Subway tunnel frp corrugated plate wave form optimization design method and frp corrugated plate

Abstract

The present application relates to the technical field of corrugated plate optimization design, and discloses a subway tunnel FRP corrugated plate waveform optimization design method and FRP corrugated plate, the method first constructs an initial FRP corrugated plate three-dimensional digital model, and establishes a gravity reverse escape vector field on it to generate a bubble stagnation potential energy distribution map;Then define a virtual grouting liquid level, perform step scanning on the model, extract the instantaneous wet perimeter and perform closed topological ring detection, and verify the local minimum point in combination with the potential energy distribution map, so as to accurately identify the bubble dead corner trap area and construct a dead corner mapping database;Finally, according to the database, a virtual diversion path is planned, an asymmetric diversion ridge structure is generated and iterative verification is carried out;The present application converts the grouting and exhaust problem of physical space into a geometric topology optimization problem of virtual space, actively eliminates the bubble stagnation dead corner at the wave peak through asymmetric geometric reconstruction in the design stage, and improves the grouting density between the FRP corrugated plate and the tunnel segment.

Description

Technical Field

[0001] This invention relates to the field of corrugated plate optimization design technology, and more specifically, to a waveform optimization design method for FRP corrugated plates in subway tunnels and an FRP corrugated plate. Background Technology

[0002] With the continuous improvement of urban rail transit networks and the increase in operational years, some subway shield tunnel segments may develop defects such as cracks, water leakage, and excessive ellipticity due to factors such as changes in geological conditions, surrounding load disturbances, and material performance degradation, affecting operational safety. To restore the load-bearing capacity of the tunnel structure and control deformation, the use of corrugated plates (such as steel corrugated plates or fiber-reinforced polymer (FRP) corrugated plates) for internal lining reinforcement has become an important engineering treatment method. This involves attaching corrugated plates to the inner wall of the segments and backfilling the gaps between the plates and segments with grout to form a shared load-bearing system.

[0003] Currently, various corrugated plate reinforcement structures and construction methods have been proposed in existing technologies. For example, Chinese patent CN115045686B discloses a method for reinforcing subway shield tunnels with corrugated steel. This method involves cleaning and grinding the inner surface of the tunnel segments, installing foundation brackets, assembling corrugated steel plates piece by piece, connecting the corrugated steel plates to the tunnel segment concrete using chemical anchors, and finally filling the gaps with epoxy resin to complete the repair and reinforcement. Furthermore, Chinese patent CN107806349B discloses a secondary lining structure for steel-FRP composite corrugated plate tunnels and its construction method. This scheme uses prefabricated steel-FRP composite corrugated plates with the corrugation lines perpendicular to the tunnel longitudinal direction. The plates have pre-drilled bolt holes and grouting holes. The secondary lining structure is formed through the assembly of prefabricated components and grouting, aiming to optimize the tunnel profile and reduce project costs.

[0004] However, although the aforementioned existing technologies have improved the material structure and macroscopic assembly process of the corrugated plates, their waveform design still generally uses the traditional symmetrical sine wave or trapezoidal wave geometric cross-section. In the specific case of upward-viewing installation on the arch of a subway tunnel, the grout, constrained by gravity, exhibits an upward flow and filling pattern. The traditional symmetrical waveform design does not fully consider the geometric constraints of the gas escape path in fluid dynamics; the tangent slope of the inner surface of the wave crest (i.e., the top of the groove facing the segment) tends to be horizontal at the apex. When the grout level rises and approaches the crest, the residual bubbles in the horizontal tangential region lose the buoyancy component required to slide upwards along the surface. This causes the bubbles to be "locked" in the geometric dead angle at the crest tip under the mechanical balance of buoyancy and viscous resistance, unable to be squeezed to the vent by the subsequent rising grout. This fluid dynamic retention effect induced by geometric defects inevitably forms hidden air pockets or grout voids between the corrugated plate and the tunnel lining segments, weakening the bonding strength of the reinforcement layer and the overall bending stiffness, thus posing a safety hazard to the long-term durability of the tunnel structure. Summary of the Invention

[0005] To overcome the aforementioned shortcomings of existing technologies, this invention provides a waveform optimization design method for FRP corrugated slabs in subway tunnels and an FRP corrugated slab itself. This method is based on the principle of "virtual bubble escape topology," transforming the grouting and venting problem in physical space into a geometric topology optimization problem in virtual space. By constructing a gravity reverse escape vector field and a bubble retention potential energy distribution map, the method accurately identifies bubble dead zone trap areas at the crests and plans virtual flow guiding paths accordingly to generate asymmetric flow guiding ridge structures. Without altering the macroscopic structural stiffness of the corrugated slab, this invention utilizes asymmetric microscopic geometry to break the mechanical balance of bubble retention, forcing bubbles to actively escape under buoyancy, thereby improving grout density and reinforcement effect.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] The waveform optimization design method for FRP corrugated plates in subway tunnels includes:

[0008] Construct an initial three-dimensional digital model of the FRP corrugated plate, establish a gravity reverse escape vector field on the initial three-dimensional digital model of the FRP corrugated plate, and generate a bubble retention potential energy distribution map based on the gravity reverse escape vector field.

[0009] Define a virtual grouting surface, control the virtual grouting surface to perform step scanning on the initial FRP corrugated plate 3D digital model, extract the instantaneous wetting perimeter, perform closed topological loop detection on the instantaneous wetting perimeter, and verify the local minimum points inside the closed topological loop by combining the bubble retention potential energy distribution map, so as to identify the bubble dead corner trap area, and construct a dead corner mapping database based on the bubble dead corner trap area;

[0010] Based on the dead angle mapping database, a virtual flow path is planned, and an asymmetric flow ridge structure is generated along the virtual flow path. The three-dimensional digital model of the FRP corrugated plate after the asymmetric flow ridge structure is generated is iteratively verified, and the optimized FRP corrugated plate design data is output.

[0011] The method for constructing the initial three-dimensional digital model of the FRP corrugated plate includes:

[0012] The system receives the design parameters and distribution pattern parameters of the FRP corrugated plate to be optimized, as well as the tunnel segment installation parameters. The design parameters of the FRP corrugated plate to be optimized include the foundation wave height, wave pitch, and plate thickness. The distribution pattern parameters include the short-segment interval reinforcement mode for local reinforcement and the segmented reinforcement mode for bending members. The tunnel segment installation parameters include the inner diameter of the tunnel segment.

[0013] A reference mounting surface is constructed based on the tunnel segment installation parameters. An initial three-dimensional digital model of the FRP corrugated plate is generated on the reference mounting surface based on the design parameters and distribution pattern parameters of the FRP corrugated plate to be optimized.

[0014] The method for establishing the gravity reverse escape vector field includes:

[0015] The initial three-dimensional digital model of the FRP corrugated plate is discretized into a mesh to obtain a set of triangular facet elements.

[0016] Define a global gravity unit vector, calculate the gravity reverse escape vector corresponding to each triangular patch element in the triangular patch element set based on the global gravity unit vector, and construct a gravity reverse escape vector field.

[0017] The method for generating the bubble retention potential energy distribution map includes:

[0018] Mark the zero potential energy endpoint on the initial FRP corrugated plate 3D digital model, calculate the relative potential energy height of each triangular facet element reaching the geometric highest boundary of the initial FRP corrugated plate 3D digital model along the direction of the gravity reverse escape vector, and summarize the relative potential energy heights of all triangular facet elements to generate a bubble retention potential energy distribution map.

[0019] The method for extracting the instantaneously wetted perimeter includes:

[0020] The virtual grouting liquid surface is controlled to perform layer-by-layer scanning of the initial FRP corrugated plate three-dimensional digital model along the direction of the gravity reverse escape vector field with a preset scanning step size, so as to obtain a discrete scanning height sequence.

[0021] At each scan height in the discrete scan height sequence, the geometric intersection line between the virtual grouting liquid surface and the inner surface of the initial FRP corrugated plate three-dimensional digital model is calculated, and the geometric intersection line is defined as the instantaneous wetting perimeter.

[0022] The aforementioned closed topological loop detection of the instantaneous wetting perimeter refers to performing topological connectivity analysis on the instantaneous wetting perimeter to determine whether the instantaneous wetting perimeter forms a closed topological loop.

[0023] The method for determining whether a closed topological loop is formed at the instantaneous wetting boundary is as follows:

[0024] The instantaneous wetting perimeter is represented as a graph structure composed of intersecting line segments, with the endpoints of the intersecting line segments as nodes of the graph and the intersecting line segments themselves as edges of the graph. The degree of each node is counted. If the degree of all nodes is even and the graph structure is connected, then the instantaneous wetting perimeter is determined to form a closed topological cycle.

[0025] The method for identifying bubble dead zone trap areas includes:

[0026] If instantaneous wetting of the perimeter forms a closed topological loop and the internal projection region of the closed topological loop does not contain the zero potential energy endpoint, then query the bubble retention potential energy distribution map, verify that there is a local minimum point of relative potential energy height inside the closed topological loop, and mark the area enclosed by the closed topological loop as the bubble dead zone trap region.

[0027] The constructed dead angle mapping database contains the location coordinates, critical retention angle, and dead angle volume of each bubble dead angle trap area;

[0028] The method for planning virtual flow guidance paths includes: retrieving the position coordinates of each bubble dead zone trap area from the dead zone mapping database and calculating the geometric center of each bubble dead zone trap area; using the relative potential energy height in the bubble retention potential energy distribution map as the path cost weight, and using the weighted geodesic algorithm on the inner surface of the FRP corrugated plate 3D digital model to plan the potential energy descent path connecting the geometric center of the bubble dead zone trap area and the zero potential energy endpoint, and defining the potential energy descent path as the virtual flow guidance path.

[0029] The method for generating the asymmetric flow-guiding ridge structure includes:

[0030] The virtual flow path generates a flow ridge skeleton line, and the local cross-section of the initial FRP corrugated plate three-dimensional digital model is split into the front and back surfaces with the flow ridge skeleton line as the center.

[0031] The critical retention angle corresponding to the bubble dead angle trap area is retrieved from the dead angle mapping database. The geometric curvature of the back flow surface is adjusted according to the critical retention angle so that the angle between the tangent vector at any point on the back flow surface and the gravity reverse escape vector is always less than 90 degrees, forming an asymmetric guide ridge structure.

