Design method and system of composite support of flexible anchor net and high-performance shotcrete

Abstract

The application discloses a composite support design method and system of flexible anchor net and high-performance sprayed concrete, and particularly relates to the field of computer-aided engineering analysis, and is used for solving the problem that the existing composite support design method ignores the lag process of the steel mesh film effect established after the concrete cracking, thereby causing the distortion of crack width calculation; the method obtains the mesh hole side length of the flexible diamond net, the steel diameter, the ultimate tensile strain of the sprayed concrete and the design bending moment, and establishes a computer-aided engineering model of the composite support section, calculates the steel mesh strain at the cracking moment, differentiates the angle difference between the long axis direction of the diamond hole and the main incident direction of the sprayed flow to determine the tension strain increment, takes the comparison result of the elastic energy and the deformation energy as the basis for judging the resistance empty window period, transitions the stiffness in the presence of the resistance empty window period through the tension strain increment, and outputs the corrected crack width, and outputs the crack width based on the complete coordination assumption in the absence of the resistance empty window period.

Description

Technical Field

[0001] This invention relates to the field of computer-aided engineering analysis technology, and more specifically, to a design method and system for composite support of flexible anchor mesh and high-performance shotcrete. Background Technology

[0002] In computer-aided engineering analysis of underground engineering and tunnel support structures, the design of composite support of flexible anchor mesh and high-performance shotcrete usually follows the theory of synergistic stress of reinforced concrete. Designers use finite element or analytical calculation models to regard the shotcrete layer and the steel mesh as a fully bonded and strain-coordinated combination, and assume that once the concrete in the tension zone reaches its ultimate tensile strain and cracks, the steel mesh at the crack immediately enters an elastic tensile state and contributes resistance according to its cross-sectional stiffness. This type of method does not distinguish the initial geometric relaxation that exists objectively due to the mesh structure and laying process of the flexible rhomboid mesh, nor does it reflect the tension deformation process that the steel mesh needs to undergo before providing an effective membrane effect. As a result, the mechanical connection between the concrete resistance drop after the peak and the establishment of the steel mesh membrane effect in the computer-aided design process is simplified to an instantaneous completion.

[0003] The above design method ignores the lag process of the establishment of the steel mesh effect after concrete cracking, making it difficult for computer-aided engineering models to accurately assess the crack width and instantaneous deflection jump of composite support under normal serviceability limits. As a result, the design optimization and performance prediction based on this type of model cannot truly reflect the transition behavior of the support structure from concrete cracking to mesh-coordinated load bearing. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the present invention provides a composite support design method and system of flexible anchor mesh and high-performance shotcrete to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] The design method for composite support using flexible anchor mesh and high-performance shotcrete includes the following steps:

[0007] S1. Obtain the mesh side length, steel bar diameter, ultimate tensile strain of shotcrete, and design bending moment of flexible diamond mesh;

[0008] S2. A computer-aided engineering model of the composite support section is established using the mesh side length, steel bar diameter, ultimate tensile strain and design bending moment. The strain of the steel mesh generated by the flexible rhombus mesh is calculated when the shotcrete reaches the ultimate tensile strain.

[0009] S3. Obtain the angle between the long axis of the rhombus holes and the main incident direction of the sprayed concrete flow after the flexible rhombus mesh is laid. When the angle falls into the preset acute angle range, determine the tension strain increment according to the mesh side length and the rebar diameter. Otherwise, add the tension term triggered by the incident deviation angle on the basis determined according to the mesh side length and the rebar diameter to obtain the tension strain increment.

[0010] S4. Determine the elastic energy released in the tension zone at the moment of cracking of shotcrete based on the strain of the steel mesh. Determine the deformation energy required for the flexible rhomboid mesh to enter the membrane effect based on the tension strain increment. Determine whether the elastic energy is less than the deformation energy. If so, there is a resistance gap period.

[0011] S5. When there is a resistance gap, the stiffness transition between the shotcrete softening section and the mesh reinforcement section is connected by tension strain increment in the computer-aided engineering model, and the corrected crack width is output; when there is no resistance gap, the crack width based on the complete synergistic assumption is output.

[0012] Furthermore, the mesh size side lengths, rebar diameters, ultimate tensile strain of shotcrete, and design bending moment of the flexible rhomboid mesh are obtained, including:

[0013] The selection of flexible diamond mesh is determined based on the classification of the surrounding rock in the section to be supported, and the mesh side length and steel bar diameter are extracted from the selection record;

[0014] The strength grade of the shotcrete is determined based on the surrounding rock classification and groundwater environment level of the section to be supported, and the ultimate tensile strain corresponding to the strength grade is extracted.

[0015] Based on the surrounding rock stress level and the tunnel excavation span, calculate the design bending moment that the composite support section needs to bear.

[0016] Furthermore, the surrounding rock classification is evaluated using basic quality indicators of the surrounding rock. The in-situ stress level is determined based on the ratio of the measured in-situ stress to the uniaxial saturated compressive strength of the surrounding rock. When this ratio exceeds the critical value, the design bending moment is multiplied by an amplification factor that is positively correlated with the excess.

[0017] Furthermore, a computer-aided engineering model of the composite support section is established using the mesh side length, rebar diameter, ultimate tensile strain, and design bending moment. The strain generated by the flexible rhomboid mesh when the shotcrete reaches its ultimate tensile strain is calculated, including:

[0018] The flexible rhombic mesh is equivalent to an orthotropic membrane layer based on the mesh side length and the steel bar diameter. The shotcrete is equivalent to a tensile softening layer based on the ultimate tensile strain. The interface between the flexible rhombic mesh and the shotcrete is equivalent to an interface transition layer based on the bonding coefficient. A computer-aided engineering model with a three-layer composite section is formed by combining these components.

[0019] In the computer-aided engineering model of the composite support section, the design bending moment is applied, and the tensile strain of each layer of shotcrete is determined layer by layer along the section height direction. The layer that first reaches the ultimate tensile strain is then extracted.

[0020] The tensile strain of the flexible rhomboid mesh at this layer in the direction of the ultimate tensile strain of the shotcrete is extracted as the strain of the reinforcing mesh.

[0021] Furthermore, the angle between the long axis of the rhomboid holes and the main incident direction of the shotcrete jet after the flexible rhomboid mesh is laid is obtained. When the angle falls within a preset acute angle range, the tension strain increment is determined according to the mesh side length and the rebar diameter; otherwise, a tension term triggered by the incident deviation angle is added to the basis determined according to the mesh side length and the rebar diameter to obtain the tension strain increment, including:

[0022] Based on the mesh posture record after the flexible rhombus mesh is laid and the spraying direction record of the shotcrete construction, the angle between the long axis of the rhombus hole and the main incident direction of the spray flow is calculated.

[0023] Compare the included angle with the preset acute angle range. If the included angle falls into the preset acute angle range, the foundation tension coefficient is determined by the ratio of the mesh side length to the rebar diameter. The product of the foundation tension coefficient and the mesh side length is used as the tension strain increment.

[0024] If the included angle does not fall within the preset acute angle range, the difference between the included angle and the boundary value of the preset acute angle range is calculated as the incident deviation angle. The product of the basic tension coefficient and the tangent of the incident deviation angle is used as the additional tension term. The sum of the product of the basic tension coefficient and the mesh side length and the additional tension term is used as the tension strain increment.

