolded position along the width of the profile; the node The orthogonal projection distance on the central axis of the profile is defined as the longitudinal parameter coordinate. This represents the axial position along the length of the profile. The three-dimensional coordinates are represented by a length-preserving mapping algorithm. Convert to two-dimensional parametric coordinates This allows us to construct a discrete sample set containing both location and numerical values. .

[0096] Building upon this foundation, the Kriging interpolation method from geostatistics is introduced to reconstruct the global field. Specifically, based on all discrete gap data point pairs on the parameterized plane, the experimental semivariogram is statistically calculated. This function quantitatively describes the spatial correlation of gap values, characterizing the degree of variation in gap error as the distance between two points increases; generally, the greater the distance, the lower the correlation and the greater the degree of variation. A theoretical model conforming to physical laws (such as a spherical model or an exponential model) is selected to curve-fit the experimental semivariogram, thereby obtaining structural parameters describing the spatial continuity of the global gap, such as nugget value, sill value, and range. Based on this theoretical model, a system of Kriging equations satisfying the conditions of unbiased estimation and minimum estimation variance is constructed. The weighting coefficients of each known sampling point to the unknown prediction point are solved, and then the gap values ​​at unsampled locations are calculated through a weighted linear combination. Since the specific derivation of the variogram, model fitting, and equation solving algorithms in the Kriging interpolation method are existing mature technologies in geostatistics, the specific calculation formulas are not elaborated here. Through the above process, the sparse discrete measurement point data is reconstructed into a continuously distributed global interface gap topological field covering the entire bottom surface. Based on the rheological test data of the selected interfacial bonding material, two scalar thresholds with units consistent with the point cloud data were pre-set, including the optimal lower limit threshold for construction thickness. With upper limit threshold , The minimum gap that the corresponding material can wet the interface. The critical gap quantity corresponding to the material flowing or forming air pockets under its own weight. Based on the global interface gap topological field. The numerical distribution characteristics divide the contact interface into three non-overlapping topological regions. When a certain region's... When the value is less than zero, it is marked as a physical interference region. This represents the FRP profile bottom surface cutting into the segment solid in the current frozen pose; when The value is in and When the time interval is reached, mark it as the effective bonding area. The characterization gap is moderate; when The value is greater than At that time, it was marked as a structural void region. Excessive gaps in the adhesive layer can lead to problems such as insufficient adhesive, hollow areas, or excessively thick adhesive layers causing creep.

[0097] Steps S102 to S103 involve performing virtual pre-assembly based on hard-point constraints and constructing a ternary topological gap field. This is to accurately reproduce the actual spatial position of the FRP profile after it is forcibly positioned by bolts in digital space and to quantify the geometric mismatch characteristics of the interface. This process is indispensable because the installation position of the rigid FRP profile is not determined by the fit between surfaces, but is entirely controlled by the high-rigidity bolt connection. If this physical constraint is not locked and morphological comparison is performed directly, the calculated gap distribution will be completely different from the actual working condition. The analysis is based on the theory of multi-constraint rigid body transformation and the principle of minimizing coaxiality deviation, using mathematical algorithms to find the optimal pose that aligns all bolt holes. Based on this, it is necessary to further transform the complex micro-gap into topological partitions with engineering guidance significance. This is based on the ray casting algorithm in computational geometry and the thickness threshold theory in rheology. The former accurately quantifies the degree of intrusion or void at each micro-element, while the latter divides the interface into interference zones that need to be ground, effective zones suitable for bonding, and void zones that must be filled, according to the physical limits of the adhesive. This provides a unique geometric input base map for subsequent mechanical simulation and generation of differentiated construction instructions.

[0098] The design method for FRP multi-cavity reinforcement structures in subway tunnels also includes the following steps:

[0099] Step S200: Based on the global interface gap topological field and the topological regions of each mechanical feature, construct a discretized stiffness data matrix, perform forced displacement simulation of bolt fastening condition in the physical interference zone, calculate the initial bending stress field and contact pressure distribution, and perform ternary logic to identify the interface mechanical defect set.

[0100] The specific process of step S200 includes:

[0101] Step S201: Based on the gap value distribution in the global interface gap topological field, the effective cementation zone and the structural voiding zone are given a rigid contact property with a maximum value by using the inverse proportional function relationship, and a discretized stiffness data matrix is ​​constructed.