[0032] An FRP corrugated plate includes a crest region, a trough region, and an asymmetric flow-guiding ridge structure disposed on the inner wall of the crest region. The asymmetric flow-guiding ridge structure is designed and generated using the aforementioned waveform optimization design method for FRP corrugated plates in subway tunnels.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] This invention abstracts the complex fluid dynamics bubble retention mechanism into a calculable geometric potential energy problem by constructing a gravity reverse escape vector field and a bubble retention potential energy distribution map. Utilizing step-by-step scanning of the virtual grouting surface and closed topological loop detection technology for instantaneous wetting perimeter, it achieves precise positioning and logical verification of bubble dead zone trap areas formed by the coupling of gravity and waveform geometry in a three-dimensional digital model. This effectively solves the technical problem of grouting voids caused by the loss of upward buoyancy due to the horizontal tangent of the inner surface of the wave crest in traditional waveform design. By planning virtual flow paths based on a dead zone mapping database and generating asymmetric flow ridge structures, without changing the macroscopic structural stiffness of the corrugated plate, the asymmetric microscopic flow geometry breaks the mechanical equilibrium state of the bubbles, forcing them to actively escape along a preset path under buoyancy. This shifts the grouting quality control from passive on-site response to proactive geometric topological optimization in the design stage, fundamentally ensuring the saturation and engineering safety of the FRP corrugated plate grouting system. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 A flowchart illustrating the waveform optimization design method for FRP corrugated plates in subway tunnels provided in this embodiment of the invention;

[0037] Figure 2 A cross-sectional schematic diagram of the cooperation between the FRP corrugated plate and the tunnel segment and the principle of air bubble retention provided in the embodiment of the present invention;

[0038] Figure 3 This is a schematic cross-sectional view of the design parameters of the FRP corrugated plate to be optimized provided in an embodiment of the present invention;

[0039] Figure 4 A cross-sectional schematic diagram of the segmented reinforcement mode for bending members and its cooperation with tunnel segments provided in an embodiment of the present invention;

[0040] Figure 5A flowchart for instantaneous wetting perimeter topology analysis and bubble dead zone identification provided in an embodiment of the present invention. Detailed Implementation

[0041] The technical solutions of 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 within the scope of protection of the present invention.

[0042] Example 1

[0043] Please see Figure 1 As shown, this embodiment provides a waveform optimization design method for FRP corrugated plates in subway tunnels, including:

[0044] Step S10: Receive the design parameters and distribution mode parameters of the FRP corrugated plate to be optimized, as well as the tunnel segment installation parameters; construct an initial three-dimensional digital model of the FRP corrugated plate; establish a gravity reverse escape vector field on the initial three-dimensional digital model of the FRP corrugated plate; and generate a bubble retention potential energy distribution map based on the gravity reverse escape vector field.

[0045] Further, step S10 includes:

[0046] Step S11: Receive the design parameters and distribution pattern parameters of the FRP corrugated plate to be optimized, as well as the tunnel segment installation parameters. The design parameters of the FRP corrugated plate to be optimized include the foundation wave height, wave pitch, and plate thickness. The distribution pattern parameters include short-segment interval reinforcement mode for local strengthening and segmented reinforcement mode for bent components. The tunnel segment installation parameters include the inner diameter of the tunnel segment. Construct a reference installation surface based on the tunnel segment installation parameters. Generate an initial three-dimensional digital model of the FRP corrugated plate on the reference installation surface based on the design parameters and distribution pattern parameters of the FRP corrugated plate to be optimized. Perform mesh discretization processing on the initial three-dimensional digital model of the FRP corrugated plate to obtain a set of triangular facet elements.

[0047] Specifically, please refer to Figure 2 The diagram shown is a cross-sectional schematic of the cooperation between the FRP corrugated plate and the tunnel segment and the principle of air bubble retention in this embodiment. Figure 2 The diagram illustrates the distribution of air bubbles within the crest grooves of a corrugated plate located beneath tunnel segments under the influence of a vertically downward gravitational vector. FRP corrugated plates are corrugated sheets made of fiber-reinforced composite materials, used in subway tunnel reinforcement projects to adhere to the inner wall of tunnel segments. The gap between the FRP corrugated plate and the segments needs to be filled densely using a grouting process. When the FRP corrugated plate is installed in the tunnel's top area, the grout flows upwards during the grouting process, combined with... Figure 2 It is known that due to the concave cavities formed in the crest region of the corrugated plate's inner wall, bubbles rise under buoyancy and become trapped in the dead corner at the top of the crest groove, forming the bubble stagnation zone shown in the figure, which prevents them from escaping. Traditional waveform designs use symmetrical sine or trapezoidal wave cross sections, and the tangent of the inner surface at the crest tends to be horizontal. In the horizontal tangent region, the bubbles lose the driving force component that propels them upward along the surface, thus causing grouting void defects. The purpose of step S10 is to transform the grouting and venting problem in physical space into a geometric topology optimization problem in computer virtual space. By constructing a digital model that reflects the geometric coupling relationship between the gravitational field and the corrugated plate surface, a quantitative geometric basis is provided for subsequent bubble escape path analysis and waveform optimization.

[0048] In step S11, please refer to Figure 3 The figure shown is a cross-sectional schematic diagram of the design parameters of the FRP corrugated plate to be optimized in this embodiment. Figure 3 The diagram visually illustrates the three core geometric quantities that determine the corrugation geometry: base wave height, wave pitch, and plate thickness. The base wave height is defined as... Figure 3 The vertical distance between the crests and troughs in the cross-section of the corrugated plate shown in the diagram directly determines the bending stiffness of the FRP corrugated plate. A larger foundation wave height results in a larger moment of inertia and a stronger ability of the corrugated plate to withstand lateral loads. For example... Figure 3 As indicated by the markings, the wave pitch is defined as the horizontal distance between two adjacent wave crests. The ratio of the wave pitch to the base wave height affects the uniformity of stress distribution in the corrugated plate and the fitting accuracy with the curved surface of the tube segment. Figure 3 The diagram further illustrates the plate thickness in a magnified view indicated by dashed lines. This thickness is defined as the wall thickness of the FRP composite laminate, which determines the in-plane stiffness and impact resistance of the corrugated plate. The distribution pattern parameters describe the arrangement of the FRP corrugated plates circumferentially in the tunnel. The short-segment interval reinforcement mode is suitable for targeted repair of locally damaged areas in the tunnel, where the corrugated plates are distributed in several independent short segments along the tunnel axis, with intervals maintained between adjacent segments. The segmented reinforcement mode for bending members is suitable for large-scale circumferential reinforcement of the tunnel. Please refer to [link / reference]. Figure 4 The diagram shown is a cross-sectional schematic of the segmented reinforcement mode of the bent component in this embodiment, in conjunction with the tunnel lining segments. When the coverage angle of the corrugated plate is greater than or equal to 90°, due to limitations in manufacturing process and installation space, it is necessary to... Figure 4 The integral bending member shown in the diagram is divided into several segments along the central angle direction. Each segment is attached to the inner wall of the tunnel segment and assembled sequentially on site. The inner diameter of the tunnel segment in the installation parameters is... Figure 4 The diameter of the cylindrical surface containing the inner wall of the tunnel segment determines the bending radius of the FRP corrugated plate.

[0049] The construction process of the reference mounting surface is as follows: A global coordinate system is established with the tunnel axis as the Z-axis. A virtual cylindrical surface coaxial with the inner wall of the tunnel segment is generated, using half the inner diameter of the segment as the radius of curvature. This virtual cylindrical surface is the reference mounting surface, representing the theoretical fitting position of the outer surface of the FRP corrugated plate. The initial generation process of the FRP corrugated plate 3D digital model is as follows: On the reference mounting surface, the corrugated section profile is generated along the tunnel circumference using the foundation wave height and wave pitch as control parameters. The corrugated section profile is stretched along the tunnel axis to form a 3D shell model. The plate thickness is achieved by shell offset, with the offset direction pointing towards the tunnel axis. For the short-segment interval reinforcement mode, several independent corrugated plate shell models are generated according to the user-specified short segment length and interval distance. For the segmented reinforcement mode of curved components, the corrugated plate shell model is geometrically divided along the central angle direction according to the coverage angle and the number of segments. The circumferential edge of each segment generates a joint profile that matches the adjacent segment.

[0050] The implementation of mesh discretization is as follows: the inner surface of the initial FRP corrugated plate 3D digital model is meshed using the Delaunay triangulation algorithm or the leading edge algorithm, generating a discrete mesh composed of a large number of triangular facet elements. Triangular facet elements are the basic geometric elements of mesh discretization. Each triangular facet element is uniquely determined by the coordinates of its three vertices and can be considered as a small planar region on the curved surface. Triangular facets are chosen as discrete elements instead of quadrilaterals or polygons because triangles are the simplest polygons in a plane, their three vertices are necessarily coplanar, and there is no warping deformation problem, which facilitates subsequent calculation of surface normals and tangent inclination. The mesh density is controlled by specifying the target element side length Lmesh. The target element side length Lmesh is set based on the following principle: Lmesh should be less than one-tenth of the wave pitch to ensure a sufficient number of sampling points to capture the continuous changes in waveform curvature within a complete wave cycle. For example, when the wave pitch is 100 mm, the target element side length Lmesh is set to 8 mm to 10 mm, thereby forming ten to twelve sampling points within one wave cycle, which can accurately characterize the curvature transition features at the crests and troughs. The system calculates and stores the centroid coordinates P(x,y,z) and the element normal vector n perpendicular to the element surface for each triangular facet element. The centroid coordinates P(x,y,z) are obtained by the arithmetic mean of the coordinates of the three vertices. The element normal vector n is obtained by the cross product of the two edge vectors of the triangular facet. The cross product result is normalized to become the unit normal vector. The data structure of the triangular facet element set contains four fields: element index, vertex coordinate list, element centroid coordinates, and element normal vector, providing a traversable geometric data foundation for subsequent vector field calculations and topology analysis.