[0025] Furthermore, the upper boundary of the preset acute angle interval is set according to the ratio of the mesh side length to the diameter of the reinforcing bar. The larger the ratio, the smaller the upper boundary. The lower boundary of the preset acute angle interval is the minimum incident angle at which the sprayed concrete flow forms effective filling in the diamond-shaped hole.

[0026] Furthermore, based on the computer-aided engineering model of the composite support section, the layer where the shotcrete first reaches its ultimate tensile strain is determined. Combining the tensile strength corresponding to the shotcrete strength grade and the volume of the tension zone at that layer, the elastic strain energy released at the moment of cracking is calculated as the elastic energy. Based on the elastic modulus of the flexible rhomboid mesh, the cross-sectional area of ​​a single steel bar corresponding to the steel bar diameter, and the tension strain increment, the external force work required to tension the flexible rhomboid mesh across that layer to the membrane effect state is calculated as the deformation energy. The elastic energy is compared with the deformation energy. If the elastic energy is less than the deformation energy, it is determined that there is a resistance gap.

[0027] Furthermore, the difference between elastic energy and deformation energy is divided by deformation energy to obtain the energy difference ratio. When the energy difference ratio is positive and exceeds the preset tolerance threshold, the resistance gap period is determined to be significant, and the additional crack width increment mapped by the energy difference ratio is superimposed when outputting the corrected crack width.

[0028] Furthermore, when a resistance gap exists, in the computer-aided engineering model of the composite support section, after the shotcrete reaches its ultimate tensile strain, the tensile stiffness of the shotcrete is reduced along the softening curve, while the tensile strain of the flexible rhombus mesh is maintained in a relaxed state before the tension strain increment, until the accumulated tensile strain of the flexible rhombus mesh reaches the tension strain increment. After that, the deformation coordination between the shotcrete and the flexible rhombus mesh is restored, and the membrane effect stiffness of the flexible rhombus mesh is incorporated into the section stiffness. The corrected crack width is calculated based on the section stiffness history including stiffness transition. When there is no resistance gap, it is assumed that the flexible rhombus mesh instantaneously enters a cooperative tensile state at the moment the shotcrete cracks, and the crack width is calculated and output according to the assumption of complete cooperation.

[0029] On the other hand, the present invention provides a composite support design system of flexible anchor mesh and high-performance shotcrete, comprising the following modules:

[0030] The parameter acquisition module is used to obtain the mesh side length of the flexible rhombus mesh, the diameter of the reinforcing bars, the ultimate tensile strain of the shotcrete, and the design bending moment.

[0031] The strain calculation module is used to establish a computer-aided engineering model of the composite support section using the mesh side length, rebar diameter, ultimate tensile strain and design bending moment, and to calculate the rebar strain generated by the flexible rhomboid mesh when the shotcrete reaches the ultimate tensile strain.

[0032] The increment determination module is used to obtain the angle between the long axis of the rhombus holes of the flexible rhombus mesh and the main incident direction of the sprayed concrete flow after the flexible rhombus mesh is laid. When the angle falls into the preset acute angle range, the tension strain increment is determined according to the mesh side length and the rebar diameter. Otherwise, the tension term triggered by the incident deviation angle is added to the basis determined according to the mesh side length and the rebar diameter to obtain the tension strain increment.

[0033] The window of resistance determination module is used to determine the elastic energy released in the tension zone at the moment of cracking of shotcrete based on the strain of the steel mesh, to determine the deformation energy required for the flexible rhomboid mesh to enter the membrane effect based on the tension strain increment, and to determine whether the elastic energy is less than the deformation energy. If so, there is a resistance window of resistance.

[0034] The results output module is used to connect the stiffness transition between the shotcrete softening section and the mesh reinforcement section in the computer-aided engineering model by using tension strain increment when there is a resistance gap, and output the corrected crack width; when there is no resistance gap, it outputs the crack width based on the complete synergistic assumption.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The parameter of tension strain increment was introduced into the computer-aided engineering model, incorporating the deformation process of the flexible rhomboid mesh from its initial relaxed state to the formation of an effective membrane effect into the design calculation process. By establishing a comparison criterion between the mesh strain at the moment of cracking and the tension strain increment, the computer-aided analysis model can distinguish between the ideal situation where the mesh participates in the load-bearing instantaneously after the shotcrete cracks and the real situation where the mesh effect is established with a lag. This corrects the defect in traditional collaborative calculations that simplifies the connection between the concrete peak resistance drop and the mesh reinforcement as instantaneous, and improves the analytical ability of the composite support design method for the transition process of cross-sectional stiffness after bending cracking.

[0037] The value of the tension strain increment is determined by the difference in the angle between the main incident direction of the jet stream and the long axis of the rhomboid hole. This enables the computer-aided engineering model to reflect the influence of construction factors on the timing of the activation of the steel mesh effect. By combining the quantitative comparison of the energy released by concrete cracking and the energy required for mesh tensioning, the existence of a resistance gap can be identified in the design stage. For cases with a gap, the calculation results of crack width that are more consistent with the actual transition behavior are output through stiffness transition correction. This provides an analytical basis that is closer to the actual response of the support structure for the matching of cross-sectional parameters and reinforcement scheme optimization of flexible anchor mesh and high-performance shotcrete. Attached Figure Description

[0038] Figure 1 This is a flowchart of the composite support design method of flexible anchor mesh and high-performance shotcrete of the present invention.

[0039] Figure 2 This is a flowchart illustrating the determination of the tension strain increment in this invention;

[0040] Figure 3 This is a schematic diagram of the composite support design system of flexible anchor mesh and high-performance shotcrete 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 of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0042] Example 1: Figure 1 The present invention provides a composite support design method for flexible anchor mesh and high-performance shotcrete, which includes the following steps:

[0043] S1. Obtain the mesh side length, steel bar diameter, ultimate tensile strain of shotcrete, and design bending moment of flexible diamond mesh;

[0044] S2. A computer-aided engineering model of the composite support section is established using the mesh side length, steel bar diameter, ultimate tensile strain and design bending moment. The strain of the steel mesh generated by the flexible rhombus mesh is calculated when the shotcrete reaches the ultimate tensile strain.

[0045] S3. Obtain the angle between the long axis of the rhombus holes and the main incident direction of the sprayed concrete flow after the flexible rhombus mesh is laid. When the angle falls into the preset acute angle range, determine the tension strain increment according to the mesh side length and the rebar diameter. Otherwise, add the tension term triggered by the incident deviation angle on the basis determined according to the mesh side length and the rebar diameter to obtain the tension strain increment.

[0046] S4. Determine the elastic energy released in the tension zone at the moment of cracking of shotcrete based on the strain of the steel mesh. Determine the deformation energy required for the flexible rhomboid mesh to enter the membrane effect based on the tension strain increment. Determine whether the elastic energy is less than the deformation energy. If so, there is a resistance gap period.

[0047] S5. When there is a resistance gap, the stiffness transition between the shotcrete softening section and the mesh reinforcement section is connected by tension strain increment in the computer-aided engineering model, and the corrected crack width is output; when there is no resistance gap, the crack width based on the complete synergistic assumption is output.