[0102] Based on global interface gap topological field Construct a discretized stiffness data matrix to describe the mechanical characteristics of the interface. The specific operation is as follows: traverse each discrete data point in the global interface gap topology field, corresponding to the grid node index of the previous step. Read its discrete gap value Define the shear modulus constant of the adhesive layer. This value is obtained by consulting the structural adhesive material property table or by laboratory shear testing. The local shear stiffness value at this point is calculated using the following logical branches. And fill the matrix: for effective cemented regions and structural void regions, i.e. Based on the physical principle that the thicker the gap, the weaker the resistance to slippage, an inverse proportional equation is used. Calculate stiffness values; for the physical interference zone, i.e. Since the FRP profile and the pipe segment are in solid contact here without an adhesive layer, and the connection is rigid, the stiffness value at this point is directly assigned to the preset maximum value. For example, take This is used to characterize the rigid contact properties. Through the above traversal calculations, a non-uniform physical property matrix is ​​output, corresponding one-to-one with the geometric nodes of the FRP bottom surface. This matrix clearly quantifies the distribution of the softness and hardness at each point on the interface.

[0103] Step S202: Within the physical interference zone, a forced deformation vector is constructed to simulate the normal displacement load generated by bolt tightening. The initial bending stress field is calculated by combining the longitudinal bending elastic modulus and cross-sectional geometric coefficient of the FRP multi-cavity profile. The contact pressure distribution is calculated by combining the equivalent compressive stiffness of the vertical support wall panel of the FRP multi-cavity profile.

[0104] Based on the generalized form of Hooke's Law, stress-pressure transformation calculations are performed under bolt tightening conditions. This process transforms the physical tightening action into matrix operations for solution. Specifically, a forced deformation vector is constructed. Simulated bolt tightening: in the physical interference zone Inside, although the main function of the bolts is to tighten the loose area, the full-circumferential clamping force they generate will force the FRP profile to press tightly against the protruding part of the segment, i.e., the interference point. In order to simulate this forced enveloping force state of the protrusion, the gap values ​​of all nodes in the interference zone are extracted. (Negative values), take their absolute values ​​to construct a forced deformation vector. The elements in the vector , For the node At this point, a single-point forced displacement must be applied to eliminate geometric interference; in the virtual model of step S103, a negative gap value indicates that the FRP entity penetrates into the segment, but in physical reality, the FRP profile is supported on the segment protrusion; to eliminate this gap and achieve a fit, the bolt must drive the FRP profile downwards, and the distance it moves is numerically exact equal to the absolute value of the virtual penetration depth. Calculate the initial bending stress field. Calculate the internal forces of FRP after it is stretched and bent: Introduce the longitudinal flexural modulus of elasticity of the FRP profile. (Determined by the material parameters of the pultrusion process), using the discretized bending normal stress formula Calculate the internal stress. In the formula, For the node Internal stress at the location, To calculate the characteristic length of the computational element, in the discrete mesh established in step S103, the computational nodes... The average Euclidean distance between it and all its first-order topological neighbors. The geometric coefficients related to the cross-sectional shape of the profile are calculated using the following formula: ,in The vertical distance from the neutral axis of the profile section to the bottom surface, calculated in step S1012. The boundary constraint constant based on plate and shell theory is taken as 3 for the local forced displacement under bolt point constraint. The initial bending stress field data covering the entire domain are output through point-by-point calculation using this equation. Calculate the contact pressure distribution. Calculate the force exerted on the FRP segment by the bolts: Based on the principle of action and reaction, when the bolts pull the FRP towards the segment, the segment surface experiences a reverse compression from the FRP. Using the formula... Calculate. In the formula, The local compressive stiffness of the FRP profile in the direction perpendicular to the tube segment is obtained by referring to... Figure 1 and Figure 3 The FRP multi-cavity cross-section shown identifies all the vertical supporting wall panels inside the profile, namely the sidewalls and internal partitions that constitute the multi-cavity structure. Mechanically, these are collectively referred to as webs or vertical ribs. These vertical wall panels are the core components resisting bolt tightening pressure. The equivalent compressive stiffness of these supporting wall panels per unit area is calculated using the following formula: ,in For the transverse elastic modulus of FRP, It is the sum of the thicknesses of all vertical supporting wall panels within a unit width. The height of the profile is given. This equation is used to output the surface contact pressure distribution of the tube segment. .

