Determination of weak zone of tunnel based on asymmetric load evolution and differential support method

Abstract

This invention relates to the field of tunnel and underground engineering design technology, specifically to a method for identifying weak areas in tunnels and providing differentiated support based on asymmetric load evolution. The method involves collecting pressure distribution and deformation data of the tunnel cross-section and constructing a continuous arc-length coordinate system along the neutral axis of the support structure. Based on the data and coordinate system, the geometric, stress, and energy states of the tunnel cross-section are analyzed to obtain geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point on the support section. A multi-index collaborative judgment model is constructed based on the above multi-dimensional index results to generate a weighted index distribution map of the tunnel cross-section's weakness. Based on the multi-dimensional results and the index distribution map, differentiated support decisions for the tunnel are designed. This invention identifies weak areas in tunnel support based on multi-dimensional physical indicators of deformation, stress, and energy, and conducts asymmetric differentiated support parameter decisions, realizing the transformation from traditional equal-strength design to asymmetric targeted support, thereby enhancing the stability and safety of the eccentrically loaded side structure.

Description

Technical Field

[0001] This invention relates to the field of tunnel and underground engineering design technology, specifically to a method for identifying weak zones in tunnels and providing differentiated support based on asymmetric load evolution. Background Technology

[0002] Due to the combined effects of multiple factors such as the anisotropy of the initial stress field, jointed structure, fault occurrence, and excavation unloading disturbance, the pressure of the surrounding rock in tunnels often exhibits significant asymmetric characteristics. In the process of deep-buried tunnel support design, accurately identifying the weak areas of the support and implementing differentiated reinforcement measures is an important mechanical basis for ensuring the safety and stability of the tunnel structure and achieving engineering economy.

[0003] Traditional methods face challenges when dealing with asymmetric load conditions: On the one hand, traditional point monitoring methods easily overlook the local geometric distortion and internal force redistribution of the support structure, leading to hidden failures such as misalignment at local nodes even when the overall convergence has not exceeded the limit, posing a potential threat to tunnel safety; on the other hand, equal-strength symmetrical design cannot take into account the stress characteristics of different areas, which may lead to insufficient support strength on the biased side, resulting in safety accidents such as crushing and collapse; at the same time, material redundancy may occur on the non-biased side, causing huge waste of resources and increasing engineering costs.

[0004] To address the problem of managing asymmetric deformation tunnels, existing technologies mainly rely on static zoning based on the principal stress direction. However, this method struggles to capture the geometric distortion characteristics that dynamically evolve with the load field during excavation, and cannot reflect the actual stress and deformation of the tunnel support structure in real time. Existing technologies achieve rigid defense by increasing the number of support layers, but lack precise positioning of the physical boundaries of weak areas, making it impossible to accurately determine which areas require key reinforcement and which areas can have their support measures appropriately simplified.

[0005] In summary, existing technologies still have many significant shortcomings in the field of asymmetric support in complex strata: Most existing models rely solely on the absolute displacement of geometric scalars for judgment, lacking criteria that can comprehensively reflect the coupling of multiple fields such as structural distortion rate, cross-sectional strength state, and functional energy absorption redundancy. This makes it difficult to comprehensively and accurately assess the safety status of tunnel support structures.

[0006] In the field of tunnel support, there is a lack of an effective judgment function that couples the three-dimensional indicators of form, force, and energy. This makes it impossible to accurately determine the evolution law of damage dissipation energy caused by non-uniform deformation of the support structure, resulting in a significant deficiency in the identification of brittle fracture risk and making it difficult to take effective preventive measures in advance.

[0007] Existing differentiated support methods remain at the level of qualitative reinforcement, lacking support parameter design methods based on edge stress limit and energy gap analysis. They cannot dynamically adjust tunnel support parameters according to the actual stress and deformation of the tunnel support structure to achieve precise support.