[0048] In the specific implementation of S1, a geological survey is conducted on the section to be supported to obtain basic data on the integrity of the surrounding rock mass, the hardness of the rock, the groundwater status, and the initial in-situ stress. The basic quality index values ​​of the surrounding rock are calculated according to the evaluation method for basic quality indexes, and the surrounding rock classification of the section to be supported is determined based on the range of these values. A flexible diamond mesh selection record is pre-established, storing the specifications of the flexible diamond mesh corresponding to different surrounding rock classifications of the section to be supported. The specifications of each flexible diamond mesh include at least the mesh opening side length and the rebar diameter. After obtaining the surrounding rock classification of the section to be supported, the specifications of the flexible diamond mesh corresponding to the classification in the selection record are queried, and the mesh opening side length and the rebar diameter of the flexible diamond mesh are directly extracted from these specifications. The correspondence between the surrounding rock classification and the specification parameters of the flexible diamond mesh in each section to be supported in the selection record of the flexible diamond mesh is determined through prior orthogonal tests or numerical simulations to ensure the matching of the flexible diamond mesh with the deformation level of the surrounding rock.

[0049] Based on the determination of the surrounding rock classification of the section to be supported, and combined with the groundwater exposure status and water quality analysis results obtained from the geological survey, the groundwater environment is classified into several levels, including dry, wet, seeping, dripping, and flowing. A mapping table between the shotcrete strength grade and the ultimate tensile strain of shotcrete is pre-constructed, simultaneously linking the surrounding rock classification and the groundwater environment level of the section to be supported to the two input conditions. After determining the surrounding rock classification and the groundwater environment level of the section to be supported, the shotcrete strength grade is obtained by querying the mapping table, and the ultimate tensile strain of the shotcrete corresponding to the strength grade is extracted from the same mapping table.

[0050] When obtaining the surrounding rock stress level, in-situ in-situ stress measurement methods, such as hydraulic fracturing or stress relief methods, are used to measure the in-situ stress at the measuring point. The maximum principal stress in the measured in-situ stress is taken as the representative value of the surrounding rock stress level. Simultaneously, surrounding rock samples are collected for indoor uniaxial saturated compressive strength tests to obtain the uniaxial saturated compressive strength of the surrounding rock. The tunnel excavation span is the maximum horizontal width of the tunnel design section, directly extracted from the tunnel design drawings. The design bending moment that the composite support section needs to bear is calculated. The surrounding rock stress level is treated as a distributed load acting on the interface between the surrounding rock and the support. The bending moment envelope value is determined using a simply supported beam model or an elastic foundation beam model, combined with the tunnel excavation span, and is taken as the design bending moment. When detailed in-situ stress field data is lacking, an empirical analogy method can also be used. Based on the surrounding rock classification of the section to be supported and the tunnel excavation span, the design bending moment is calculated by referring to the support reaction force of adjacent existing tunnels.

[0051] The specific process for evaluating the basic quality indicators of surrounding rock used in surrounding rock classification is as follows: The saturated uniaxial compressive strength of the rock is measured as an indicator of rock hardness, and the rock mass integrity index is measured as an indicator of rock mass integrity. These indicators are then substituted into a linear combination relationship to calculate the basic quality indicators of the surrounding rock. The surrounding rock is then classified according to the levels of these basic quality indicators for the sections requiring support. The method for determining the geostress level is as follows: The ratio of the measured geostress to the uniaxial saturated compressive strength of the surrounding rock is calculated, and this ratio is used as the geostress level ratio. A critical value for the geostress level ratio is pre-set based on engineering experience or numerical tests. When the geostress level ratio exceeds the critical value, it indicates that the deformation pressure of the surrounding rock will increase significantly under high geostress conditions, requiring an amplification of the design bending moment. The design bending moment is multiplied by an amplification factor that is positively correlated with the excess. The amplification factor is determined as follows: the excess is equal to the ratio of the ground stress level minus the critical value of the ground stress level ratio. The amplification factor is equal to the sum of 1 and the excess multiplied by the amplification slope. The amplification slope is selected comprehensively based on the importance level of the project and the allowable deformation of the surrounding rock. The larger the excess, the larger the amplification factor, but the amplification factor shall not exceed the pre-set upper limit value. The upper limit value is determined based on the principle of balancing the economy and safety of the support structure.

[0052] In the specific implementation of S2, the flexible rhombic mesh is equivalent to an orthotropic membrane layer. The equivalent elastic modulus and equivalent thickness of the orthotropic membrane layer in the two orthogonal principal directions are determined based on the mesh size and rebar diameter of the flexible rhombic mesh. Taking a section to be supported as an example, the rebar diameter of the flexible rhombic mesh is 5mm, the mesh size is 120mm, the long axis direction of the rhombic mesh is taken as the first principal direction, and the direction perpendicular to the long axis direction of the rhombic mesh is taken as the second principal direction. In the first principal direction, a 1m width is measured along this direction. Within this 1m width, 8 diamond-shaped holes are counted. The cross-sectional area of ​​the reinforcing steel contributed by each diamond-shaped hole in the first principal direction is calculated by converting the cross-sectional area of ​​a single reinforcing steel bar (19.6mm²), resulting in a reinforcing steel cross-sectional area per unit width of 157mm² / m in the first principal direction. The membrane thickness is taken as the reinforcing steel diameter of 5mm. The equivalent elastic modulus in the first principal direction is taken as the elastic modulus of the reinforcing steel material: 200GPa × 157mm² / m / 5mm = 6.28GPa / m. In the second principal direction, a 1m width is measured along this direction, and 6 diamond-shaped holes are counted. The cross-sectional area of ​​the reinforcing steel per unit width in the second principal direction is taken as 118mm² / m. The equivalent elastic modulus in the second principal direction is taken as the elastic modulus of the reinforcing steel material: 200GPa × 118mm² / m / 5mm = 4.72GPa / m. This gives the orthotropic membrane layer the characteristic of unequal stiffness in the two principal directions.

[0053] The shotcrete is considered as a tensile softening layer, and its ultimate tensile strain is used as the cracking boundary strain of the tensile softening layer. The shotcrete strength grade selected for a certain tunnel section is C30. Referring to the material property data corresponding to C30 shotcrete, its elastic modulus is 25 GPa, tensile strength is 2.0 MPa, ultimate tensile strain is 150 με, and fracture energy parameter is 100 N / m. The stress-strain relationship of C30 shotcrete is divided into a pre-peak linear elastic segment and a post-peak softening segment. The stiffness of the pre-peak linear elastic segment is taken as the elastic modulus of 25 GPa. The post-peak softening segment is described by linear softening. The slope of the linear softening segment is obtained by multiplying the tensile strength (2.0 MPa) / ultimate tensile strain (150 με) by the softening rate reduction factor. The softening rate reduction factor is calculated by inversely using the fracture energy parameter (100 N / m) and the crack width. In this example, the softening rate reduction factor is taken as 0.1, resulting in a softening segment slope of 2.0 MPa / 150 με × 0.1 ≈ 1.33 MPa / με. The thickness of the tensile softening layer is taken as the total thickness of the shotcrete layer at the design section, which is 250 mm in this example.