[0105] Step S203: Perform ternary logic discrimination on the initial bending stress field, contact pressure distribution and discretized stiffness data matrix to identify the interface mechanical defect set. The interface mechanical defect set includes the stress concentration defect set and the substrate crushing defect set located in the physical interference zone, as well as the stiffness degradation defect set located in the structural voiding zone.

[0106] The multiphysics simulation results output in step S202 are subjected to threshold-based ternary logic discrimination to comprehensively identify structural safety hazards in a digital manner. Stress concentration discrimination, i.e., FRP body safety, is performed on the physical interference zone; specifically, a long-term allowable flexural strength threshold for the FRP composite material is set. Traversing the initial bending stress field Stress value at each discrete point in Execute logical judgment, if Then the coordinates of that point are marked as 1 and included in the stress concentration defect set. This defect indicates that the secondary internal forces generated within the FRP profile to achieve forced bonding alone have exceeded the material's safety limits, posing a risk of cracking upon installation. For the physical interference zone, a substrate crushing assessment, i.e., segment interface safety, is performed by setting a local compressive strength threshold for the shield tunnel segment concrete. Traversing the contact pressure distribution on the surface of the tube segments Pressure value at each discrete point in Execute logical judgment, if If the coordinates of this point are then marked as 1, it will be included in the set of base material crushing defects. This defect indicates that at the physical interference point, the FRP profile exerts excessive local pressure on the concrete segment, which can easily lead to local crushing or spalling of the concrete surface, thereby damaging the reinforced foundation. This identification result will serve as a mandatory constraint condition for generating the grinding command in the subsequent step S301. Stiffness degradation is assessed at the entire contact interface, specifically by setting a minimum shear stiffness threshold to ensure the coordinated stress distribution between the FRP and concrete. Iterate through the stiffness matrix generated in step S201. Local shear stiffness value Execute logical judgment, if If the coordinates of this point are then marked as 1, it will be included in the set of stiffness degradation defects. Such defects are typically concentrated in structural voids, indicating that the adhesive layer is too thick due to structural voids, resulting in a soft interface connection. The FRP cannot effectively share the load of the segments, thus constituting an ineffective reinforcement area. , as well as All data were obtained based on full-scale mechanical property calibration tests of FRP multi-cavity profiles and shield tunnel segment concrete. Specifically, the ultimate bending strength of the FRP profile was determined through a four-point bending failure test, using the same loading method as the actual working conditions. The benchmark for value selection; the crushing load on the surface of the tunnel lining segment is determined by the local contact loading test of FRP-concrete as the benchmark. The benchmark for value selection; the critical stiffness at interface failure determined by the FRP-concrete double shear bond-slip test is used as the reference. The benchmark for the value.

[0107] Steps S201 to S203, which involve constructing a discretized stiffness data matrix and performing forced displacement simulation and ternary logic defect identification, aim to map microscopic geometric gap data to macroscopic mechanical stress distribution and interface stiffness characteristics. The rationale for this series of steps is that the gap thickness directly determines the bonding hardness of the interface, and the forced displacement to eliminate the gap generates a significant initial internal force. Simulation is necessary to identify which areas will fail due to excessive stress or insufficient bonding. The analysis is based on the generalized Hooke's law, converting displacement into stress. An inverse physical relationship is used to establish a mapping between gap and shear stiffness. Combined with laboratory-measured material failure thresholds, this allows for precise location and digital characterization of three types of safety hazards: substrate cracking, base material crushing, and stiffness degradation.

[0108] The design method for FRP multi-cavity reinforcement structures in subway tunnels also includes the following steps:

[0109] Step S300: For the set of interface mechanical defects, calculate the grinding volume required to eliminate interference and the medium volume required to fill voids, generate an interface adaptive compensation strategy, and calculate the effective cross-sectional moment of inertia.

[0110] Step S301: For the physical interference zone corresponding to the set of stress concentration defects and the set of base material crushing defects, with the goal of eliminating contact interference, calculate the volume of concrete to be removed from the surface of the segment and generate stress relief grinding volume data.