[0008] Therefore, a collaborative judgment and decision-making method is needed that can couple the evolution law of asymmetric loads, accurately identify the physical boundaries of weak areas in multi-physics fields, and drive the precise redistribution of support parameters. This method can compensate for the lack of applicability of existing symmetric design methods in complex biased strata and provide a scientific and reliable mechanical basis for achieving targeted support with on-demand energy allocation and rigidity-toughness matching in biased strata rock tunnels. Summary of the Invention

[0009] To address the shortcomings of existing methods and the limitations of practical applications, and to solve the problem of the limited applicability of existing symmetrical designs under complex biased geological conditions, it is necessary to study the mechanical properties of tunnels in biased geological formations. This research will provide theoretical support for targeted support with a scientific match between stiffness and toughness, enable the identification of weak areas in tunnel support structures, and promote the transformation of tunnel support design from the traditional equal-strength model to the asymmetric targeted support model. This invention provides a method for identifying weak zones and providing differentiated support for tunnels based on asymmetric load evolution, comprising the following steps: collecting pressure distribution data and deformation data of the tunnel cross-section; constructing a continuous arc-length coordinate system along the neutral axis of the support structure based on the pressure distribution data and the deformation data; analyzing the geometric, stress, and energy states of the tunnel cross-section according to the pressure distribution data, the deformation data, and the continuous arc-length coordinate system, and obtaining geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section; constructing a multi-index collaborative judgment model based on the geometric deformation analysis results, the eccentricity evaluation results, and the toughness judgment results; generating a weighted index distribution map of the weakness of the tunnel cross-section through the multi-index collaborative judgment model; and designing differentiated support decisions for the tunnel based on the geometric deformation analysis results, the eccentricity evaluation results, the toughness judgment results, and the weighted index distribution map of the weakness.

[0010] This invention can make differentiated support decisions for different areas of the tunnel cross section, which can avoid the waste of resources caused by over-support, while ensuring that the support effect meets the engineering requirements and effectively reduce support costs.

[0011] Optionally, the step of analyzing the geometry, stress, and energy state of the tunnel cross-section based on the pressure distribution data, the deformation data, and the continuous arc length coordinate system, and obtaining the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point on the support section, includes: analyzing the relationship between the geometric linear deformation and spatial position of the support structure based on the continuous arc length coordinate system; constructing a displacement space gradient operator analysis formula based on the relationship, the pressure distribution data, and the deformation data; obtaining the displacement space gradient at any point on the support section using the displacement space gradient operator analysis formula; obtaining the ultimate shear strain of the support material, and determining the displacement space gradient threshold by referring to the ultimate shear strain of the support material; and determining the local shear deformation weak area by using the displacement space gradient threshold and the displacement space gradient.

[0012] The displacement spatial gradient of this invention reflects the deformation rate and direction of the tunnel support structure at different locations, which helps to analyze and understand the stress characteristics of the tunnel cross section, thereby accurately grasping the stress state of the tunnel.

[0013] Optionally, the step of analyzing the geometry, stress, and energy state of the tunnel cross-section based on the pressure distribution data, the deformation data, and the continuous arc length coordinate system, and obtaining the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section includes: determining the initial design curvature of the support structure; performing inversion analysis based on the continuous arc length coordinate system and the initial design curvature to obtain the instantaneous curvature; constructing a curvature deviation analysis function based on the initial design curvature and the instantaneous curvature; obtaining the difference between the instantaneous curvature and the initial design curvature of the support structure after deformation through the curvature deviation analysis function; performing coupling analysis on the displacement space gradient and the difference to obtain a comprehensive deformation identification factor; and combining the comprehensive deformation identification factor with the local shear deformation weak zone to obtain the geometric deformation analysis results at any point of the support section.

[0014] This invention comprehensively considers the changes in the deformation rate, direction, and overall curvature of the support structure in space, which can more comprehensively reflect the actual deformation characteristics of tunnel support, avoid the one-sidedness of a single indicator, and improve the accuracy and scientific nature of the geometric deformation assessment of tunnel support.

[0015] Optionally, the coupled analysis of the displacement spatial gradient and the difference to obtain the comprehensive deformation identification factor includes: The comprehensive deformation recognition factor satisfies the following relationship: , in, To comprehensively identify deformation factors, These are the weighting coefficients of the displacement space gradient operator. Let be the modulus of the spatial gradient of the displacement. The maximum displacement gradient across the entire cross section. This is the weighting coefficient for curvature deviation. The value is the difference between the instantaneous curvature of the support structure after deformation and the initial design curvature. The initial design curvature.