[0054] The interface between the flexible diamond mesh and the shotcrete was considered as an equivalent transition layer. Direct shear tests were conducted on C30 shotcrete and a 5mm diameter flexible diamond mesh composite specimen to obtain the bond coefficient. Six sets of 300mm×300mm×100mm composite specimens were prepared and tested on a direct shear apparatus after 28 days of curing. Normal pressures of 0.1MPa, 0.3MPa, 0.5MPa, 0.7MPa, 1.0MPa, and 1.5MPa were applied, and the shear strength under each normal pressure was recorded. A curve showing the relationship between shear strength and normal pressure was plotted, and the slope of the curve was used as the bond coefficient. In this example, the bond coefficient was measured to be 1.2MPa / mm. When experimental data is unavailable, it can be estimated based on the water-cement ratio of 0.45 and the strength grade of the C30 shotcrete. The lower the water-cement ratio and the higher the strength grade of the shotcrete, the larger the bond coefficient value. The thickness of the interface transition layer is taken as a preset ratio of 120mm mesh side length. The preset ratio is calculated based on the value of the adhesion coefficient. In this example, the adhesion coefficient is 1.2MPa / mm, and the preset ratio is taken as 0.08, so the thickness of the interface transition layer is 120mm×0.08=9.6mm.

[0055] A computer-aided engineering model of a three-layer composite section was constructed by combining an orthotropic membrane layer, a tension softening layer, and an interface transition layer. These layers were arranged sequentially along the section height from the tension side to the compression side. The orthotropic membrane layer, with a thickness of 5 mm, was placed as the outermost layer on the tension side of the composite support section. The interface transition layer was centrally located with a thickness of 9.6 mm, and the tension softening layer, with a thickness of 250 mm, was located near the neutral axis. Displacement transfer between the three layers was controlled by the bonding coefficient of the interface transition layer (1.2 MPa / mm). Under applied load, relative slippage occurred between the orthotropic membrane layer and the tension softening layer. The amount of relative slippage was inversely proportional to the bonding coefficient; a higher bonding coefficient resulted in a smaller relative slippage.

[0056] In the computer-aided engineering model of the composite support section, a design bending moment is applied. This design bending moment is then applied as a pair of equal and opposite concentrated forces to both ends of the computer-aided engineering model of the composite support section, with a force spacing of 1m, causing unidirectional bending deformation of the section. The tension side of the section corresponds to the surrounding rock side. The tension softening layer is divided into 20 sub-layers along the section height direction, with each sub-layer having a thickness of 250mm / 20=12.5mm. The average tensile strain of each sub-layer is calculated layer by layer from the outermost edge of the tension side towards the neutral axis. The average tensile strain of each sublayer is calculated based on the plane section assumption. The nominal tensile strain of each sublayer is determined by the product of the section curvature and the distance of each sublayer from the neutral axis. The section curvature is calculated based on the design bending moment, the section stiffness of the composite support section, and the section moment of inertia. The section stiffness of the composite support section is determined by section conversion based on the equivalent elastic modulus of the first principal direction of the orthotropic membrane layer (6.28 GPa / m), the equivalent elastic modulus of the second principal direction (4.72 GPa / m), the elastic modulus of C30 shotcrete (25 GPa), and the bond coefficient (1.2 MPa / mm). Starting from the first sublayer at the outermost edge of the tension side, the nominal tensile strain of each sublayer is compared with the ultimate tensile strain of C30 shotcrete (150 με). When comparing the sixth sublayer, the nominal tensile strain of the sixth sublayer is 152 με, which is the first time the ultimate tensile strain of C30 shotcrete (150 με) has been reached and exceeded. The comparison of sublayers is then stopped, and the sixth sublayer is marked as the layer that first reached the ultimate tensile strain.

[0057] The tensile strain of the flexible rhomboid mesh at the layer that first reaches its ultimate tensile strain in the first principal direction is extracted and taken as the strain of the reinforcing mesh. In the first principal direction, the sixth sublayer that first reaches its ultimate tensile strain is 6 × 12.5 mm = 75 mm from the outermost edge of the tension side. The interface transition layer at the corresponding position of the sixth sublayer exhibits tensile deformation corresponding to the nominal tensile strain of 152 με. The orthotropic membrane layer at the corresponding point in the first principal direction experiences synchronous tensile stress. Due to the finite value of the bonding coefficient of 1.2 MPa / mm, the actual tensile strain of the orthotropic membrane layer at the corresponding point is less than that of the interface transition layer. Therefore, the actual tensile strain of the orthotropic membrane layer at the corresponding point, 125 με, is taken as the strain of the reinforcing mesh. The dimensionality of the reinforcing mesh strain 125 με is consistent with the ultimate tensile strain 150 με of C30 shotcrete, both being micro-strain units. This dimensional consistency ensures that the reinforcing mesh strain can be directly compared with the tensile strain increment in subsequent measurements using similar physical quantities.

[0058] Figure 2A flowchart for determining the tension strain increment of this invention is provided. In specific implementation S3, after the flexible rhombus mesh is laid, a 3D laser scanner is used to scan the spatial morphology of the laid mesh surface to obtain the spatial 3D coordinates of each rhombus hole node on the mesh surface, forming a mesh surface attitude record after laying. The mesh surface attitude record includes the x-axis, y-axis, and z-axis coordinates of each rhombus hole node. The coordinate system is based on the tunnel axis as the x-axis, the tunnel circumferential direction as the y-axis, and the tunnel radial direction pointing towards the surrounding rock as the z-axis. The coordinates of the four corner nodes of any rhombus hole are extracted from the mesh surface attitude record. The direction vectors of the two diagonals of the rhombus hole are calculated, and the longer diagonal direction is taken as the major axis direction of the rhombus hole. The major axis direction of the rhombus hole is represented in unit vector form.

[0059] During shotcrete construction, the attitude and flow sensors on the shotcrete robot record the shotcrete construction parameters, forming a shotcrete direction record. This record includes the spatial coordinates of the spray nozzle and the spray flow exit direction vector at each moment. The exit direction vector is represented as a unit vector, pointing in the direction of the shot stream's movement. The shotcrete direction record is spatially matched with the shotcrete coverage area according to a time sequence to determine the shotcrete moment corresponding to the location of the target diamond-shaped hole. The exit direction vector at that moment is then extracted as the main incident direction of the shot stream.

[0060] The angle between the major axis of the rhombus orifice and the main incident direction of the jet stream is calculated by taking the inverse cosine of the absolute value of the dot product of the unit vector of the major axis of the rhombus orifice and the unit vector of the main incident direction of the jet stream. The angle value is between 0° and 90°. Using data from a specific paving section, the flexible diamond mesh has a mesh side length of 120mm and a steel bar diameter of 5mm. After the mesh is laid, a typical diamond hole is selected. After scanning with a 3D laser scanner, the unit vectors along the major axis of the diamond hole are 0.87, 0.35, and 0.35. The corresponding unit vectors along the main incident direction of the jet flow in the jet direction record are 0.94, 0.24, and 0.24. The dot product of the two unit vectors is 0.87×0.94+0.35×0.24+0.35×0.24=0.9858. The angle after taking the inverse cosine is 9.6°, indicating that the major axis of the diamond hole is nearly parallel to the main incident direction of the jet flow, with a small incident deviation.

[0061] A preset acute angle range is established. The upper boundary of this range is set based on the ratio of the mesh side length to the rebar diameter of the flexible diamond mesh. The larger the ratio, the smaller the upper boundary. For example, in this example, the ratio of the mesh side length of 120mm to the rebar diameter of 5mm is 24, and the upper boundary of the preset acute angle range corresponding to this ratio is set to 15°. The lower boundary of the preset acute angle range is taken as the minimum incident angle at which the sprayed concrete flow effectively fills the diamond holes. The minimum incident angle is determined through on-site spraying calibration tests. The test method involves spraying concrete onto the diamond mesh surface of the specimen at different incident angles under the same spraying distance and pressure conditions, observing the degree of filling of the diamond holes, and taking the incident angle at which the filling rate first reaches 90% or more as the minimum incident angle. For example, in this example, the calibrated minimum incident angle is 5°, thus the preset acute angle range is from 5° to 15°.