[0111] For stress concentration defect sets Set of crush defects in substrate A pretreatment scheme for the pipe segment surface designed to eliminate physical interference was constructed, specifically by extracting these two sets in the physical interference region. This involves all discrete nodes within the grid. To address the issue that single-point distance data cannot directly guide volumetric grinding, a discrete infinitesimal element integration algorithm based on grid topology is introduced to precisely define the topological infinitesimal area of ​​each node. : Identify the current discrete node For all first-order adjacent triangular faces sharing a vertex, calculate the geometric area of ​​each triangular face. Based on the finite element method's nodal force distribution principle, add one-third of the area of ​​each adjacent triangular face to the node. This allows us to obtain the effective governed area of ​​the node on the discrete surface. Determine the theoretical cutting depth: Read the discrete gap values ​​at each point. The absolute value of this value is defined as the theoretical cutting depth. The physical basis for defining it as such lies in the principle of geometric interference equivalence. Specifically, under a virtual frozen pose, a negative gap value quantifies the geometric depth of the FRP solid intrusion into the segment solid. To relieve the resulting contact stress and restore both to the ideal tangential contact state, i.e., the critical state of zero contact pressure, an equal amount of segment matrix material must be removed in physical space. This is the minimum geometric removal required to eliminate rigid interference. Safety checks and volume generation are performed: To prevent damage to the steel reinforcement cover of the tunnel lining segments due to excessive grinding, a grinding safety threshold is set. For example, take 20% of the design protective layer thickness of the tunnel lining segments. Then calculate the grinding volume commanded at that point. ;like If this occurs, a manual review alarm is triggered. Finally, the volumes of all valid grinding points are summed across the entire domain to generate stress-relieving grinding volume data.

[0112] Step S302: For the structural void zone corresponding to the stiffness degradation defect, the discrete infinitesimal integral algorithm is used to perform volume integration on the gap field, calculate the total cumulative grouting volume data of the whole domain and generate variable thickness filling volume data.

[0113] Stress-relieving grinding volume data, total grouting volume data accumulated across the entire domain, and variable-thickness filling volume data are used as interface adaptive compensation strategies.

[0114] For stiffness degradation defect set A variable-thickness medium filling scheme was constructed to ensure the density of the interface filling. The structural void regions in the global interface gap topological field were locked. The discrete infinitesimal integral algorithm is used: traversing every discrete node in the region. The topological element area of ​​the node is calculated using the same method as in step S301. Extract the positive discrete gap values. The theoretical adhesive layer thickness is based on the principle of continuous medium filling. A positive gap value quantifies the physical void height between the FRP bottom surface and the inner surface of the segment. To ensure that shear force can be continuously transmitted between the interfaces without interruption, thus repairing stiffness degradation, the filling medium must completely occupy this physical void. This refers to the physical thickness of the medium required to achieve full grout filling. Calculate the theoretical filling volume required for this micro-element region. Based on the cross-sectional structural characteristics of FRP profiles, differentiated instructions are generated: for closed box-shaped cross-sections, the total volume after summing the entire region is calculated. Defined as the total grouting volume control threshold, this data, as a single volume scalar, will serve as the input benchmark for setting the quantitative cutoff threshold of the grouting equipment in subsequent step S402. This is to prevent excessive grouting pressure from causing bulging of the profile, as grouting is for filling interface gaps. For open groove cross-sections, this specifically involves adapting the adhesive application process to maintain the theoretical filling volume of each node. Based on the discrete spatial distribution characteristics, volume sequence data distributed along the profile axis is constructed. This sequence precisely describes the difference in adhesive required at each point on the adhesive application path. It will be directly used as the input reference for back-calculating the variable-speed motion trajectory of the adhesive application robot in the subsequent step S402, ensuring that the robot moves slowly and applies more adhesive in areas with large gaps, and moves quickly and applies less adhesive in areas with small gaps, thereby achieving precise filling of non-uniform void areas.

[0115] Step S303: Based on the distribution characteristics of the global interface shear stiffness, calculate the global weighted average shear stiffness and solve the composite structure cooperative stiffness correction coefficient.

[0116] The effective moment of inertia of the FRP multi-cavity profile is obtained by reducing the theoretical moment of inertia of the composite structure by using the composite structure synergistic stiffness correction coefficient.