[0016] The formula of this invention couples the modulus of the displacement spatial gradient with the curvature deviation, which can comprehensively consider the local and overall deformation information of the tunnel support structure.

[0017] Optionally, the step of analyzing the geometry, stress, and energy state of the tunnel cross-section based on the pressure distribution data, the deformation data, and the continuous arc length coordinate system, and obtaining the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section includes: analyzing the difference ratio of the resultant loads on both sides of the continuous arc length coordinate system based on the pressure distribution data, the deformation data, and the deformation data; obtaining the bending moment and axial force at any point of the support section based on the pressure distribution data and the deformation data; obtaining the eccentricity at any point of the support section based on the bending moment and the axial force; deriving the eccentricity compression coefficient at any point of the support section based on the eccentricity; setting eccentricity evaluation conditions with reference to the tunnel support structure and tunnel eccentricity characteristics; and obtaining the eccentricity evaluation result at any point of the support section based on the eccentricity compression coefficient and the eccentricity evaluation conditions.

[0018] This invention analyzes the difference ratio of the resultant loads on both sides using a continuous arc-length coordinate system, which can provide a deeper understanding of the load imbalance and other situations borne by the tunnel support structure, and provide load information for accurately assessing the stress state of the support structure.

[0019] Optionally, deriving the eccentricity to obtain the eccentric compression coefficient at any point on the support section includes: The eccentricity satisfies the following relationship: , in, For the support section at the location Eccentricity at the location, For the protection section at the position The bending moment caused by the asymmetric load at the point, For the support section at the location Axial force caused by load at the point; The eccentric compression coefficient satisfies the following relationship: , in, The normalized eccentric compression coefficient, For the support section at the location Eccentricity at the location, For the thickness of the support structure, For the protection section at the position The bending moment caused by the asymmetric load at the point, For the support section at the location Axial force caused by load.

[0020] This invention calculates the eccentric compression coefficient of each cross section, which allows for comparative analysis of the degree of eccentricity of different cross sections, enabling targeted monitoring and reinforcement, and further improving the safety of the project.

[0021] Optionally, the step of analyzing the geometry, stress, and energy state of the tunnel cross-section based on the pressure distribution data, deformation data, and continuous arc length coordinate system, and obtaining the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section, includes: obtaining the energy release density of the surrounding rock based on the volumetric deformation after unloading and expansion of the surrounding rock, the pressure distribution data, the deformation data, and the continuous arc length coordinate system; analyzing the ultimate resistance energy of the support structure based on the recoverable elastic energy storage and irrecoverable damage energy dissipation of the support structure; establishing a toughness saturation index analysis function based on the energy release density of the surrounding rock and the ultimate resistance energy; obtaining the toughness saturation index at any point of the support section through the toughness saturation index analysis function; and classifying the toughness saturation index at any point of the support section to obtain the toughness judgment result at any point of the support section. The toughness saturation index analysis function of this invention quantifies the toughness state of the support structure, and can intuitively reflect the support structure's ability to resist the energy release of the surrounding rock under current working conditions.

[0022] Optionally, the ultimate resistance energy of the support structure based on the deformation-recoverable elastic energy storage and irrecoverable damage energy dissipation analysis of the support structure includes: The ultimate resistance energy satisfies the following relationship: , in, For the support structure in position Total ultimate resistance energy density at the location, For the support section at the location Elastic energy storage density at that location, For the support section at the location Damage energy density at the site For the protection section at the position The bending moment caused by the asymmetric load at the point, The elastic modulus of the material. For the moment of inertia, For the support section at the location Axial force caused by load at the point, The equivalent shear area of ​​the support section. The geometric distortion energy conversion coefficient, Let be the modulus of the spatial gradient of the displacement.

[0023] The formula of this invention involves multiple parameters, which can describe the geometric characteristics, stress state and material properties of the support structure from different perspectives, thereby reflecting the influencing factors of the ultimate resistance energy of the support structure more comprehensively and accurately, and making the theoretical analysis closer to the actual engineering situation.