[0051] Mesh discretization transforms continuous surface geometry into a discrete set of planar elements, enabling the quantification and analysis of local geometric features of complex surfaces element by element. Traditional continuous surface equations require analytical solutions to obtain curvature and normal information, a computationally complex process that struggles to handle irregular surfaces generated by parametric modeling. Discretized triangular facet elements, however, can directly obtain local geometric parameters through vector operations on vertex coordinates, avoiding the need to solve complex surface equations. Mesh discretization also allows for the independent definition of the subsequent gravity reverse escape vector field on each triangular facet element. Triangular facet elements at different locations can obtain differentiated vector assignments based on their spatial orientation, thus establishing a local coupling relationship between surface geometry and the gravity field. The purpose of introducing distributed mode parameters is to enable waveform optimization results to directly adapt to the constraints of mold manufacturing and on-site installation in actual engineering projects. For the short-segment interval reinforcement mode, waveform optimization must ensure that the corrugation characteristics of each short segment are independent and complete, without considering inter-segment continuity. For the segmented reinforcement mode of bent components, waveform optimization must reserve waveform continuity compensation margin at the segment joints to ensure unobstructed grouting channels after segment assembly. Distributed mode parameters introduce the process constraints of actual construction into the design stage in advance, avoiding forced modifications to the optimized waveform during mold manufacturing or on-site installation due to non-compliance with process conditions, and ensuring seamless integration between design results and production manufacturing.

[0052] Step S12: Define a global gravity unit vector in the global coordinate system where the initial FRP corrugated plate 3D digital model is located, calculate the gravity reverse escape vector corresponding to each triangular facet unit based on the global gravity unit vector, and construct the gravity reverse escape vector field.

[0053] In step S12, the global gravity unit vector is defined in the global coordinate system of the initial FRP corrugated plate 3D digital model. The global coordinate system has the tunnel axis as the Z-axis and the vertical downward direction as the negative Y-axis. The direction of the global gravity unit vector g points to the Earth's center, and it is represented in this coordinate system as g=(0,-1,0). The magnitude of the global gravity unit vector g is 1, representing only directional information and not including the dimension of gravitational acceleration. This setting simplifies the mathematical model of geometric topology analysis by having subsequent vector calculations only involve direction determination and not force magnitude calculation. For each triangular facet element in the triangular facet element set, its corresponding gravity reverse escape vector F is calculated. The gravity reverse escape vector F is defined as the reverse vector of the global gravity unit vector g, i.e., F=-g=(0,1,0). The physical meaning of the gravity reverse escape vector F is the absolute direction in which the bubble tends to escape under the action of buoyancy. Since the direction of buoyancy is always opposite to the direction of gravity and points upward along the vertical line, F always points in the positive Y-axis direction and does not change with the spatial position and attitude of the triangular facet unit.

[0054] Although the gravity escape vector F is constant in the global coordinate system, the angle between the gravity escape vector F and the element normal vector n varies significantly for triangular facet elements at different positions on the corrugated plate surface. When the FRP corrugated plate is installed at the top of the tunnel, with the inner surface of the corrugated plate facing the Earth's center, the element normal vector n of the triangular facet element located at the crest is approximately vertically downward, forming an approximately 180° angle with the gravity escape vector F; the element normal vector n of the triangular facet element located on the sidewall of the crest has a horizontal component, forming an acute or obtuse angle with the gravity escape vector F; and the element normal vector n of the triangular facet element located at the bottom of the trough is approximately vertically upward, forming an approximately 0° angle with the gravity escape vector F. The gravity reverse escape vector field is constructed by binding the gravity reverse escape vector F of each triangular facet element to the element's centroid coordinates P(x,y,z), forming a vector field distribution that traverses the entire inner surface of the initial FRP corrugated plate 3D digital model. The data structure of the gravity reverse escape vector field is a set of key-value pairs, where the key is the element index of the triangular facet element, and the value is a combination of the gravity reverse escape vector F and the element's centroid coordinates P.

[0055] The purpose of defining and constructing a gravity reverse escape vector field using a global gravity unit vector is to embed constant physical gravity field information into a static geometric model. This allows subsequent analysis to determine the escape tendency of bubbles without solving fluid dynamics equations. The gravity reverse escape vector can be viewed as a virtual pointer penetrating each triangular facet element, indicating the absolute physical direction in which the bubble is expected to move under ideal conditions. The gravity reverse escape vector field pre-places dynamic physical constraints within the static geometric model. Traditional CAD models only record geometry without containing physical field information. When fluid analysis is required, the geometric model must be imported into dedicated CFD software and boundary conditions must be set. However, by constructing a gravity reverse escape vector field, the geometric model itself carries physical information related to the bubble's escape direction. This allows subsequent bubble dead zone identification to be completed by determining the angle between the vector and the normal, eliminating the need to solve complex Navier-Stokes equations and significantly reducing computational complexity. The synergy between the gravity reverse escape vector field and the triangular patch unit set lies in the fact that the triangular patch unit provides a discretized surface geometry carrier, which allows the continuously distributed vector field to be stored and traversed in the form of discrete data points. This discretized vector field representation method allows the subsequent potential energy height calculation to be performed unit by unit, avoiding the integral operation of the continuous field.

[0056] Step S13: Mark the zero potential energy endpoint on the initial FRP corrugated plate three-dimensional digital model, calculate the relative potential energy height of each triangular facet unit reaching the geometric highest boundary of the initial FRP corrugated plate three-dimensional digital model along the direction of the gravity reverse escape vector, and summarize the relative potential energy heights of all triangular facet units to generate a bubble retention potential energy distribution map.

[0057] In step S13, the zero potential energy endpoint is determined on the initial FRP corrugated plate 3D digital model by the user-specified vent coordinates. The vent is a pre-reserved process through-hole on the FRP corrugated plate, serving as an outlet for air discharge during grouting, located at or near the geometrically highest point of the FRP corrugated plate. The system receives the vent coordinates marked by the user on the initial FRP corrugated plate 3D digital model and marks this coordinate point as the zero potential energy endpoint. The physical meaning of the zero potential energy endpoint is the ultimate target position for bubble escape, assigned a zero potential energy value as a benchmark within the potential energy analysis framework. Simultaneously, the system receives the grouting hole coordinates marked by the user. The grouting hole is the inlet for grout injection, located at or near the geometrically lowest point of the FRP corrugated plate. The grouting hole coordinates are used for subsequent verification of the rationality of the starting point of the bubble escape path.

[0058] The calculation process for relative potential height is as follows: For each triangular facet element in the triangular facet element set, obtain the element's centroid coordinates P(x,y,z). Extract the projection component of the element's centroid coordinates P along the direction of the gravity escape vector F. This projection component is the Y-axis coordinate value Py of the element's centroid coordinates P. Obtain the Y-axis coordinate value Ymax of the geometric highest boundary of the initial FRP corrugated plate 3D digital model. The geometric highest boundary is the position with the largest Y-axis coordinate on the inner surface of the model. Calculate the vertical distance from the element's centroid coordinates P to the geometric highest boundary. This vertical distance is defined as the relative potential height hpot, and the calculation formula is hpot = Ymax - Py. The physical meaning of the relative potential height hpot is: the vertical distance that a bubble needs to travel to move upwards along the direction of the gravity escape vector from the location of the triangular facet element until it reaches the geometric highest boundary. The larger the relative potential energy height hpot, the farther the triangular facet element is from the geometric highest boundary, and the greater the path resistance that the bubble needs to overcome to escape from that position; the smaller the relative potential energy height hpot, the closer the triangular facet element is to the geometric highest boundary, and the easier it is for the bubble to escape from that position. The relative potential energy height at the zero potential energy endpoint is zero, serving as the reference point for potential energy distribution.

[0059] The generation process of the bubble retention potential energy distribution map is as follows: The relative potential energy heights (hpot) of all triangular facet units are aggregated into a one-dimensional array, establishing a mapping relationship between relative potential energy height values ​​and triangular facet unit indices. The relative potential energy height array is normalized by dividing each relative potential energy height value by the maximum value in the array, ensuring the normalized relative potential energy heights fall within the range of 0 to 1. The normalized relative potential energy height values ​​are mapped to color chromatograms using a warm / cool color gradient mapping rule: regions with relative potential energy height values ​​close to 0 are mapped to cool colors, and regions with relative potential energy height values ​​close to 1 are mapped to warm colors. The mapped color information is then rendered onto the inner surface of the initial FRP corrugated plate 3D digital model, generating a bubble retention potential energy distribution map covering the entire model. The data structure of the bubble retention potential energy distribution map includes four fields: triangular facet unit index, original relative potential energy height value, normalized relative potential energy height value, and mapped color value.

[0060] The purpose of defining and generating a bubble retention potential energy distribution map using relative potential energy height is to transform the complex three-dimensional structure of corrugated plates into an intuitive potential energy topography map. This allows the location of waveform defects to shift from qualitative judgments based on engineering experience to quantitative analysis based on potential energy distribution. Relative potential energy height draws on the concept of gravitational potential energy in physics, abstracting the escape dynamics of bubbles under buoyancy as a process of decreasing potential energy. Bubbles tend to move from high-potential-energy regions to low-potential-energy regions, eventually converging at a zero-potential-energy endpoint. The bubble retention potential energy distribution map transforms the implicit risk of bubble retention into explicit color distribution characteristics. Designers can quickly locate potential bubble dead zones by observing warm-colored clusters in the potential energy distribution map, allowing for the prediction of construction risks during the design phase without the need for grouting tests or CFD simulations. The synergy between the bubble retention potential energy distribution map and the gravity reverse escape vector field lies in the fact that the gravity reverse escape vector field provides a directional reference for calculating the potential energy height, while the bubble retention potential energy distribution map further condenses the vector field information into a scalar field. The scalar field is easier to visualize and threshold than the vector field, providing a global view of the potential energy distribution for subsequent closed topological loop detection.

[0061] Step S10 involves constructing an initial 3D digital model of the FRP corrugated plate, transforming the physical corrugated plate into a computable digital twin; establishing a gravity reverse escape vector field to embed constant physical gravity constraints into the geometric model; and generating a bubble retention potential energy distribution map to abstract the dynamic process of bubble escape into a potential energy decrease process. Without step S10, subsequent bubble dead zone identification would lack a discretized geometric carrier, the virtual grouting surface would be unable to intersect with the model surface to generate a wetting perimeter; subsequent potential energy verification would lack a reference benchmark for potential energy distribution, making it impossible to determine whether there are local minima of relative potential energy height within the closed topological loop; and subsequent guide ridge path planning would lack guidance in potential energy direction, making it impossible to determine the path of bubble convergence towards the vent.