[0117] Based on the distribution characteristics of the global interface shear stiffness, a regression analysis method using experimental data is employed to determine the cooperative working coefficient, and the cross-sectional design parameters are adjusted accordingly to address the problem that traditional design methods cannot quantify the effects of soft connections and voids. Discretized stiffness data matrix is ​​retrieved. To simplify the complex, non-uniform soft and hard distribution across the entire domain into a macroscopic index, the area of ​​topological infinitesimal elements is utilized. As a weight, the weighted average across the entire domain is calculated using the following formula: This indicator Physically, it characterizes the overall average bonding tightness between the current FRP profile and the segment, and calculates the global weighted average shear stiffness. Synergy coefficients were generated based on experimental scatter regression. Specifically, this involves pre-constructing a characteristic curve of interface stiffness versus synergy coefficient. The construction process involves: producing multiple sets of standard FRP-concrete composite beam specimens in the laboratory; controlling the adhesive coating thickness and fullness to create samples with different interface stiffness states; and conducting four-point bending tests on each set of specimens to measure their combined flexural stiffness. And calculate its stiffness compared with the theoretical rigid connection. The ratio of the two values ​​is used to obtain the true synergy coefficient of the specimen. 'g' represents the specimen number, and the average interfacial stiffness corresponding to that specimen is calculated. This yields a discrete two-dimensional data point set; nonlinear least squares regression analysis is then performed on the scattered points to fit a continuous empirical formula curve. During the design process, the calculated... By directly substituting the formula of the fitted curve, the corresponding composite structure synergistic stiffness correction coefficient can be calculated. Utilization coefficient Theoretical moment of inertia of FRP multi-cavity profile Perform physical quantity reduction and calculate the effective cross-sectional moment of inertia. Its engineering significance lies in mathematically equating a complex nonlinear composite system of FRP-adhesive layer-segment into a single FRP profile with reduced stiffness, thereby enabling the correction in subsequent load-bearing capacity calculations. Substituting into standard material mechanics formulas, the actual deflection and stress after reinforcement are accurately calculated. Theoretical moment of inertia of the cross section. The method of obtaining the value is to extract the geometric contour parameters of the ideal section based on the standardized production design drawings of FRP multi-cavity profiles, and use the parallel axis shifting theorem or CAD section property analysis tools to calculate the bending moment of inertia of the ideal section relative to its own centroidal axis. This value represents the theoretical upper limit of the profile's stiffness under the condition of no manufacturing deviation and no installation defects. The specific solution of the theoretical section moment of inertia is existing technology and will not be elaborated here.

[0118] Steps S301 to S303, which calculate the stress-relieving grinding volume and the variable-thickness filling volume, and determine the composite structure's synergistic stiffness correction coefficient, aim to transform the identified mechanical defects into actionable quantitative construction parameters and structural performance reduction indices. This process is essential because it not only addresses how to eliminate safety hazards through physical removal or filling, but also how to correct theoretical calculation models to reflect the true load-bearing capacity under non-ideal bonding conditions. The analysis is based on the use of discrete infinitesimal integral algorithms to accurately calculate the material volume of the area to be treated, and regression analysis based on experimental data to establish a nonlinear mathematical correlation between the interface average stiffness and the overall synergistic working coefficient, thereby achieving a safe correction from theoretical design to engineering entity.

[0119] The design method for FRP multi-cavity reinforcement structures in subway tunnels also includes the following steps:

[0120] Step S400: The interface adaptive compensation strategy is converted into segment pretreatment instructions and medium filling control instructions, and the reinforcement performance is verified based on the effective cross-sectional moment of inertia, and a safety warning is given;

[0121] Step S401: Convert the stress relief grinding volume data into tool path code of CNC grinding equipment or contour line construction drawing of manual grinding, as a pretreatment instruction for the tube segment surface;