[0024] Optionally, the step of constructing a multi-index collaborative judgment model based on the geometric deformation analysis results, the eccentricity evaluation results, and the toughness judgment results, and generating a weighted index distribution map of the tunnel cross-section through the multi-index collaborative judgment model, includes: introducing a weighted index of weakness; and performing collaborative characterization of the geometric deformation analysis results, the eccentricity evaluation results, and the toughness judgment results based on the weighted index of weakness and the multi-index collaborative judgment model to generate a weighted index distribution map of the tunnel cross-section of weakness. The multi-indicator collaborative judgment model satisfies the following relationship: , in, Location of tunnel cross section The stability state identifier at the location. The geometric distortion index. This is the critical threshold for geometric distortion. The coefficient for eccentric compression is... The toughness saturation index; The multi-indicator collaborative judgment model satisfies the following relationship: , in, For the support structure in position The overall weakness weighted index of the location, The weighting coefficient for the geometric deformation index. This is the normalized geometric distortion index. The weighting coefficients for the internal force redistribution index. This is the normalized eccentric compression coefficient. The weighting coefficients for energy dissipation indicators. This is the normalized toughness saturation index.

[0025] This invention comprehensively considers three key dimensions of indicators: geometric deformation, eccentricity, and toughness. It can comprehensively and systematically evaluate the stability of tunnel cross sections and effectively avoid the limitations of evaluation based on a single indicator.

[0026] Optionally, the differentiated tunnel support design decision based on the geometric deformation analysis results, the eccentricity evaluation results, the toughness judgment results, and the weakness weighted index distribution map includes: making asymmetric anchoring decisions for geometric deformation design based on the geometric deformation analysis results and the weakness distribution map; making variable cross-section stiffness decisions for large eccentric compression design based on the eccentricity evaluation results and the weakness distribution map; making asymmetric buffer layer decisions for energy risk design based on the toughness judgment results and the weakness distribution map; and realizing differentiated tunnel support through the asymmetric anchoring decisions, the variable cross-section stiffness decisions, and the asymmetric buffer layer decisions.

[0027] The differentiated support decision-making of this invention is designed according to the actual needs of different parts of the tunnel, avoiding over-support and other situations that occur under traditional support methods, thereby improving the maintenance efficiency and quality of the tunnel. Attached Figure Description

[0028] Figure 1 This is a flowchart of the tunnel weak zone identification and differentiated support method based on asymmetric load evolution according to the present invention. Figure 2 This is a schematic diagram of the torsional deformation and deformation index of the tunnel under asymmetric load according to the present invention. Figure 3 This is a schematic diagram showing the relationship between the arc length coordinates and polar coordinates of the tunnel support structure of the present invention; Figure 4 This is a schematic diagram illustrating the evaluation of the eccentricity of the tunnel under asymmetric load according to the present invention. Figure 5 This is a schematic diagram of the toughness classification of the tunnel support structure of the present invention; Figure 6 This is a schematic diagram illustrating the asymmetric anchorage length and density distribution of the present invention. Detailed Implementation

[0029] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0030] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0031] Please see Figure 1 In the field of tunnel engineering, traditional symmetrical design models are difficult to adapt to the non-uniform mechanical properties of rock masses in biased strata. To solve related problems, this invention analyzes the mechanical properties of tunnels in biased strata, explores key issues such as stress distribution, deformation patterns, and failure mechanisms under complex geological environments, provides a theoretical basis for the scientific matching of stiffness and toughness, and constructs a method capable of accurately identifying weak areas in tunnel support structures. This invention provides a method for identifying weak areas in tunnels and differentiated support based on asymmetric load evolution. The method includes the following steps: S1. Example: To construct a digital tunnel cross-section model and provide data support and location index for subsequent calculations, pressure distribution data and deformation data of the tunnel cross-section are collected in real time. A continuous arc length coordinate system along the neutral axis of the support structure is constructed to transform the actual irregular tunnel cross-section into a model that can be mathematically calculated. The specific implementation details are as follows: Based on the geometry of the tunnel cross-section, geological conditions, and the physical characteristics of the monitored quantities, this implementation selects appropriate types of sensors. For pressure distribution data acquisition, earth pressure cells can be used, which are evenly and reasonably arranged at different locations on the tunnel cross-section, including key parts such as the arch crown, arch waist, sidewalls, and invert, to ensure comprehensive and accurate acquisition of pressure information at all points on the cross-section. For deformation data acquisition, displacement sensors, such as vibrating wire displacement gauges and laser displacement sensors, are used, and are similarly arranged at various points on the cross-section according to certain rules to facilitate monitoring of displacement changes at different locations.