[0062] Step S20: Define the virtual grouting liquid surface, control the virtual grouting liquid surface to perform step scanning on the initial FRP corrugated plate three-dimensional digital model, extract the instantaneous wetting perimeter, perform closed topological loop detection on the instantaneous wetting perimeter, and verify the local minimum points inside the closed topological loop by combining the bubble retention potential energy distribution map, so as to identify the bubble dead corner trap area, and construct a dead corner mapping database based on the bubble dead corner trap area;

[0063] Further, step S20 includes:

[0064] Step S21: Define a virtual grouting surface in the global coordinate system where the initial FRP corrugated plate three-dimensional digital model is located, with the normal vector aligned with the direction of the gravity reverse escape vector field. Control the virtual grouting surface to perform layer-by-layer scanning of the initial FRP corrugated plate three-dimensional digital model along the direction of the gravity reverse escape vector field with a preset scanning step size, and obtain a discrete scanning height sequence.

[0065] Specifically, step S20 transforms the physical phenomenon of the grout level gradually rising during grouting into a geometric calculation process of a virtual plane stepping and scanning in the opposite direction of gravity. Traditional computational fluid dynamics simulations require solving the Navier-Stokes equations describing two-phase flow, with computational grids reaching millions to capture the dynamic evolution of the gas-liquid interface. A single simulation typically takes hours and carries convergence risks, making it difficult to quickly provide feedback on the specific location of geometric defects during waveform design iterations. Step S20 simplifies the fluid dynamics problem into a geometric slicing problem, using Boolean operations for the intersection of planes and surfaces to replace the numerical solution of partial differential equations. This reduces computational complexity by several orders of magnitude while retaining the ability to identify bubble retention locations, making rapid iteration of waveform optimization possible.

[0066] In step S21, the virtual grouting surface is an infinitely extending ideal plane defined in the global coordinate system of the initial FRP corrugated plate 3D digital model, used to simulate the instantaneous state of the grout surface during the grouting process. The normal vector of the virtual grouting surface is set to be consistent with the direction of the gravity reverse escape vector F constructed in step S12, that is, the normal vector points to the positive Y-axis direction. This setting ensures that the virtual grouting surface always maintains a horizontal attitude in the global coordinate system, which is consistent with the physical characteristic that the grout surface is horizontal due to gravity constraint during the actual grouting process. The position of the virtual grouting surface is uniquely determined by its height coordinate in the Y-axis direction. The change of the height coordinate simulates the dynamic process of the grout surface gradually rising as the grouting process progresses.

[0067] The starting height h0 of the layer-by-layer scan is set to the minimum value of the Y-axis coordinate on the inner surface of the initial FRP corrugated plate 3D digital model, i.e., the height of the lowest point of the model's geometry. This position corresponds to the spatial height of the bottom of the trough after the corrugated plate is installed at the top of the tunnel. The ending height hend of the layer-by-layer scan is set to the maximum value of the Y-axis coordinate on the inner surface of the initial FRP corrugated plate 3D digital model, i.e., the height of the highest point of the model's geometry. This position corresponds to the spatial height of the region where the zero potential energy endpoint is located. The preset scan step size Δh is set based on the following: Δh should be less than one-twentieth of the base wave height to ensure sufficient sampling density in the wave crest region to capture the critical moment of closed topological loop formation. For example, when the base wave height is 50 mm, the preset scan step size Δh is set to 2 mm to 2.5 mm, thereby forming twenty to twenty-five scan layers in a single wave crest region, which can accurately locate the formation height of the closed topological loop. The virtual grouting liquid level is controlled to rise layer by layer along the positive Y-axis starting from the initial height h0, with a preset scanning step size Δh as the increment, forming a discrete scanning height sequence {h0, h1, h2, ..., h n}, where the i-th scan height h i =h0+i×Δh, 1≤i≤n, where n is the value that satisfies h n The largest integer index ≤ hend. The generation of discrete scan height sequences discretizes the continuous liquid level rise process into a finite number of height sampling points, allowing subsequent geometric intersection operations to be performed independently at each sampling point, avoiding the need for continuous tracking calculations.

[0068] By employing a virtual grouting surface for layer-by-layer scanning, the complex gas-liquid two-phase flow in actual grouting is simplified into a planar stepping motion along a single direction. This transforms the fluid simulation, which originally required solving time-varying partial differential equations, into a static geometric intersection calculation. The virtual grouting surface is scanned at each height h. iThe state at a given height is only related to that height value and is decoupled from time parameters. This means that the scanning process does not need to consider fluid dynamic parameters such as slurry flow velocity, viscosity coefficient, and grouting pressure; subsequent topology analysis can be completed solely based on geometric position information. The layer-by-layer scanning method eliminates the need for computationally intensive CFD simulation software to identify bubble retention locations. The entire scanning process can be completed on ordinary engineering computers, significantly reducing the hardware threshold and time cost of waveform optimization.

[0069] Step S22: At each scanning height of the discrete scanning height sequence, calculate the geometric intersection of the virtual grouting liquid surface and the inner surface of the initial FRP corrugated plate three-dimensional digital model, and define the geometric intersection as the instantaneous wetting perimeter; perform topological connectivity analysis on the instantaneous wetting perimeter to determine whether the instantaneous wetting perimeter forms a closed topological loop. If the instantaneous wetting perimeter forms a closed topological loop and the internal projection area of ​​the closed topological loop does not contain the zero potential energy endpoint, then query the bubble retention potential energy distribution map, verify that there is a local minimum point of relative potential energy height inside the closed topological loop, and mark the area enclosed by the closed topological loop as the bubble dead angle trap area.

[0070] In step S22, refer to Figure 5 This is a flowchart of instantaneous wetting perimeter topology analysis and bubble dead zone identification provided in this embodiment, at each scan height h in the discrete scan height sequence. i At the location, calculate the geometric intersection line between the virtual grouting surface and the inner surface of the initial FRP corrugated plate 3D digital model. The geometric intersection line is calculated using a plane-triangular patch intersection algorithm: traverse the set of triangular patch elements generated in step S11, and for each triangular patch element, determine whether the virtual grouting surface intersects with that triangular patch element; if the three vertices of the triangular patch element have Y-axis coordinates located at h... i The vertices above and below are used to determine the intersection of the virtual grouting surface with the triangular facet element. The coordinates of the intersection points between the virtual grouting surface and each side of the triangular facet element are calculated using linear interpolation. Two intersection points on the same triangular facet element are connected to form an intersection line segment. All intersection line segments are then spliced ​​together according to spatial adjacency to form a complete geometric intersection line. The calculated geometric intersection line is defined as the instantaneous wetting perimeter. The physical meaning of the instantaneous wetting perimeter is: at the scanning height h... i The boundary line between the corresponding virtual grouting liquid surface and the inner surface of the corrugated plate divides the inner surface of the corrugated plate into a wetted area below the liquid surface and an unwetted area above the liquid surface.

[0071] The instantaneous wetting perimeter may exhibit two topological forms: an open curve form and a closed topological loop form. An open curve form consists of one or more curve segments with a start and an end point, located on the geometric boundaries of the initial FRP corrugated plate 3D digital model. For example, when the virtual grouting surface is located in the trough region, the instantaneous wetting perimeter typically presents as an open curve traversing the width of the model. A closed topological loop form consists of one or more closed curves connected end-to-end, forming a closed loop without a start or end point. For example, when the virtual grouting surface rises to the crest region, the intersection of the recessed cavity at the crest and the virtual grouting surface may form a closed topological loop encircling the crest.

[0072] The implementation method for performing topological connectivity analysis on the instantaneous wetting perimeter is as follows: Represent the instantaneous wetting perimeter as a graph structure composed of intersecting line segments, with the endpoints of the intersecting line segments as nodes and the intersecting line segments themselves as edges; count the degree of each node, i.e., the number of edges connected to that node; see [reference needed]. Figure 5 If all nodes have even degrees and the graph is connected, then the instantaneously wetted perimeter forms a closed topological cycle; if there are nodes with odd degrees, then the instantaneously wetted perimeter is an open curve. This method is based on Euler's path theory in graph theory: in a connected graph, a closed cycle requires each node to have a pair of "entry" and "exit" edges, therefore the degree of each node must be even (usually 2, representing one entry and one exit; or 4, 6, etc., representing multiple paths intersecting there). For a closed topological cycle, since the curves are connected end-to-end to form a closed cycle, each node is an intermediate node, connected by exactly two edges—one "entry" to the node and the other "exit"—therefore, the degree of each node is 2 (even). For an open curve, there must be two special nodes: a start point and a finish point. The start point has only one "leaving" edge, and the finish point has only one "entering" edge; both have a degree of 1 (odd). Even if the open curve branches or merges at some point in the middle, the degree of the branching point is 3 (one entry and two exits or two entry and one exit), and the degree of the merging point is also 3 (two entry and one exit or one entry and two exits), still odd. Therefore, by checking for the existence of odd-degree nodes, we can clearly distinguish between closed topological cycles (all nodes have even degrees) and open curves (at least two odd-degree nodes). When instantaneous wetting of the perimeter forms a closed topological cycle, see [reference needed]. Figure 5Further determine whether the internal projection region of the closed topological loop contains the zero potential energy endpoint marked in step S13: Project the closed topological loop onto the XZ plane to form a two-dimensional closed polygon; use the ray method to determine whether the projection point of the zero potential energy endpoint on the XZ plane is located inside the two-dimensional closed polygon; if the projection point of the zero potential energy endpoint is located inside the polygon, it indicates that the area enclosed by the closed topological loop is connected to the vent, and the bubble can escape to the vent along the potential energy decrease direction, and this area does not constitute a bubble dead angle; if the projection point of the zero potential energy endpoint is located outside the polygon, it indicates that the area enclosed by the closed topological loop is isolated from the vent, and the bubble cannot reach the vent through the potential energy decrease path, and this area has the geometric conditions to become a bubble dead angle.