[0122] Grinding volume including global discrete point instructions The stress-relieving grinding volume data is transformed into digital construction execution instructions through coordinate system mapping. For CNC grinding equipment equipped with an automated end effector, a transformation matrix is ​​established between the equipment tool coordinate system and the global coordinate system where the micro-morphology data is located. Traverse each target grinding node in the data packet. Set its spatial coordinates The data is converted into machine tool machining path points, and the theoretical cutting depth corresponding to these points is transformed into the cutting depth parameters of the tool along the normal direction. This generates a G-code sequence that conforms to ISO standards, driving the grinding head to perform variable-depth conformal cutting. For manual processing scenarios, the three-dimensional discrete grinding depth data is projected onto a two-dimensional unfolded plane. A contour line generation algorithm is used to draw a contour line construction drawing containing different color gradients. The extreme value areas and boundary ranges of the grinding depth are clearly marked in the drawing, serving as a visual operation guide for on-site workers using handheld grinding tools. This ensures that the amount of concrete removed from the physical interference zone strictly meets the preset requirements for eliminating contact stress.

[0123] Step S402: Convert the total cumulative grouting volume data of the entire domain into the quantitative cutoff threshold of the grouting pump, and convert the variable thickness filling volume data into the extrusion rate control sequence of the adhesive coating equipment as the medium filling control command;

[0124] The variable thickness infill volume data is converted into medium filling control commands under different construction processes. For FRP profiles with open groove cross-sections, based on the kinematic model of the glue-applying robot, the discrete theoretical infill volume distributed along the profile axis is... Transformed into a time-series glue dispensing rate control signal: maintaining a constant output flow rate of the glue dispensing pump, through volume sequence data. The reverse engineering robot passes through the nodes Instantaneous movement speed on the path segment This is done so that the speed is inversely proportional to the filling demand at that location, i.e., moving slowly where the gap is large and moving quickly where the gap is small, generating a variable speed motion trajectory file. For FRP profiles with closed box-shaped cross-sections, the total cumulative grouting volume data is converted into a quantitative cutoff threshold for the grouting pump and written into the PLC controller of the intelligent grouting equipment; during the grouting process, the cumulative injection volume from the flow sensor is collected in real time. Grouting pressure value with pressure sensor Execute dual closed-loop control logic: when or When the preset safety pressure is exceeded, the shut-off valve is immediately triggered to close, thereby achieving precise quantitative filling of the structural void area.

[0125] Step S403: Using the effective section moment of inertia, recalculate the ultimate bearing capacity of the reinforced segment. If it meets the specification requirements, output the final construction plan; otherwise, issue a safety warning.

[0126] Using the corrected effective section moment of inertia Strengthening effectiveness verification and closed-loop design iteration were performed on FRP-concrete composite structures. Based on the composite beam theory in structural mechanics, a bearing capacity verification equation was constructed. ,in The design bending moment of the tunnel segment under extreme working conditions. This is the distance from the edge of the cross-section to the neutral axis. If the verification results show... If the stress is less than the allowable stress of the material, the reinforcement scheme of the current FRP profile of the given model is deemed qualified for the construction section, and the final construction scheme including grinding and filling instructions is output. If the verification fails, the current design scheme is deemed unable to meet the safety requirements after considering the impact of interface defects. The system outputs a structural safety warning signal, prompting the engineer to intervene manually and take remedial measures such as replacing the reinforcement method or reassessing the load conditions for the risky segment.

[0127] Steps S401 to S403, which transform the compensation strategy into construction instructions and perform reinforcement performance verification based on the effective section moment of inertia, are crucial for ensuring the manufacturability of the digital design scheme and its compliance with final structural safety standards. This stage is indispensable because it forms a closed loop from virtual design to physical construction, guiding on-site operations and providing a safety net for the entire reinforcement system through verification after physical quantity reduction. The analysis primarily relies on path interpolation algorithms in CNC machining to generate execution code, as well as composite beam theory in structural mechanics. By substituting the corrected section properties, the bearing capacity under the ultimate limit state is checked, ensuring that the delivered reinforcement project still meets stringent subway operation safety standards after considering all manufacturing deviations and interface defects.

[0128] Example 2

[0129] A fiber composite material is a composite reinforcement system consisting of a bent pultruded FRP multi-cavity profile as the skeleton, filled with high-strength self-compacting concrete or grout, wrapped with a multidirectional fiber reinforcement layer and coated with a nano-protective layer, and connected with tunnel segments by adhesive bolts to form a composite reinforcement system that works together to bear the load.