[0062] The calculated included angle of 9.6° was compared with the preset acute angle range of 5° to 15°. Since 9.6° falls within this range, the tension strain increment was determined based on the included angle falling within the preset acute angle range. The foundation tension coefficient was determined using the ratio of the mesh side length to the reinforcing bar diameter of the flexible rhomboid mesh, which is 24. This foundation tension coefficient reflects the deformation ratio required for the rhomboid holes to be tensioned from a relaxed state to a force-transmitting state when the jet stream is incident. The correspondence between the foundation tension coefficient and the ratio of the mesh side length to the reinforcing bar diameter was pre-established through a tension calibration test. The test method involved taking rhomboid mesh samples with different combinations of mesh side lengths and reinforcing bar diameters, stretching the rhomboid holes on a universal testing machine, recording the strain history of the rhomboid holes from a relaxed state to a force-transmitting state, and extracting the strain value corresponding to the strain initiation point as the foundation tension coefficient. For example, in this case, the ratio of the mesh side length to the rebar diameter is 24. Referring to the pre-established table of correspondence between the foundation tension coefficient and the ratio of the mesh side length to the rebar diameter, the foundation tension coefficient is set to 0.008. The product of the foundation tension coefficient (0.008) and the mesh side length (120mm), 0.96mm, is taken as the value of the tension strain increment. The corresponding dimensionless tension strain increment is 0.96mm divided by the mesh side length (120mm), which is 8000 microstrain.

[0063] When an angle does not fall within the preset acute angle range, for example, if another rhomboid hole has an angle of 22° due to a laying posture deviation, exceeding the upper boundary of the preset acute angle range by 15°, the difference between the angle of 22° and the upper boundary of the preset acute angle range by 15° is calculated, resulting in an incident deviation angle of 7°. The additional tension term is obtained by multiplying the basic tension coefficient 0.008 by the tangent of the incident deviation angle 7°. The tangent of the incident deviation angle 7° is 0.1228. The product of the basic tension coefficient 0.008 and 0.1228 is 0.00098. The strain corresponding to the additional tension term is the dimensionless quantity corresponding to 0.00098 multiplied by the mesh side length of 120mm, which equals 0.118mm, i.e., 980 microstrain. At this time, the tension strain increment is 8000 microstrain obtained by multiplying the basic tension coefficient and the mesh side length, plus the additional tension term 980 microstrain, totaling 8980 microstrain. Consistent with the output of similar physical quantities when the corner is inserted into the preset acute angle range, this ensures a direct comparison between the tension strain increment and the strain of the steel mesh in subsequent steps. The reason for introducing the incident deviation angle to trigger the additional tension term is that when the jet stream deviates from the long axis direction of the rhomboid hole, the lateral scouring effect of the jet stream on the mesh wires is enhanced while the positive tensioning effect is weakened. The flexible rhomboid mesh needs to undergo greater tension deformation before it can enter the membrane effect state.

[0064] In the specific implementation of S4, the information of the first layer to reach the ultimate tensile strain is directly extracted from the computer-aided engineering model of the composite support section. This information includes the layer number, the distance from the layer to the outermost edge of the tension side, and the nominal tensile strain value of the layer. Based on the shotcrete strength grade determined in the previous step, the tensile strength value of the shotcrete is extracted from the material property database corresponding to the shotcrete strength grade. The tensile strength value of the shotcrete is consistent with the material property database used to extract the elastic modulus in the previous step. The volume of the tension zone is determined as follows: Multiply the thickness of the layer that first reaches its ultimate tensile strain by the unit calculated width of the composite support section along the tunnel longitudinal direction, and then multiply by the calculated length of the tension zone of the composite support section along the tunnel circumferential direction. The thickness of the layer that first reaches its ultimate tensile strain is the thickness of each sub-layer when dividing the tensile softening layer. The thickness of each sub-layer has already been given in the previous steps; for example, the thickness of each sub-layer is 12.5mm, the unit calculated width is 1m, and the calculated length of the tension zone along the tunnel circumferential direction is 1m. Therefore, the volume of the tension zone is 12.5mm × 1000mm × 1000mm = 12.5 × 10 6mm³. The elastic strain energy released at the moment of cracking is calculated as follows: multiply the tensile strength of the shotcrete by the nominal tensile strain of the layer that first reaches the ultimate tensile strain, multiply by the volume of the tension zone, and then multiply by half. This calculation is based on the strain energy density per unit volume of a linear elastic body, obtained by integrating the product of stress and strain within half the range. Using C30 shotcrete with a tensile strength of 2.0 MPa, a nominal tensile strain of 152 με, and a tension zone volume of 12.5 × 10⁻⁶ mm³,... 6 Taking mm³ as an example, the elastic strain energy is equal to 0.5 × 2.0 MPa × 152 × 10 -6 ×12.5×10 6 mm³ = 1900 N·mm, taking the elastic strain energy as the elastic energy.

[0065] The deformation energy is calculated based on the elastic modulus of the flexible rhomboid mesh, the cross-sectional area of ​​a single rebar corresponding to the rebar diameter, and the tensile strain increment. The elastic modulus of the flexible rhomboid mesh is taken from the elastic modulus of the rebar material used in the flexible rhomboid mesh. In a previous step, the elastic modulus of the rebar material was given as 200 GPa, which is 200 × 10³ MPa. The cross-sectional area of ​​a single rebar corresponding to the rebar diameter is calculated from the rebar diameter. In a previous step, it was given that with a rebar diameter of 5 mm, the cross-sectional area of ​​a single rebar is π × 5 mm × 5 mm / 4 = 19.6 mm². The tensile strain increment is the value determined in a previous step. Taking the case where the corner is within a preset acute angle interval as an example, the tensile strain increment is 8000 με. The number of rebars participating in the membrane effect in the flexible rhomboid mesh that crosses the layer that first reaches the ultimate tensile strain is determined by counting the number of rhomboid mesh wires in the crack propagation direction that crosses the layer that first reaches the ultimate tensile strain within the tension zone corresponding to the layer that first reaches the ultimate tensile strain. The crack propagation direction across the layer that first reaches its ultimate tensile strain is taken as the circumferential direction of the composite support section. The number of mesh wires crossing within a 1m calculated length along the circumferential direction is determined by the mesh size side length of 120mm. The number of mesh wire spacings within the 1m calculated length is approximately 8 (1000mm / 120mm), with each spacing corresponding to 2 mesh wires. Therefore, the number of mesh wires crossing the layer that first reaches its ultimate tensile strain is approximately 16. The external force work required to tension the flexible rhomboid mesh across the layer that first reaches its ultimate tensile strain to the membrane effect state is calculated as follows: the tension required to tension a single mesh wire from a relaxed state to the membrane effect state does work along the strain path during the tensioning process. The external force work is equal to the tension force of a single mesh wire multiplied by the tension elongation of a single mesh wire in the tensioning direction, multiplied by the number of mesh wires crossing the layer that first reaches its ultimate tensile strain, and then multiplied by half. The tension force of a single wire mesh is calculated by multiplying the elastic modulus of the reinforcing steel material (200 × 10³ MPa) by the cross-sectional area of ​​a single reinforcing steel (19.6 mm²), and then by the tension strain increment (8000 × 10⁻⁶). -6The tension force is approximately 31.4 kN. The tension elongation of a single wire is calculated by multiplying the tension strain increment of 8000 με by the initial length of the rhomboid hole in the tension direction. The initial length of the rhomboid hole in the tension direction is taken as the side length of the mesh hole, which is 120 mm. The tension elongation of a single wire is approximately 0.96 mm. The external force required for a single wire is approximately 0.5 × 31.4 kN × 0.96 mm ≈ 15100 N·mm. The total external force required for the 16 wires that cross the layer that first reaches the ultimate tensile strain is 16 × 15100 N·mm = 241600 N·mm. The total external force is taken as the deformation energy.