[0073] When the internal projection region of the closed topological loop does not contain the zero potential energy endpoint, the bubble retention potential energy distribution map generated in step S13 is further queried to verify whether there is a local minimum point of relative potential energy height inside the closed topological loop. The verification process of the local minimum point is as follows: extract the cell index of all triangular facet cells enclosed inside the closed topological loop; retrieve the relative potential energy height values ​​corresponding to these triangular facet cells from the bubble retention potential energy distribution map; traverse each triangular facet cell and obtain the relative potential energy height values ​​of its adjacent triangular facet cells; if the relative potential energy height value of a certain triangular facet cell is less than the relative potential energy height values ​​of all its adjacent triangular facet cells, then the location of the triangular facet cell is determined to be a local minimum point. The physical meaning of the local minimum point is: in the potential energy topography map, this point is located in a local "concave" position, corresponding to the local highest point of the Y coordinate in geometry, that is, the top region of the inner wall of the wave crest. Because bubbles tend to move towards locations with lower potential energy, once a bubble reaches a local minimum, the potential energy at all surrounding locations is higher than that point, and there are no adjacent locations with lower potential energy for the bubble to continue moving. Simultaneously, since the tangent to the inner surface of the wave crest region tends to be horizontal, the buoyancy component in the tangential direction approaches zero, and the bubble loses the driving force component for moving along the surface. Therefore, it will be trapped at that location and unable to slide along the surface to escape. When a local minimum is verified to exist inside the closed topological loop, the area enclosed by the closed topological loop is marked as the bubble trap region. k , where the subscript k is the sequential number of the bubble dead zone trap area.

[0074] A dual-determination mechanism combining closed topological loop detection and local minimum point verification offers higher recognition accuracy compared to a single determination relying solely on closed topological loops. The formation of a closed topological loop is a necessary but not sufficient condition for the existence of bubble dead zones. A closed topological loop indicates that the virtual grouting surface at the scanning height completely surrounds a certain area on the inner surface of the corrugated plate. However, whether the surrounded area leads to bubble entrapment depends on the potential energy distribution characteristics within that area. Verification using the bubble entrapment potential energy distribution map for local minimum points can eliminate areas where closed topological loops are formed but no local minimum exists in the internal potential energy distribution. Bubbles in these areas, although surrounded by geometric boundaries, can still move along the direction of decreasing potential energy to the area communicating with the vent. This dual-determination mechanism makes the identification of bubble dead zone trap areas more accurate, avoids increased workload in subsequent waveform optimization due to over-marking, and ensures that true bubble dead zones are not missed.

[0075] The bubble retention potential energy distribution map constructed in step S22 and step S10 forms a data synergy: the bubble retention potential energy distribution map provides relative potential energy height information for each triangular facet unit, enabling the potential energy distribution characteristics inside the closed topological loop to be quickly queried and analyzed without recalculating the potential energy value in step S22; the closed topological loop detection determines the spatial range for potential energy distribution analysis, limiting the search for local minima of relative potential energy height to inside the closed topological loop rather than the entire model surface, avoiding computational redundancy caused by global traversal. The synergy between the two ensures that the identification of bubble dead zone trap regions has both geometric boundary constraints and physical potential energy verification, providing double assurance of the reliability of the identification results.

[0076] Step S23: Extract the tangent inclination of the triangular facet unit corresponding to the formation of a closed topological loop in each bubble dead corner trap region as the critical retention angle, calculate the volume above the closed topological loop that is not covered by the virtual grouting liquid surface as the dead corner volume, and use the position coordinates, critical retention angle and dead corner volume as the geometric feature parameters of the bubble dead corner trap region, and store the geometric feature parameters of each bubble dead corner trap region in the dead corner mapping database.

[0077] In step S23, for each identified bubble dead zone trap area, a trap is formed. k The tangent inclination of the triangular facet unit corresponding to the formation of the closed topological loop is extracted, and this tangent inclination is recorded as the critical retention angle. The extraction process of the critical retention angle is as follows: trace back the discrete scan height sequence to locate the bubble dead angle trap region Trap. kThe corresponding scanning height hcrit at the initial formation of the closed topological loop; obtaining the set of intersection segments forming the closed topological loop at the scanning height hcrit; for each intersection segment, determining its triangular facet element; calculating the tangent vector of each triangular facet element. The calculation process of the tangent vector is as follows: first, calculate the cross product of the normal vector n of the triangular facet element and the gravity reverse escape vector F to obtain the horizontal tangent direction; then calculate the cross product of the horizontal tangent direction and the normal vector n to obtain the maximum tilt direction vector along the surface. After normalization, this vector is the tangent vector, and its direction points to the direction of the fastest decrease in potential energy; calculate the tilt angle between the tangent vector and the horizontal plane, which is the tangent tilt of the triangular facet element; take the arithmetic mean of the tangent tilt of all triangular facet elements participating in the formation of the closed topological loop as the Trap region for the bubble dead angle. k The critical retention angle αcrit. The physical meaning of the critical retention angle αcrit is: when the angle between the local tangent of the inner surface of the corrugated plate and the horizontal plane is less than or equal to αcrit, the bubble will lose the driving force component for moving upwards along the surface, resulting in retention at that position. The smaller the value of the critical retention angle αcrit, the easier it is for the bubble to remain at a near-horizontal surface position; the larger the value of the critical retention angle αcrit, the steeper the surface position required for the bubble to remain. For example, when αcrit is close to zero, it indicates that the bubble remains in the almost horizontal crest top region, which is the most common bubble dead angle shape in traditional symmetrical waveform designs.

[0078] The calculation process for the dead zone volume is as follows: using the bubble dead zone trap area as an example. k The corresponding closed topological loop serves as the bottom boundary, and the curved surface of the initial FRP corrugated plate 3D digital model, located above and within the projection area of ​​the closed topological loop, serves as the top boundary, forming a closed 3D spatial region. The volume of this closed region is calculated using the voxelization method or the divergence theorem method, and the calculation result is recorded as the dead-angle volume. The physical meaning of the dead-angle volume is: assuming that air bubbles within the dead-angle trap region cannot escape during grouting, the dead-angle volume is the volume of the final grouting void defect. The dead-angle volume provides a quantitative indicator of the defect severity for subsequent waveform optimization. The larger the dead-angle volume, the more serious the harm of the dead-angle trap region to the grouting quality, and it should be given higher priority in subsequent optimization.

[0079] Trap the bubble dead zone area kThe process of storing geometric feature parameters into the dead-angle mapping database is as follows: A data record is created with the bubble dead-angle trap region number k as the primary key; the position coordinates are stored as the first field of this data record, defined as the three-dimensional coordinates of the geometric center of the closed topological loop in the global coordinate system, obtained by arithmetically averaging the coordinates of all intersection points on the closed topological loop; the critical retention angle αcrit is stored as the second field of this data record; the dead-angle volume is stored as the third field; the scan height hcrit is stored as the fourth field, used for tracing the formation process of the closed topological loop; and the sequence of intersection point coordinates of the closed topological loop is stored as the fifth field, used for accurately reconstructing the geometric boundary of the closed topological loop. The dead-angle mapping database adopts a relational data structure, supporting spatial index queries by position coordinates, sorting by dead-angle volume to determine optimization priorities, and filtering by critical retention angle to match different waveform correction strategies. For example, Table 1 shows a typical data record structure of the dead-angle mapping database:

[0080] Table 1. Typical data record structure of the dead zone mapping database

[0081]

[0082] The dead zone mapping database centralizes the bubble dead zone information scattered throughout the model into structured data, allowing the subsequent waveform optimization step S30 to directly retrieve geometric feature parameters from the dead zone mapping database without re-performing closed topology loop detection. The critical retention angle αcrit, as a key input parameter for waveform correction, directly determines the adjustment range of the geometric curvature of the backflow surface in the subsequent asymmetric guide ridge structure: a smaller critical retention angle αcrit indicates that the tangent of the original waveform in this region is closer to horizontal, requiring a larger curvature adjustment range; a larger critical retention angle αcrit indicates that the original waveform already has a certain inclination in this region, requiring a relatively smaller curvature adjustment range. The dead zone volume serves as the priority ranking criterion, allowing subsequent waveform optimization to prioritize larger bubble dead zone trap regions, eliminating the geometric defects that most severely impact grouting quality within a limited design iteration cycle. If step S20 is missing, the waveform optimization in the subsequent step S30 will not be able to know the specific location, critical retention angle, and dead zone volume of the bubble dead zone trap area. The planning of the guide ridge path will lack starting point information, and the adjustment of the curvature of the back flow surface will lack angle parameter basis. The optimization process will degenerate into aimless and blind geometric modification, which will not only fail to ensure that the bubble dead zone is effectively eliminated, but may also affect the structural stiffness of the corrugated plate due to excessive modification.

[0083] Step S20 employs a combination of virtual grouting surface step-by-step scanning and closed topological loop detection. This transforms the solution for the dynamic evolution of the gas-liquid interface in traditional computational fluid dynamics simulations into a geometric operation involving the intersection of planes and curved surfaces. This shifts the identification of bubble dead zones from relying on large-scale numerical calculations to topological analysis based on discrete geometry. The layer-by-layer scanning of the virtual grouting surface simulates the physical process of the liquid surface gradually rising during actual grouting. Each scanning height corresponds to the instantaneous state of the liquid surface at that height. After the scanning process is complete, the wetting perimeter morphology at each height position during the entire process of the liquid surface rising from the bottom to the top can be obtained, equivalent to a time-discrete snapshot of the entire grouting process. Closed topological loop detection transforms the geometric morphology of the wetting perimeter into topological features for judgment. Open curve morphology corresponds to effective channels where bubbles can escape along the curve opening direction, while closed topological loop morphology corresponds to potential dead zones where bubbles are surrounded by curves and cannot escape. Combining the bubble retention potential energy distribution map for local minimum point verification further filters out closed topological loop regions that truly cause bubble retention, excluding regions that, although geometrically closed, still allow bubble escape due to their potential energy distribution. Extracting the critical retention angle quantifies the geometric features of the bubble dead angle into angular parameters that can be used for subsequent waveform correction, giving the design of the asymmetric guide ridge a clear geometric constraint objective. The construction of the dead angle mapping database integrates scattered bubble dead angle information into a structured dataset, providing a convenient data retrieval interface and priority ranking criteria for subsequent waveform optimization.