[0130] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0131] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0132] The foregoing description is illustrative of the invention and should not be construed as limiting it. Although several exemplary embodiments of the invention have been described, those skilled in the art will readily understand that many modifications can be made to the exemplary embodiments without departing from the novel teachings and advantages of the invention. Therefore, all such modifications are intended to be included within the scope of the invention as defined in the claims. It should be understood that the foregoing description is illustrative of the invention and should not be construed as limiting it to the specific embodiments disclosed, and modifications to the disclosed embodiments and other embodiments are intended to be included within the scope of the appended claims. The invention is defined by the claims and their equivalents.

Claims

1. A design method for a multi-cavity FRP reinforcement structure for subway tunnels, characterized in that, Includes the following steps: The three-dimensional point cloud data of the inner surface of the shield tunnel segment and the theoretical design surface of the FRP multi-cavity profile are obtained, and the global interface gap topological field is constructed to divide the contact interface into various mechanical characteristic topological regions. Based on the global interface gap topological field and the topological regions of various mechanical characteristics, a discretized stiffness data matrix is ​​constructed. Forced displacement simulation of bolt fastening condition is performed in the physical interference zone to calculate the initial bending stress field and contact pressure distribution. Ternary logic is used to identify the interface mechanical defect set. For the set of interface mechanical defects, the grinding volume required to eliminate interference and the medium volume required to fill voids are calculated, an interface adaptive compensation strategy is generated, and the effective cross-sectional moment of inertia is calculated. The interface adaptive compensation strategy is converted into segment pretreatment instructions and medium filling control instructions, and the reinforcement effectiveness is verified based on the effective cross-sectional moment of inertia to provide safety warnings.

2. The design method for a multi-cavity FRP reinforcement structure for subway tunnels according to claim 1, characterized in that, The steps for dividing the topological regions of each mechanical feature include: Based on the three-dimensional point cloud data of the inner surface of the shield tunnel segment and the theoretical design surface of the FRP multi-cavity profile, the elastic rebound mechanism of the pultrusion process and the chordal geometric physical constraints are introduced to perform reverse reconstruction based on the solid shape of the theoretical design surface to obtain the corrected theoretical design surface. The modified theoretical design surface is imported into the coordinate system where the micro-morphology data is located, and the center axis vector of the preset bolt hole of the FRP profile and the center axis vector of the installed rebar hole on the inner surface of the segment are extracted. Based on the preset bolt hole center axis vector and the already constructed rebar hole center axis vector, a coaxiality deviation objective function is constructed. The constrained least squares registration is performed to solve the optimal rigid body transformation matrix, which drives the modified theoretical design surface to undergo pose transformation and locks the virtual pre-assembled pose.

3. The design method for a multi-cavity FRP reinforcement structure for subway tunnels according to claim 2, characterized in that, The step of dividing the topological regions of each mechanical feature further includes: Under the virtual pre-assembly pose, the directed Euclidean distance between the bottom surface of the corrected theoretical design surface and the inner surface of the segment is calculated, a global interface gap topological field is constructed, and the interface is divided into various mechanical feature topological regions based on a preset threshold. Each mechanical feature topological region includes a physical interference region, an effective bonding region, and a structural voiding region.

4. The design method for a multi-cavity FRP reinforcement structure for subway tunnels according to claim 2, characterized in that, The steps for obtaining the modified theoretical design surface include: Based on the local three-dimensional Cartesian coordinate system, the preset bolt hole positions of the FRP multi-cavity profile are retrieved as physical stiffness hard points. Using the physical stiffness hard points as the dividing line, the three-dimensional point cloud data is divided into multiple independent standard segment units along the longitudinal direction. The three-dimensional point cloud data in each standard segment unit is projected onto a plane perpendicular to the profile axis to extract the true profile point set of the cross section. Perform geometric center fitting based on the moment of inertia of the cross section on the set of true contour points of the cross section to generate the actual centroid trajectory line; The theoretical neutral axis of the FRP multi-cavity profile is constructed, and the installation normal deviation value and the section torsion angle value are calculated by comparing the spatial position of the actual centroid trajectory line with the theoretical neutral axis.