[0032] Next, the tunnel support structure is analyzed. Based on the geometry and stress characteristics of the support structure, the position of its neutral axis is determined. For common circular tunnel lining structures, the neutral axis is usually a horizontal axis passing through the center of the circle. For non-circular tunnels, the position of its neutral axis can be determined through mechanical analysis methods, such as the section equilibrium method or finite element analysis.

[0033] In this embodiment, a point on the neutral axis of the support structure is taken as the origin of the coordinate system, and continuous arc length coordinates are defined along the direction of the neutral axis. Starting from the origin of the coordinate system, the arc length of each point on the neutral axis is measured in a clockwise or counterclockwise direction, and the arc length value of each point is used as the coordinate value of that point in the coordinate system. For other points on the tunnel cross section, they are mapped to a continuous arc length coordinate system along the neutral axis through geometric relationships, thereby establishing a continuous arc length coordinate system for the entire tunnel cross section.

[0034] The aforementioned continuous arc length coordinate system along the neutral axis of the support structure transforms the irregular tunnel cross-section into a calculable mathematical curve. Each point in the coordinate system corresponds to a unique and definite arc length coordinate, which is beneficial for subsequent use of mathematical functions to quantify the shape and position of the tunnel cross-section and provides an accurate position index for subsequent calculation of pressure, deformation and other indicators at each point.

[0035] The pressure distribution data and deformation data (displacement field) on the tunnel cross-section are obtained based on the continuous arc length coordinate system, which facilitates subsequent mathematical calculations and data analysis, and is conducive to in-depth analysis of the mechanical properties and deformation laws of the tunnel cross-section.

[0036] S2. Based on pressure distribution data, deformation data, and the continuous arc length coordinate system, analyze the geometric, stress, and energy state of the tunnel cross-section, and obtain the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point on the support section. The implementation details are as follows: I. Obtain the geometric deformation analysis results at any point on the support section.

[0037] In tunnel engineering, traditional methods using absolute displacement (cumulative displacement) as an indicator of surrounding rock stability fail to reflect local abrupt changes and neglect structural linear evolution under asymmetric pressure (biased pressure) conditions. This embodiment illustrates the torsional deformation and deformation indices of a tunnel under asymmetric loading; please refer to the diagram for details. Figure 2 ,in Design radius for the tunnel The polar angle of the infinitesimal arc length. Let the arc length be a infinitesimal element. The radius after tunnel deformation. For the initial design curvature, The curvature after tunnel deformation.

[0038] To address the aforementioned issues, this embodiment introduces a displacement space gradient operator and curvature deviation to determine the instability risk of the tunnel support structure from the perspective of geometric linear evolution, thereby obtaining the geometric deformation analysis results at any point on the support section. The specific implementation steps are as follows: The first step is to analyze the relationship between the geometric linear deformation of the support structure and its spatial position based on the continuous arc length coordinate system.

[0039] Strain is the derivative of displacement with respect to spatial coordinates. The greater the displacement gradient of the support structure, the greater the relative displacement per unit length, which corresponds to the phenomenon of internal strain concentration. Under asymmetric pressure, the displacement gradient will produce peak values ​​at the junction of the biased and non-biased sides and at the joint slip surface passing through the support structure. These points are the geometric weak points where the support structure will suffer shear failure or dislocation.

[0040] The second step is to construct the displacement space gradient operator analysis formula based on the relationship, pressure distribution data, and deformation data.

[0041] Displacement spatial gradient in this embodiment It can measure the rate of change of displacement along the arc length of the support structure, characterizing strain concentration phenomena. This indicates that the structure undergoes overall rigid body displacement without generating additional internal forces; if The appearance of a peak value indicates a sudden and drastic displacement in a local area, which is the direct cause of the misalignment of the support structure and the shear cracking of the shotcrete.