[0084] Step S20 employs closed topological loop detection for bubble dead-angle identification, discretizing the continuous fluid dynamics problem into a connectivity judgment problem in graph theory. This provides a clear mathematical definition for determining the existence of bubble dead-angles, avoiding discrepancies in CFD simulation results caused by differences in mesh precision and convergence criteria, thus ensuring the consistency and repeatability of the identification results. Furthermore, combining the bubble retention potential energy distribution map with local minimum point verification provides a physical potential energy basis for identifying bubble dead-angle trap regions, avoiding misjudgments that might result from relying solely on geometric topology while ignoring physical constraints. The identification results are consistent with actual grouting processes. The retention behavior of air bubbles in the process has a stronger correlation; the critical retention angle is extracted and quantified into an angle parameter, so that the curvature adjustment of the subsequent waveform optimization has a clear numerical target. The optimization process changes from qualitative shape improvement to quantitative parameter optimization, and the controllability and predictability of the optimization results are improved; a dead angle mapping database is constructed and dead angle volume information is stored, so that the processing priority of multiple air bubble dead angle trap areas can be sorted according to the severity of defects. Under the condition of limited computational resources and design constraints for waveform optimization, the geometric defects that have the most serious impact on grouting quality can be eliminated first, and the optimization efficiency is improved.

[0085] Step S30: Retrieve the geometric feature parameters of the bubble dead angle trap area from the dead angle mapping database, plan the virtual flow guide path, generate an asymmetric flow guide ridge structure along the virtual flow guide path, perform iterative verification on the three-dimensional digital model of the FRP corrugated plate after generating the asymmetric flow guide ridge structure, perform process adaptation processing according to the distribution mode parameters, and output the optimized FRP corrugated plate design data.

[0086] Further, step S30 includes:

[0087] Step S31: Retrieve the position coordinates of each bubble dead angle trap area from the dead angle mapping database and calculate the geometric center of each bubble dead angle trap area; use the relative potential energy height in the bubble retention potential energy distribution map as the path cost weight, and use the weighted geodesic algorithm to plan the potential energy descent path connecting the geometric center of the bubble dead angle trap area and the zero potential energy endpoint on the inner surface of the FRP corrugated plate three-dimensional digital model, and define the potential energy descent path as a virtual flow guide path;

[0088] Specifically, step S30 performs directional correction of the micro-geometry of the crest region without changing the macroscopic wave height of the FRP corrugated plate. In traditional waveform design, the crest cross-section is a symmetrical arc or trapezoid, and the tangent of the inner surface of the crest top region tends to be horizontal. Bubbles in this region lose the driving force component for upward movement along the surface and become trapped. Step S30 generates an asymmetric flow-guiding ridge structure on the inner wall of the crest, so that the tangent of the inner surface of the crest region always remains inclined relative to the horizontal plane. Under the action of buoyancy, the bubbles can continue to move upward along the inclined inner surface until they reach the vent, thereby actively eliminating the geometric conditions for bubble trapping during the design stage. While eliminating bubble dead zones, the asymmetric flow-guiding ridge structure, as a local bulge feature of the inner wall of the corrugated plate, forms a geometric shape similar to a reinforcing rib along the axial direction of the corrugated plate, which enhances the axial bending stiffness of the FRP corrugated plate and realizes the integrated design of venting function and structural function.

[0089] In step S31, the trap area for each bubble dead zone is retrieved from the dead zone mapping database. k The location coordinates are the three-dimensional coordinates of the geometric center of the closed topological loop stored in step S23 in the global coordinate system. The geometric center of the bubble dead zone trap area serves as the starting point of the virtual flow path. Its physical meaning is the spatial location where bubbles are most likely to stagnate within this area. Planning the flow path from this location ensures that the path covers the core area of ​​the entire bubble dead zone trap area. When there are multiple bubble dead zone trap areas in the dead zone mapping database, they are processed in descending order of dead zone volume. Virtual flow paths are planned first for bubble dead zone trap areas with larger dead zone volumes. This processing order ensures that the geometric defects that have the most serious impact on grouting quality can be corrected first.

[0090] The weighted geodesic algorithm is used to plan virtual flow paths on the inner surface of a 3D digital model of an FRP corrugated sheet. A geodesic is a local shortest path connecting two points on a curved surface. Without weight constraints, a geodesic only considers geometric distance and not other physical factors. The weighted geodesic algorithm introduces path cost weights on top of the traditional geodesic algorithm, ensuring that the planned path considers not only geometric distance but also the weight distribution of points along the path. The specific implementation of using the relative potential energy height in the bubble retention potential energy distribution map as the path cost weight is as follows: For each triangular facet unit in the triangular facet unit set, its corresponding relative potential energy height is retrieved from the bubble retention potential energy distribution map; the path cost of this triangular facet unit is defined to be proportional to the relative potential energy height, specifically calculated as the path cost equal to the relative potential energy height multiplied by a preset cost coefficient; when the relative potential energy height approaches zero, the path cost approaches zero, ensuring the lowest possible passage cost in the destination area. The logic for setting the path cost is as follows: the greater the relative potential energy height, the farther the location is from the zero potential energy endpoint, the greater the path cost, and the weighted geodesic algorithm will tend to leave the area as soon as possible; the smaller the relative potential energy height, the closer the location is to the zero potential energy endpoint, the smaller the path cost, and the weighted geodesic algorithm will tend to enter the area as soon as possible.

[0091] The weighted geodesic algorithm is implemented using a surface extension of Dijkstra's algorithm: all triangular facet cells in the set are treated as nodes in a graph, and edges are established between adjacent triangular facet cells. The weight of each edge is the Euclidean distance between the centroids of two adjacent triangular facet cells multiplied by the arithmetic mean of the path costs of the two cells. Using the triangular facet cell containing the geometric center of the bubble dead zone as the source node and the triangular facet cell containing the zero potential energy endpoint as the target node, a Dijkstra shortest path search is performed. After the search is completed, the search proceeds back from the target node to the source node, and the centroid coordinates of all triangular facet cells along the backtracking path are connected sequentially to form a virtual flow path. The virtual flow path is represented as an ordered sequence of points in three-dimensional space, where the line segments connecting adjacent points are approximately located on the inner surface of the three-dimensional digital model of the FRP corrugated plate.

[0092] The method of planning virtual guiding paths using a weighted geodesic algorithm incorporates potential energy field information into the path planning process. This ensures that the planned path not only geometrically connects the bubble dead zone trap region to the zero potential energy endpoint but also physically satisfies the potential energy constraint for bubble escape. Traditional geodesic algorithms only pursue the shortest geometric distance, and the planned path may traverse regions of local potential energy maxima. When a bubble moves along this path, it must first overcome the potential energy rise before continuing, which contradicts the physical characteristic of spontaneous bubble movement under buoyancy. The planning result of the virtual guiding path directly determines the spatial orientation of the subsequent guiding ridge skeleton line, and thus the geometric shape of the asymmetric guiding ridge structure. Therefore, the rationality of the virtual guiding path directly affects the effectiveness of bubble dead zone elimination.

[0093] Step S32: Generate a flow guide ridge skeleton line along the virtual flow guide path, and split the local cross-section of the initial FRP corrugated plate three-dimensional digital model into the frontal and back surfaces with the flow guide ridge skeleton line as the center.

[0094] In step S32, a guide ridge skeleton line is generated along the virtual guide path. The guide ridge skeleton line is the central axis of the asymmetric guide ridge structure, and its spatial position determines the distribution direction of the asymmetric guide ridge structure on the inner surface of the FRP corrugated plate. The generation process of the guide ridge skeleton line is as follows: taking the virtual guide path as a reference, at each sampling point on the path, a small bulge height δridge is offset in the opposite direction of the unit normal vector n. The offset point sequence constitutes the guide ridge skeleton line. The initial value of the small bulge height δridge is set based on the following: δridge should be less than one-tenth of the base wave height to ensure that the guide ridge structure does not significantly change the macroscopic waveform characteristics of the corrugated plate. For example, when the base wave height is 50 mm, the initial value of the small bulge height δridge is set to 3 mm to 5 mm. This bulge height is sufficient to form a perceptible convex feature on the inner wall of the wave crest, while not significantly affecting the overall stiffness of the corrugated plate. The physical meaning of offsetting in the opposite direction of the unit normal vector n is: to make the guide ridge skeleton line bulge from the inner surface of the corrugated plate towards the tunnel axis, forming a local high point where bubbles tend to gather under the action of buoyancy. After the bubbles gather near the guide ridge skeleton line, they move towards the zero potential energy endpoint along the guide ridge direction.

[0095] The process of dividing the local cross-section of the initial FRP corrugated plate 3D digital model into an upstream and downstream surface, centered on the guide ridge line, is as follows: At each sampling point on the guide ridge line, a cross-section perpendicular to the tangent direction of the guide ridge line is constructed; this cross-section intersects with the inner surface of the initial FRP corrugated plate 3D digital model to form a cross-sectional profile; using the sampling point on the guide ridge line as the dividing point, the cross-sectional profile is divided into two parts: the part located on the side of the grout surface rising from the source direction (i.e., below) is defined as the upstream surface, and the part located on the side of the grout surface rising to the destination direction (i.e., above) is defined as the downstream surface. The upstream surface faces the direction of grout rising, and the grout surface contacts the upstream surface first during grouting; the downstream surface faces away from the direction of grout rising, and the grout surface contacts the downstream surface only after crossing the guide ridge line during grouting. The geometric curvatures of the frontal and back surfaces can be adjusted independently. This splitting process allows subsequent step S33 to perform differentiated curvature corrections on the back surface while maintaining the original geometric shape of the frontal surface.

[0096] The method of splitting the cross-section into an upstream and downstream surface transforms the geometry of the wave crest region from a symmetrical to an asymmetrical structure. In traditional symmetrical waveform design, the wave crest cross-section is a bilaterally symmetrical arc or trapezoid, with the same curvature on both sides, and the tangent at the crest apex tends to be horizontal. After splitting the cross-section into two independent adjustable surfaces, the upstream and downstream surfaces can be set with different curvature parameters. The crest apex is no longer a symmetrical arc apex, but an asymmetrical ridge line formed by the intersection of the upstream and downstream surfaces with different curvatures. The asymmetrical geometry means that there are no points with horizontal tangents in the wave crest region. Bubbles at any position in the wave crest region are subjected to a buoyancy component pointing towards the ridge line, thus continuously moving along the ridge line towards the zero potential energy endpoint.