5. The design method for a multi-cavity FRP reinforcement structure for subway tunnels according to claim 4, characterized in that, The steps for obtaining the modified theoretical design surface also include: Within the standard segment unit, an indeformable physical chord is constructed by connecting the anchor points at both ends, and the vertical distance from the arch of the actual centroid trajectory line to the physical chord is measured to obtain the actual sagitta. By introducing the plane section assumption of mechanics of materials, and performing chord vector geometric inversion based on the physical chord length and the actual chord height, the true physical radius of curvature is derived. The axial base curvature of the FRP multi-cavity profile is corrected using the actual physical radius of curvature, and the installation normal deviation value and the cross-sectional torsion angle value are superimposed on this basis to generate a variable-rate air-torsion reconstruction solid envelope, which is then used as the corrected theoretical design surface.

6. The design method for a multi-cavity FRP reinforcement structure for subway tunnels according to claim 1, characterized in that, The steps for performing ternary logic to determine the set of interface mechanical defects include: Based on the gap value distribution in the global interface gap topological field, the effective cementation zone and the structural voiding zone are given a rigid contact property with a maximum value by using the inverse proportional function relationship, and a discretized stiffness data matrix is ​​constructed. Within the physical interference zone, a forced deformation vector is constructed to simulate the normal displacement load generated by bolt tightening. The initial bending stress field is calculated by combining the longitudinal bending elastic modulus and cross-sectional geometric coefficient of the FRP multi-cavity profile. The contact pressure distribution is calculated by combining the equivalent compressive stiffness of the vertical support wall panel of the FRP multi-cavity profile. The initial bending stress field, contact pressure distribution, and discretized stiffness data matrix are subjected to ternary logic discrimination to identify the interface mechanical defect set. The interface mechanical defect set includes the stress concentration defect set and the substrate crushing defect set located in the physical interference zone, as well as the stiffness degradation defect set located in the structural voiding zone.

7. The design method for a multi-cavity FRP reinforcement structure for subway tunnels according to claim 6, characterized in that, The steps for calculating the effective cross-sectional moment of inertia include: For the physical interference zone corresponding to the set of stress concentration defects and the set of base material crushing defects, with the goal of eliminating contact interference, the volume of concrete to be removed from the surface of the segment is calculated to generate stress relief grinding volume data. For the structural void zone corresponding to the stiffness degradation defect, the discrete infinitesimal integral algorithm is used to perform volume integration on the gap field, calculate the total cumulative grouting volume data of the whole domain and generate variable thickness filling volume data. Stress-relieving grinding volume data, total grouting volume data accumulated across the entire domain, and variable-thickness filling volume data are used as interface adaptive compensation strategies.

8. The design method for a multi-cavity FRP reinforcement structure for subway tunnels according to claim 7, characterized in that, The step of calculating the effective cross-sectional moment of inertia further includes: Based on the distribution characteristics of the global interface shear stiffness, the global weighted average shear stiffness is calculated, and the composite structure synergistic stiffness correction coefficient is solved. The effective moment of inertia of the FRP multi-cavity profile is obtained by reducing the theoretical moment of inertia of the composite structure by using the composite structure synergistic stiffness correction coefficient.

9. The design method for a multi-cavity FRP reinforcement structure for subway tunnels according to claim 8, characterized in that, The steps for calculating the effective cross-sectional moment of inertia include: The stress relief grinding volume data is converted into tool path code for CNC grinding equipment or contour line construction drawing for manual grinding, and used as pretreatment instructions for the tunnel segment surface. The total cumulative grouting volume data of the entire domain is converted into the quantitative cutoff threshold of the grouting pump, and the variable thickness filling volume data is converted into the extrusion rate control sequence of the adhesive coating equipment as a medium filling control command. Using the effective cross-sectional moment of inertia, the ultimate bearing capacity of the reinforced tunnel segment is recalculated. If it meets the specification requirements, the final construction plan is output; otherwise, a safety warning is issued.

10. A fiber composite material, characterized in that, Based on the design method of FRP multi-cavity reinforcement structure for subway tunnels according to any one of claims 1-9, the fiber composite material is a composite reinforcement system consisting of a bent pultruded FRP multi-cavity profile as the skeleton, filled with high-strength self-compacting concrete or grout, wrapped with a multi-directional fiber reinforcement layer and coated with a nano-protective layer, and connected with the tunnel segments through double-connection of adhesive bolts to form a composite reinforcement system that works together to bear the load.

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