[0066] Comparing the elastic energy (1900 N·mm) with the deformation energy (241600 N·mm), the elastic energy (1900 N·mm) is less than the deformation energy (241600 N·mm), satisfying the criterion that elastic energy is less than deformation energy. Therefore, it is determined that a resistance gap exists. The meaning of this determination is that the elastic strain energy released when the shotcrete cracks at the layer that first reaches its ultimate tensile strain is insufficient to drive the flexible diamond mesh spanning that layer from its initial relaxed state to a state capable of providing a membrane effect. After the shotcrete cracks, there is a transitional phase in its resistance contribution. During this transitional phase, the tensile contribution of the shotcrete has diminished while the membrane effect of the flexible diamond mesh has not yet been established, forming a resistance gap.

[0067] The difference between the elastic energy and the deformation energy is calculated as 1900 N·mm - 241600 N·mm = -239700 N·mm, which is negative. Dividing the difference between the elastic energy and the deformation energy by the deformation energy yields the energy difference ratio, which is approximately -239700 N·mm / 241600 N·mm ≈ -0.992. Since the energy difference ratio is negative, it does not meet the condition that the energy difference ratio is positive and exceeds the preset tolerance threshold. Therefore, in this example, the resistance gap is not considered significant. The preset tolerance threshold is set according to the surrounding rock deformation control level, which is determined by the relationship between the surrounding rock in-situ stress level ratio and the uniaxial saturated compressive strength of the surrounding rock. When the surrounding rock deformation control level is strict, the preset tolerance threshold is set to a smaller value, such as 0.05; when the surrounding rock deformation control level is ordinary, the preset tolerance threshold is set to a larger value, such as 0.15. When there is another working condition where the elastic energy is 200,000 N·mm and the deformation energy is 180,000 N·mm, the energy difference ratio is 200,000 N·mm - 180,000 N·mm / 180,000 N·mm = 20,000 N·mm / 180,000 N·mm ≈ 0.111. If the preset tolerance threshold is 0.05, the energy difference ratio of 0.111 exceeds the preset tolerance threshold of 0.05, and the resistance gap is determined to be significant. When outputting the corrected crack width, the additional crack width increment mapped by the energy difference ratio is superimposed. The mapping method of the additional crack width increment is: multiply the energy difference ratio by the preset additional crack width benchmark value. The preset additional crack width benchmark value is taken as the benchmark crack width corresponding to the shotcrete under the ultimate tensile strain state. The benchmark crack width is determined by multiplying the ultimate tensile strain by the crack spacing, so that the additional crack width increment is proportional to the value of the energy difference ratio.

[0068] In the specific implementation of S5, following the conclusion of the previous step that a resistance gap exists, a stiffness transition treatment is performed in the computer-aided engineering model of the composite support section. The stiffness transition treatment divides the stress process of the section after the shotcrete reaches its ultimate tensile strain into two stages: the first stage is the coexistence of the shotcrete softening stage and the flexible rhomboid mesh relaxation stage; the second stage is the stage in which the flexible rhomboid mesh enters the membrane effect and cooperates with the residual shotcrete in bearing the load. The transition node between the two stages is the moment when the accumulated tensile strain of the flexible rhomboid mesh reaches the tension strain increment.

[0069] In the first stage, the tensile stiffness of the shotcrete decreases along the softening curve. The softening curve is described by the post-peak softening segment defined by the tensile softening layer in the previous step, and the softening rate is controlled by the fracture energy parameter of the shotcrete. Taking C30 shotcrete as an example, the post-peak softening segment adopts linear softening with a slope of 1.33 MPa / με. When the tensile strain of the shotcrete exceeds the ultimate tensile strain of 150 με due to bending deformation of the composite support section, the flexural stiffness of the section contributed by the shotcrete is gradually reduced from the elastic stiffness before cracking according to the slope of the softening segment. The reduction method is as follows: the tensile strain of the shotcrete from the ultimate tensile strain of 150 με to the final tensile strain is discretized into multiple incremental steps. Within each incremental step, the tensile strain of the shotcrete is increased by a preset strain step size. The preset strain step size is set according to the calculation accuracy requirements, for example, a preset strain step size of 50 με. The smaller the value of the preset strain step size, the higher the resolution of the stiffness transition. For each additional preset strain step, the tensile stiffness of the shotcrete is multiplied by a softening reduction factor based on the stiffness of the previous step. The softening reduction factor is equal to the ratio of the secant modulus of the softened segment to the elastic modulus corresponding to the current strain step. The secant modulus of the softened segment is calculated from the slope of the softened segment. The tensile stiffness of the shotcrete at the cracking point is the elastic modulus before cracking (25 GPa) multiplied by the cross-sectional area of ​​the tensile softened layer. As the tensile strain increases, the tensile stiffness of the shotcrete decreases monotonically until the final tensile strain is reached, at which point the tensile stiffness drops to the residual value. The residual value is set according to the ratio of the fracture energy parameter and the crack width; for example, the residual value is taken as 0.05 times the stiffness before cracking.

[0070] During the same process in the first stage, the flexible rhomboid mesh remains in a relaxed state before the tension strain increment. The tensile strain of the flexible rhomboid mesh in this stage has not yet accumulated to the tension strain increment, therefore the membrane effect of the flexible rhomboid mesh has not yet been activated. In the computer-aided engineering model of the composite support section, the tensile strain of the flexible rhomboid mesh accumulates from the initial strain value of the reinforcing mesh extracted in the previous step. The initial strain value of the reinforcing mesh is 125 με corresponding to the cracking moment, while the tension strain increment is 8000 με determined in the previous step. The difference between the initial strain value of the reinforcing mesh and the tension strain increment is 7875 με. This difference is the tensile strain difference that the flexible rhomboid mesh needs to accumulate in the first stage. Within each incremental step of the first stage, as the bending deformation of the composite support section continues, the flexible rhomboid mesh on the tension side of the section undergoes synchronous stretching in accordance with the change of the tension softening layer. However, due to the bonding coefficient of the interface transition layer (1.2 MPa / mm) controlling the relative slippage between the orthotropic membrane layer and the tension softening layer, the rate of increase in tensile strain of the flexible rhomboid mesh is lower than the rate of increase in nominal tensile strain at the outermost edge of the tension softening layer. The accumulation rate of tensile strain of the flexible rhomboid mesh is jointly determined by the increment of section curvature, the distance of the orthotropic membrane layer from the neutral axis, and the bonding coefficient. The larger the bonding coefficient, the faster the accumulation of tensile strain of the flexible rhomboid mesh; the smaller the bonding coefficient, the slower the accumulation of tensile strain of the flexible rhomboid mesh. When the accumulated tensile strain of the flexible rhomboid mesh first reaches or exceeds the tension strain increment of 8000 με, the first stage ends, and the second stage begins.