[0097] Step S33: Retrieve the critical retention angle corresponding to the bubble dead angle trap area from the dead angle mapping database, and adjust the geometric curvature of the back flow surface according to the critical retention angle so that the angle between the tangent vector at any point on the back flow surface and the gravity reverse escape vector is always less than 90 degrees, forming an asymmetric guide ridge structure.

[0098] In step S33, the trap area for each bubble dead zone is retrieved from the dead zone mapping database. kThe corresponding critical retention angle αcrit directly reflects the inclination of the tangent on the inner surface when the bubble is retained in this region. The smaller the critical retention angle αcrit, the closer the tangent of the original waveform is to the horizontal in this region, and the easier it is for the bubble to be retained. The process of adjusting the geometric curvature of the backflow surface according to the critical retention angle αcrit is as follows: the target constraint for curvature adjustment is set to ensure that the angle β between the tangent vector at any point on the backflow surface and the reverse gravity escape vector F is always less than 90 degrees; the backflow surface is discretized into several cross-sectional curves perpendicular to the guide ridge skeleton line. For each cross-sectional curve, the angle β between the tangent vector at each point on it and the reverse gravity escape vector F is calculated; if there is an angle β greater than or equal to 90 degrees at a certain point, the curvature of the region where that point is located needs to be increased so that the tangent vector deviates from the horizontal direction. The specific implementation of curvature adjustment adopts the control point displacement method of B-spline surface: the backflow surface is represented as a B-spline surface, and the position of the control point of the B-spline surface is adjusted so that the tangent vector at each point on the surface satisfies the angle constraint. The formula for calculating the displacement of the control point is Δp = λ × (β - β) / 2. target )×nlocal, where Δp is the displacement vector of the control point, λ is the curvature adjustment coefficient, nlocal is the local normal vector at the control point, and β target β is the threshold for the included angle of the target. target Based on the dynamic setting of the critical retention angle αcrit, the calculation formula is β. target =90° - αcrit - Δsafe, where Δsafe is the safety margin, ranging from 5° to 10°. For example, when αcrit is 10°, β... target Set to 75° to 70°; when αcrit is 5°, β target Set to 80° to 75°. A smaller critical retention angle αcrit indicates that the original waveform is more prone to bubble retention, requiring a stricter target angle threshold to ensure sufficient tilt. When the angle β is greater than the target angle threshold β... target At that time, β-β target If the value is positive, the control point is shifted outward along the normal vector direction, causing the curved surface at that point to bulge towards the tunnel axis, increasing the inclination of the tangent vector relative to the horizontal plane and decreasing the included angle β; this is adjusted iteratively until β ≤ β target The curvature adjustment coefficient λ is set based on the following principle: λ should ensure that the change in the included angle β after a single adjustment is moderate, avoiding excessive adjustment that could lead to morphological distortion of the backflow surface. For example, the curvature adjustment coefficient λ is adaptively adjusted based on the critical retention angle αcrit. When αcrit < 10°, λ is set to a value of 0.7 to 0.8, employing a larger adjustment range; when αcrit ≥ 10°, λ is set to a value of 0.5 to 0.6, employing a smaller adjustment range, gradually approaching the target constraint through multiple iterations.

[0099] An angle β less than 90 degrees indicates an acute angular relationship between the tangent vector of the backflow surface and the vertically upward gravity escape vector F. The projection of the tangent into the vertical plane has an upward component and remains inclined with respect to the horizontal plane; there are no points where the tangent is horizontal. When a bubble adheres to the backflow surface, the tangential component of buoyancy always points in the direction of decreasing potential energy, driving the bubble to move along the guide ridge line of the backflow surface, and then along the guide ridge line towards the zero potential energy endpoint. If the angle β equals 90 degrees, it indicates that the tangent at that point is horizontal, the tangential component of buoyancy is zero, and the bubble loses its driving force to move along the surface at that point, resulting in stagnation. If the angle β is greater than 90 degrees, it indicates that the tangent at that point is inclined downward with respect to the horizontal plane, the tangential component of buoyancy points in the direction of increasing potential energy, and the bubble will tend to move away from the zero potential energy endpoint, resulting in more severe stagnation. Therefore, an angle β always being less than 90 degrees is a necessary condition to ensure that the bubble can continuously move towards the zero potential energy endpoint. After curvature adjustment, the upstream surface retains its original geometry, while the downstream surface's curvature increases, increasing its inclination relative to the horizontal plane. The upstream and downstream surfaces intersect at the guide ridge skeleton line, forming an asymmetric guide ridge structure. The cross-sectional shape of this asymmetric guide ridge structure resembles the longitudinal section of a water droplet, with the upstream surface corresponding to the rounded end of the droplet and the downstream surface to the sharp end. The guide ridge skeleton line corresponds to the tip of the droplet. This teardrop-like cross-sectional shape eliminates the local extreme points at the tangent level in the wave crest region. Under buoyancy, bubbles spontaneously gather at the guide ridge skeleton line and move along it towards the zero potential energy endpoint.

[0100] Step S34: Regenerate the bubble retention potential energy distribution map of the three-dimensional digital model of the FRP corrugated plate after generating the asymmetric flow guide ridge structure, and re-execute the closed topology loop detection of steps S21 to S22. If a new closed topology loop is detected and there is a new local minimum point in the bubble retention potential energy distribution map, increase the bulge height of the flow guide ridge skeleton line and repeat step S33. If all instantaneous wetting boundaries are open curves and there are no local minimum points in the bubble retention potential energy distribution map except for the zero potential energy endpoint, the optimization is determined to be successful. Perform process adaptation processing according to the distribution mode parameters and output the optimized FRP corrugated plate design data.

[0101] In step S34, iterative verification is performed on the three-dimensional digital model of the FRP corrugated plate after generating the asymmetric flow-guiding ridge structure. The purpose of iterative verification is to check whether the asymmetric flow-guiding ridge structure successfully eliminates all bubble dead-angle trap regions identified in step S20, and whether new bubble dead-angles are introduced during waveform correction. The specific process of iterative verification is as follows: Steps S11 to S13 are re-executed on the three-dimensional digital model of the FRP corrugated plate after generating the asymmetric flow-guiding ridge structure to generate an updated set of triangular facet elements, a gravity reverse escape vector field, and a bubble retention potential energy distribution map; the closed topological loop detection in steps S21 to S22 is re-executed using the updated model to obtain a new instantaneous wetting perimeter topological morphology; and the detection results are analyzed and judged.

[0102] The iterative verification judgment logic is as follows: if all instantaneous wetting boundaries are open curves, and there are no local minima in the updated bubble retention potential energy distribution map except for the zero potential energy endpoint, then the optimization is considered successful, and the waveform optimization process terminates; if a new closed topological loop is detected and a new local minima exist in the bubble retention potential energy distribution map, then it is determined that the current asymmetric guide ridge structure has failed to completely eliminate bubble dead corners or has introduced new bubble dead corners during the correction process. It is necessary to increase the ridge height δridge of the guide ridge skeleton line and repeat the curvature adjustment process in step S33. The increment of the ridge height δridge is set to half of the initial value. For example, if the initial ridge height δridge is 4 mm, the increment is 2 mm in the first iteration and 1 mm in the second iteration, gradually approaching the ridge height value that can eliminate all bubble dead corners with decreasing increments. A maximum iteration limit is set for the iterative process. When the iteration count reaches the limit and the verification is still not passed, the system outputs the current waveform model and marks the bubble dead corner trap areas that have not been completely eliminated, allowing designers to intervene manually.

[0103] After successful iterative verification, process adaptation processing is performed based on the distribution pattern parameters received in step S11. The purpose of process adaptation processing is to transform the optimized waveform features into engineering data that can be directly used for mold manufacturing and on-site installation. For the short-segment reinforcement mode, the process adaptation processing includes: extracting the cross-sectional contour parameters of the optimized waveform to generate a mold cavity curve adapted to the pultrusion process or vacuum induction process; generating axial truncation positions according to the user-specified short segment length to ensure that the corrugation features of each short segment are independent and complete; and outputting a CNC machining instruction file containing mold curve parameters and axial dimensions. For the segmented reinforcement mode of curved components, the process adaptation process includes: calculating the central angle range of each segment based on the number of segments and the coverage angle, and performing geometric segmentation at the segment boundaries; performing cross-segment escape continuity checks at the joint contours of adjacent segments to determine whether air bubbles will form new topological dead angles due to segment assembly tolerances or geometrical abrupt changes at the joint contours; if there is a risk of cross-segment air bubble retention, automatically adjusting the connection curvature of the asymmetric guide ridges on both sides of the joint to ensure that the grouting material can flow continuously across the segments along the asymmetric guide ridges after segment assembly; and outputting a design data file containing the mold parameters of each segment and the joint mating dimensions. The optimized FRP corrugated plate design data output format includes: a 3D geometric model file, using a common CAD exchange format to support subsequent finite element analysis and mold design; a waveform parameter table, containing optimized values ​​for the front surface curvature, back surface curvature, guide ridge height, and guide ridge direction parameters; a mold processing instruction file, containing mold cavity curve coordinates and processing paths adapted to pultrusion or vacuum induction processes; and a process specification document, containing construction guidance information such as suggested locations for grouting holes and venting holes, segmented installation sequence, and joint sealing requirements.

[0104] Step S30 employs an asymmetric flow-guiding ridge growth algorithm to perform microscopic geometric reconstruction of the waveform, eliminating bubble dead-angle trap regions without altering the macroscopic wave height of the corrugated plate. The macroscopic wave height of the corrugated plate is the primary geometric parameter determining its bending stiffness; a larger wave height results in a larger moment of inertia and stronger bending resistance. The asymmetric flow-guiding ridge structure generates slightly raised ridge lines on the inner wall of the wave crest, adjusting only the local geometry of the wave crest region without changing the vertical distance between the wave crest and trough, i.e., the macroscopic wave height. Therefore, it does not weaken the overall bending stiffness of the corrugated plate. The asymmetric flow-guiding ridge structure forms continuous raised features along the flow-guiding ridge skeleton line, functionally equivalent to axial stiffeners on the inner wall of the corrugated plate, enhancing its axial bending stiffness. The exhaust function and structural function are integrated on the same geometric feature, avoiding the dilemma of increasing material thickness to improve stiffness or sacrificing structural performance to improve exhaust, thus achieving integrated structural and functional design.