[0071] The second stage begins when the accumulated tensile strain of the flexible rhomboid mesh first reaches or exceeds the tension strain increment of 8000 με. At this point, deformation compatibility between the shotcrete and the flexible rhomboid mesh is restored. This means removing the relative slippage restriction between the flexible rhomboid mesh and the tensile softening layer caused by the limited bond coefficient in the first stage, and combining the residual tensile stiffness of the shotcrete with the membrane effect stiffness of the flexible rhomboid mesh in a cross-section. The basis for restoring deformation compatibility is that when the flexible rhomboid mesh is tensioned to the tension strain increment, the rhomboid holes have transitioned from a relaxed state to a force-transmitting state. The geometric relaxation of the mesh wires within the rhomboid holes has been eliminated by tensioning. Under these conditions, the mechanical interlocking force and chemical bond force between the mesh wires and the shotcrete are sufficient to transmit interfacial shear force, thus satisfying the deformation compatibility condition. The membrane effect stiffness of the flexible rhomboid mesh is the additional bending stiffness provided by the flexible rhomboid mesh within the cross section after entering the membrane effect. The membrane effect stiffness is determined by multiplying the equivalent elastic modulus of the orthotropic membrane layer in the first principal direction (6.28 GPa / m) by the thickness of the orthotropic membrane layer (5 mm) and then by the square of the distance of the orthotropic membrane layer from the neutral axis. After cross section conversion, this stiffness is added to the total cross section stiffness of the composite support section. The cross section conversion follows the principle of superposition of parallel stiffness of composite laminate structures.

[0072] The corrected crack width is calculated based on the section stiffness history including stiffness transition. The crack width is calculated as follows: On the section stiffness history, corresponding to the section curvature and neutral axis position at each increment, the crack opening displacement at the outermost edge of the tension side is calculated. The crack opening displacement is obtained by subtracting the elastic recoil of the shotcrete itself on both sides of the crack from the cumulative tensile deformation of the tensile softening layer in each increment. The elastic recoil of the shotcrete itself on both sides of the crack is the unloading rebound strain of the shotcrete in the corresponding increment multiplied by the crack spacing. In the first stage, due to the continuous decrease in tensile stiffness of the shotcrete and the lack of a membrane effect provided by the flexible diamond mesh, the crack opening displacement increases rapidly. In the second stage, due to the incorporation of the membrane effect stiffness of the flexible diamond mesh, the overall section stiffness of the composite support section recovers, and the rate of increase in crack opening displacement slows down or tends to stabilize. The corrected crack width is obtained by summing the crack opening displacements of each increment. Taking the eight crack spacing sections divided within a 1m circumferential calculation length in this example as an example, the corrected crack width calculated after the stiffness transition is 0.18mm.

[0073] If no resistance gap is determined in the previous steps, a simplified crack width calculation path is executed. In this simplified path, it is assumed that the flexible rhomboid mesh instantaneously enters a state of coordinated tension at the moment the shotcrete cracks, without undergoing a first-stage transition process. When calculating the crack width based on the complete coordination assumption, the shotcrete and the flexible rhomboid mesh maintain deformation coordination from the moment of cracking. While the tensile stiffness of the shotcrete decreases along the softening curve, the membrane effect stiffness of the flexible rhomboid mesh is simultaneously incorporated into the section stiffness, and there is no independent relaxation accumulation stage. The crack width is directly solved from the section equilibrium equations after cracking, outputting the crack width based on the complete coordination assumption. Taking the section parameters and load conditions of this example, the crack width based on the complete coordination assumption is 0.09 mm.

[0074] Example 2: Figure 3 A structural schematic diagram of the composite support design system of flexible anchor mesh and high-performance shotcrete of the present invention is given. The composite support design system of flexible anchor mesh and high-performance shotcrete includes the following modules:

[0075] The parameter acquisition module is used to obtain the mesh side length of the flexible rhombus mesh, the diameter of the reinforcing bars, the ultimate tensile strain of the shotcrete, and the design bending moment.

[0076] The strain calculation module is used to establish a computer-aided engineering model of the composite support section using the mesh side length, rebar diameter, ultimate tensile strain and design bending moment, and to calculate the rebar strain generated by the flexible rhomboid mesh when the shotcrete reaches the ultimate tensile strain.

[0077] The increment determination module is used to obtain the angle between the long axis of the rhombus holes of the flexible rhombus mesh and the main incident direction of the sprayed concrete flow after the flexible rhombus mesh is laid. When the angle falls into the preset acute angle range, the tension strain increment is determined according to the mesh side length and the rebar diameter. Otherwise, the tension term triggered by the incident deviation angle is added to the basis determined according to the mesh side length and the rebar diameter to obtain the tension strain increment.

[0078] The window of resistance determination module is used to determine the elastic energy released in the tension zone at the moment of cracking of shotcrete based on the strain of the steel mesh, to determine the deformation energy required for the flexible rhomboid mesh to enter the membrane effect based on the tension strain increment, and to determine whether the elastic energy is less than the deformation energy. If so, there is a resistance window of resistance.

[0079] The results output module is used to connect the stiffness transition between the shotcrete softening section and the mesh reinforcement section in the computer-aided engineering model by using tension strain increment when there is a resistance gap, and output the corrected crack width; when there is no resistance gap, it outputs the crack width based on the complete synergistic assumption.

[0080] It is worth noting that the calculations involved in the embodiments are all dimensionless numerical calculations, and the preset parameters and thresholds in the calculations are set by those skilled in the art according to the actual situation. The above embodiments can be implemented in whole or in part by software, hardware, firmware or other arbitrary combinations. When implemented in software, the above embodiments can be implemented in whole or in part in the form of a computer program product.

Claims

1. A composite support design method using flexible anchor mesh and high-performance shotcrete, characterized in that, Includes the following steps: S1. Obtain the mesh side length, steel bar diameter, ultimate tensile strain of shotcrete, and design bending moment of flexible diamond mesh; S2. A computer-aided engineering model of the composite support section is established using the mesh side length, steel bar diameter, ultimate tensile strain and design bending moment. The strain of the steel mesh generated by the flexible rhombus mesh is calculated when the shotcrete reaches the ultimate tensile strain. S3. Obtain the angle between the long axis of the rhombus holes and the main incident direction of the sprayed concrete flow after the flexible rhombus mesh is laid. When the angle falls into the preset acute angle range, determine the tension strain increment according to the mesh side length and the rebar diameter. Otherwise, add the tension term triggered by the incident deviation angle on the basis determined according to the mesh side length and the rebar diameter to obtain the tension strain increment. S4. Determine the elastic energy released in the tension zone at the moment of cracking of shotcrete based on the strain of the steel mesh. Determine the deformation energy required for the flexible rhomboid mesh to enter the membrane effect based on the tension strain increment. Determine whether the elastic energy is less than the deformation energy. If so, there is a resistance gap period. S5. When there is a resistance gap, the stiffness transition between the shotcrete softening section and the mesh reinforcement section is connected by tension strain increment in the computer-aided engineering model, and the corrected crack width is output; when there is no resistance gap, the crack width based on the complete synergistic assumption is output.

2. The composite support design method of flexible anchor mesh and high-performance shotcrete according to claim 1, characterized in that, Obtain the mesh side lengths, rebar diameters, ultimate tensile strain of shotcrete, and design bending moment of the flexible rhomboid mesh, including: The selection of flexible diamond mesh is determined based on the classification of the surrounding rock in the section to be supported, and the mesh side length and steel bar diameter are extracted from the selection record; The strength grade of the shotcrete is determined based on the surrounding rock classification and groundwater environment level of the section to be supported, and the ultimate tensile strain corresponding to the strength grade is extracted. Based on the surrounding rock stress level and the tunnel excavation span, calculate the design bending moment that the composite support section needs to bear.

3. The composite support design method of flexible anchor mesh and high-performance shotcrete according to claim 2, characterized in that, The classification of surrounding rock is evaluated using basic quality indicators of surrounding rock. The stress level is determined based on the ratio of the measured stress to the uniaxial saturated compressive strength of the surrounding rock. When this ratio exceeds the critical value, the design bending moment is multiplied by an amplification factor that is positively correlated with the excess.

4. The composite support design method of flexible anchor mesh and high-performance shotcrete according to claim 1, characterized in that, A computer-aided engineering model of the composite support section was established using the mesh side length, rebar diameter, ultimate tensile strain, and design bending moment. The strain generated by the flexible rhomboid mesh when the shotcrete reaches its ultimate tensile strain was calculated, including: The flexible rhombic mesh is equivalent to an orthotropic membrane layer based on the mesh side length and the steel bar diameter. The shotcrete is equivalent to a tensile softening layer based on the ultimate tensile strain. The interface between the flexible rhombic mesh and the shotcrete is equivalent to an interface transition layer based on the bonding coefficient. A computer-aided engineering model with a three-layer composite section is formed by combining these components. In the computer-aided engineering model of the composite support section, the design bending moment is applied, and the tensile strain of each layer of shotcrete is determined layer by layer along the section height direction. The layer that first reaches the ultimate tensile strain is then extracted. The tensile strain of the flexible rhomboid mesh at this layer in the direction of the ultimate tensile strain of the shotcrete is extracted as the strain of the reinforcing mesh.

5. The composite support design method of flexible anchor mesh and high-performance shotcrete according to claim 1, characterized in that, After the flexible diamond mesh is laid, obtain the angle between the long axis of the diamond holes and the main incident direction of the shotcrete jet. When the angle falls within a preset acute angle range, determine the tension strain increment based on the mesh side length and the rebar diameter; otherwise, add a tension term triggered by the incident deviation angle to the basis determined by the mesh side length and the rebar diameter to obtain the tension strain increment, including: Based on the mesh posture record after the flexible rhombus mesh is laid and the spraying direction record of the shotcrete construction, the angle between the long axis of the rhombus hole and the main incident direction of the spray flow is calculated. Compare the included angle with the preset acute angle range. If the included angle falls into the preset acute angle range, the foundation tension coefficient is determined by the ratio of the mesh side length to the rebar diameter. The product of the foundation tension coefficient and the mesh side length is used as the tension strain increment. If the included angle does not fall within the preset acute angle range, the difference between the included angle and the boundary value of the preset acute angle range is calculated as the incident deviation angle. The product of the basic tension coefficient and the tangent of the incident deviation angle is used as the additional tension term. The sum of the product of the basic tension coefficient and the mesh side length and the additional tension term is used as the tension strain increment.

6. The composite support design method of flexible anchor mesh and high-performance shotcrete according to claim 5, characterized in that, The upper boundary of the preset acute angle interval is set according to the ratio of the mesh side length to the diameter of the steel bar. The larger the ratio, the smaller the upper boundary. The lower boundary of the preset acute angle interval is the minimum incident angle at which the sprayed concrete flow forms effective filling in the diamond-shaped hole.

7. The composite support design method of flexible anchor mesh and high-performance shotcrete according to claim 1, characterized in that, Based on the computer-aided engineering model of the composite support section, the layer where the shotcrete first reaches the ultimate tensile strain is determined. Combining the tensile strength corresponding to the shotcrete strength grade and the volume of the tension zone at that layer, the elastic strain energy released at the moment of cracking is calculated as the elastic energy. Based on the elastic modulus of the flexible rhombic mesh, the cross-sectional area of ​​a single steel bar corresponding to the steel bar diameter, and the tension strain increment, the external force work required to tension the flexible rhombic mesh across that layer to the membrane effect state is calculated as the deformation energy. Comparing the elastic energy with the deformation energy, if the elastic energy is less than the deformation energy, it is determined that there is a resistance gap.

8. The composite support design method of flexible anchor mesh and high-performance shotcrete according to claim 7, characterized in that, The energy difference ratio is obtained by dividing the difference between the elastic energy and the deformation energy by the deformation energy. When the energy difference ratio is positive and exceeds the preset tolerance threshold, the resistance gap period is determined to be significant, and the additional crack width increment mapped by the energy difference ratio is superimposed when outputting the corrected crack width.

9. The composite support design method of flexible anchor mesh and high-performance shotcrete according to claim 1, characterized in that, When a resistance gap exists, in the computer-aided engineering model of the composite support section, after the shotcrete reaches its ultimate tensile strain, the tensile stiffness of the shotcrete is reduced along the softening curve, while the tensile strain of the flexible rhombus mesh is maintained in a relaxed state before the tension strain increment, until the accumulated tensile strain of the flexible rhombus mesh reaches the tension strain increment. After that, the deformation coordination between the shotcrete and the flexible rhombus mesh is restored, and the membrane effect stiffness of the flexible rhombus mesh is incorporated into the section stiffness. The corrected crack width is calculated based on the section stiffness history including stiffness transition. When there is no resistance gap, it is assumed that the flexible rhombus mesh instantaneously enters a cooperative tensile state at the moment the shotcrete cracks, and the crack width is calculated and output according to the assumption of complete cooperation.

10. A composite support design system of flexible anchor mesh and high-performance shotcrete, used to implement the composite support design method of flexible anchor mesh and high-performance shotcrete as described in any one of claims 1-9, characterized in that, Includes the following modules: The parameter acquisition module is used to obtain the mesh side length of the flexible rhombus mesh, the diameter of the reinforcing bars, the ultimate tensile strain of the shotcrete, and the design bending moment. The strain calculation module is used to establish a computer-aided engineering model of the composite support section using the mesh side length, rebar diameter, ultimate tensile strain and design bending moment, and to calculate the rebar strain generated by the flexible rhomboid mesh when the shotcrete reaches the ultimate tensile strain. The increment determination module is used to obtain the angle between the long axis of the rhombus holes of the flexible rhombus mesh and the main incident direction of the sprayed concrete flow after the flexible rhombus mesh is laid. When the angle falls into the preset acute angle range, the tension strain increment is determined according to the mesh side length and the rebar diameter. Otherwise, the tension term triggered by the incident deviation angle is added to the basis determined according to the mesh side length and the rebar diameter to obtain the tension strain increment. The window of resistance determination module is used to determine the elastic energy released in the tension zone at the moment of cracking of shotcrete based on the strain of the steel mesh, to determine the deformation energy required for the flexible rhomboid mesh to enter the membrane effect based on the tension strain increment, and to determine whether the elastic energy is less than the deformation energy. If so, there is a resistance window of resistance. The results output module is used to connect the stiffness transition between the shotcrete softening section and the mesh reinforcement section in the computer-aided engineering model by using tension strain increment when there is a resistance gap, and output the corrected crack width; when there is no resistance gap, it outputs the crack width based on the complete synergistic assumption.

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