[0105] Step S30 transforms the elimination of air bubble traps from a passive response during the construction phase to a proactive prevention during the design phase. In traditional processes, designers cannot predict the location and severity of air bubble traps during the waveform design phase. When construction workers discover voids during grouting, they can only resort to rework, which not only increases construction costs and time but may also damage the cured grout layer. Step S30 identifies air bubble trap areas and generates an asymmetric flow-guiding ridge structure during the design phase, giving the corrugated plate geometric features that guide air bubbles to actively escape before it leaves the factory. Construction workers can achieve a dense grouting effect without additional venting measures during grouting, shifting the quality control checkpoint from the construction site to the design phase and fundamentally preventing void defects. Step S30 uses a weighted geodesic algorithm to plan a virtual guide path, incorporating potential energy field information into the path planning process. This ensures that the guide ridge line extends along the direction of decreasing potential energy, conforming to the physical law of bubbles spontaneously moving upwards under buoyancy. This allows for complete escape from the bubble dead zone trap area to the zero potential energy endpoint without external force. The wave crest cross-section is split into an upstream and downstream surface, allowing independent adjustment of the curvature on both sides. While maintaining the original geometry of the upstream surface, the curvature of the downstream surface is modified separately, limiting the range of geometric modification to the critical bubble retention area and avoiding excessive alteration to the overall waveform. The curvature of the downstream surface is adjusted according to the critical retention angle, ensuring that the included angle β is always... The constraint of less than 90 degrees provides a clear quantitative target for curvature adjustment. The optimization process changes from qualitative shape improvement to quantitative parameter optimization, which improves the controllability and predictability of the optimization results. The iterative verification mechanism ensures that the asymmetric flow guide ridge structure has indeed eliminated all bubble dead zone trap areas, avoiding the risk of missing some bubble dead zones or introducing new bubble dead zones in a single optimization. The waveform optimization process has convergence guarantee. The process adaptation processing transforms the optimized waveform features into engineering data that can be directly used for mold manufacturing and on-site installation, so that the design results can be seamlessly connected to the subsequent production and manufacturing links, avoiding the information gap between design and production.

[0106] Example 2

[0107] Based on Example 1, this embodiment provides an FRP corrugated plate made of fiber-reinforced composite material, which is used to cover the inner wall of tunnel segments in subway tunnel reinforcement projects.

[0108] The FRP corrugated plate includes a crest region, a trough region, and an asymmetric flow-guiding ridge structure disposed on the inner wall of the crest region. The asymmetric flow-guiding ridge structure is designed and generated using the waveform optimization design method for FRP corrugated plates in subway tunnels described in Example 1. The asymmetric flow-guiding ridge structure includes a flow-guiding ridge skeleton line, a frontal surface, and a backal surface. The flow-guiding ridge skeleton line extends along the inner wall of the crest region, extending from the geometric center of the bubble dead zone area towards the vent location; the frontal surface is located on the side of the flow-guiding ridge skeleton line facing the direction of slurry rise, maintaining the geometric curvature of the original waveform; the backal surface is located on the side of the flow-guiding ridge skeleton line away from the direction of slurry rise, and its geometric curvature is adjusted so that the angle between the tangent vector at any point on the backal surface and the reverse gravity escape vector is always less than 90 degrees.

[0109] The cross-section of the asymmetric flow guide ridge structure has an asymmetric convex shape. This asymmetric geometry means that there are no points on the inner wall of the crest region where the tangent is parallel to the horizontal plane. When the FRP corrugated plate is installed on the top of the tunnel for grouting, the bubbles gather along the back flow surface of the flow guide ridge skeleton line under the action of buoyancy, and move along the flow guide ridge skeleton line towards the exhaust hole, thereby eliminating the void defect caused by the bubbles staying at the top of the crest in the traditional symmetrical waveform design.

[0110] The parts of the technical solutions provided in the embodiments of this application that are consistent with the implementation principles of corresponding technical solutions in the prior art have not been described in detail to avoid excessive elaboration.

[0111] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A waveform optimization design method for FRP corrugated plates in subway tunnels, characterized in that, The method includes: Construct an initial three-dimensional digital model of the FRP corrugated plate, establish a gravity reverse escape vector field on the initial three-dimensional digital model of the FRP corrugated plate, and generate a bubble retention potential energy distribution map based on the gravity reverse escape vector field. Define a virtual grouting surface, control the virtual grouting surface to perform step scanning on the initial FRP corrugated plate 3D digital model, extract the instantaneous wetting perimeter, perform closed topological loop detection on the instantaneous wetting perimeter, and verify the local minimum points inside the closed topological loop by combining the bubble retention potential energy distribution map, so as to identify the bubble dead corner trap area, and construct a dead corner mapping database based on the bubble dead corner trap area; Based on the dead angle mapping database, a virtual flow path is planned, and an asymmetric flow ridge structure is generated along the virtual flow path. The three-dimensional digital model of the FRP corrugated plate after the asymmetric flow ridge structure is generated is iteratively verified, and the optimized FRP corrugated plate design data is output.

2. The waveform optimization design method for FRP corrugated plates in subway tunnels according to claim 1, characterized in that, The method for constructing the initial three-dimensional digital model of the FRP corrugated plate includes: The system receives the design parameters and distribution pattern parameters of the FRP corrugated plate to be optimized, as well as the tunnel segment installation parameters. The design parameters of the FRP corrugated plate to be optimized include the foundation wave height, wave pitch, and plate thickness. The distribution pattern parameters include the short-segment interval reinforcement mode for local reinforcement and the segmented reinforcement mode for bending members. The tunnel segment installation parameters include the inner diameter of the tunnel segment. A reference mounting surface is constructed based on the tunnel segment installation parameters. An initial three-dimensional digital model of the FRP corrugated plate is generated on the reference mounting surface based on the design parameters and distribution pattern parameters of the FRP corrugated plate to be optimized.

3. The waveform optimization design method for FRP corrugated plates in subway tunnels according to claim 2, characterized in that, The method for establishing the gravity reverse escape vector field includes: The initial three-dimensional digital model of the FRP corrugated plate is discretized into a mesh to obtain a set of triangular facet elements. Define a global gravity unit vector, calculate the gravity reverse escape vector corresponding to each triangular patch element in the triangular patch element set based on the global gravity unit vector, and construct a gravity reverse escape vector field.

4. The waveform optimization design method for FRP corrugated plates in subway tunnels according to claim 3, characterized in that, The method for generating the bubble retention potential energy distribution map includes: Mark the zero potential energy endpoint on the initial FRP corrugated plate 3D digital model, calculate the relative potential energy height of each triangular facet element reaching the geometric highest boundary of the initial FRP corrugated plate 3D digital model along the direction of the gravity reverse escape vector, and summarize the relative potential energy heights of all triangular facet elements to generate a bubble retention potential energy distribution map.

5. The waveform optimization design method for FRP corrugated plates in subway tunnels according to claim 4, characterized in that, The method for extracting the instantaneously wetted perimeter includes: The virtual grouting liquid surface is controlled to perform layer-by-layer scanning of the initial FRP corrugated plate three-dimensional digital model along the direction of the gravity reverse escape vector field with a preset scanning step size, so as to obtain a discrete scanning height sequence. At each scan height in the discrete scan height sequence, the geometric intersection line between the virtual grouting liquid surface and the inner surface of the initial FRP corrugated plate three-dimensional digital model is calculated, and the geometric intersection line is defined as the instantaneous wetting perimeter.

6. The waveform optimization design method for FRP corrugated plates in subway tunnels according to claim 5, characterized in that, The aforementioned closed topological loop detection of the instantaneous wetting boundary refers to performing topological connectivity analysis on the instantaneous wetting boundary to determine whether the instantaneous wetting boundary forms a closed topological loop; The method for determining whether a closed topological loop is formed at the instantaneous wetting boundary is as follows: The instantaneous wetting perimeter is represented as a graph structure composed of intersecting line segments, with the endpoints of the intersecting line segments as nodes of the graph and the intersecting line segments themselves as edges of the graph. The degree of each node is counted. If the degree of all nodes is even and the graph structure is connected, then the instantaneous wetting perimeter is determined to form a closed topological cycle.

7. The waveform optimization design method for FRP corrugated plates in subway tunnels according to claim 6, characterized in that, The method for identifying bubble dead zone trap areas includes: If instantaneous wetting of the perimeter forms a closed topological loop and the internal projection region of the closed topological loop does not contain the zero potential energy endpoint, then query the bubble retention potential energy distribution map, verify that there is a local minimum point of relative potential energy height inside the closed topological loop, and mark the area enclosed by the closed topological loop as the bubble dead zone trap region.

8. The waveform optimization design method for FRP corrugated plates in subway tunnels according to claim 7, characterized in that, The constructed dead angle mapping database contains the location coordinates, critical retention angle, and dead angle volume of each bubble dead angle trap area; The method for planning virtual flow paths includes: retrieving the location coordinates of each bubble dead zone trap area from the dead zone mapping database, and calculating the geometric center of each bubble dead zone trap area; Using the relative potential energy height in the bubble retention potential energy distribution map as the path cost weight, a weighted geodesic algorithm is used to plan the potential energy descent path connecting the geometric center of the bubble dead zone trap area and the zero potential energy endpoint on the inner surface of the FRP corrugated plate three-dimensional digital model. The potential energy descent path is defined as a virtual flow guiding path.

9. The waveform optimization design method for FRP corrugated plates in subway tunnels according to claim 8, characterized in that, The method for generating the asymmetric flow-guiding ridge structure includes: The virtual flow path generates a flow ridge skeleton line, and the local cross-section of the initial FRP corrugated plate three-dimensional digital model is split into the front and back surfaces with the flow ridge skeleton line as the center. The critical retention angle corresponding to the bubble dead angle trap area is retrieved from the dead angle mapping database. The geometric curvature of the back flow surface is adjusted according to the critical retention angle so that the angle between the tangent vector at any point on the back flow surface and the gravity reverse escape vector is always less than 90 degrees, forming an asymmetric guide ridge structure.

10. An FRP corrugated sheet, characterized in that, The FRP corrugated plate includes a crest region, a trough region, and an asymmetric flow-guiding ridge structure disposed on the inner wall of the crest region. The asymmetric flow-guiding ridge structure is designed and generated using the waveform optimization design method for FRP corrugated plates in subway tunnels as described in any one of claims 1-9.

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