[0042] The tunnel design radius is set based on the continuous path coordinates along the support neutral axis. Let the coordinates of the arc length of the support structure (the central axis of the steel arch frame) in the cross-section be... For the relationship between the arc length coordinates and polar coordinates of the tunnel support structure in this embodiment, please refer to [link / reference needed]. Figure 3 ,in These are polar coordinates in the coordinate system. The polar angle of the infinitesimal arc is the arc length.

[0043] Furthermore, at any point under the pressure of the surrounding rock The displacement vector under action satisfies the following relationship: , Therefore, the spatial gradient operator analysis formula satisfies the following relationship: , in, For the displacement space gradient, The rate of change of the displacement vector along the arc length direction. The coordinates are the coordinates of the continuous path along the neutral axis of the support. Design radius for the tunnel The derivative of the displacement vector with respect to the polar angle. For radial displacement components, Polar angle, For tangential displacement components, A radial unit vector, Let be the derivative of the tangential displacement component with respect to the polar angle. It is a tangential unit vector.

[0044] The third step is to use the displacement space gradient operator to analyze the displacement space gradient at any point on the support section.

[0045] Furthermore, in order to quickly identify weak areas in practical engineering applications, the displacement space gradient modulus is extracted as a quantitative criterion, and the modulus of the displacement space gradient satisfies the following relationship: , in, Let be the modulus of the spatial gradient of the displacement. Design radius for the tunnel Let be the derivative of the radial displacement component with respect to the polar angle. For radial displacement components, Polar angle, For tangential displacement components, This is the derivative of the displacement vector with respect to the polar angle.

[0046] Due to the tangential displacement in actual tunnel engineering Much smaller than radial displacement Therefore, the calculation of the modulus of the displacement space gradient can be simplified to a master criterion based on radial convergence non-uniformity, and satisfies the following relationship: , in, Let be the modulus of the spatial gradient of the displacement. Design radius for the tunnel The derivative of the displacement vector with respect to the polar angle. The rate of change of radial displacement along the arc length direction. The radial displacement components are distributed along the arc length coordinates. These are the coordinates of the continuous path along the neutral axis of the support.

[0047] The fourth step involves obtaining the ultimate shear strain of the support material by referring to the pressure distribution and deformation data of the tunnel cross-section. Simultaneously, the displacement spatial gradient threshold is determined based on the strain value, and this threshold is set to... .

[0048] The fifth step involves determining the local shear deformation weak zone using the aforementioned displacement space gradient threshold and displacement space gradient. In a specific embodiment, when... > This allows us to determine that the arc length location is a weak area of ​​local shear deformation.

[0049] The sixth step is to determine the initial design curvature of the support structure and to perform inversion analysis based on the continuous arc length coordinate system and the initial design curvature to obtain the instantaneous curvature.

[0050] In this embodiment, the support structure is a circular arched steel arch frame, which has a definite initial design curvature during the initial design phase. The initial design curvature of its support structure is set to satisfy the following relationship: , in, For the initial design curvature, The design radius for the tunnel.

[0051] Under asymmetric loads, the support structure will evolve from a perfect circle / quasi-circle to an ellipse or irregular polygon. In this embodiment, the deformation is mainly determined by the displacement field. Inversion of instantaneous curvature .

[0052] Step 7: Construct a curvature deviation analysis function based on the initial design curvature and instantaneous curvature.

[0053] This implementation features a curvature deviation analysis function that obtains the curvature deviation index value. The curvature deviation analysis function satisfies the following relationship: , in, This is the difference between the instantaneous curvature of the support structure after deformation and the initial design curvature. For the support structure in the displacement field Instantaneous curvature under action, The coordinates are the coordinates of the continuous path along the neutral axis of the support. For the initial design curvature, Design radius for the tunnel This represents the radial displacement component of the support structure at that point. This is the derivative of the displacement vector with respect to the polar angle.

[0054] The eighth step is to quickly obtain the difference between the instantaneous curvature of the support structure after deformation and the initial design curvature by using the curvature deviation analysis function.

[0055] The ninth step involves performing a coupled analysis of the displacement space gradient and the difference to obtain the comprehensive deformation identification factor.

[0056] In this embodiment, in order to achieve quantitative identification of weak areas, and By coupling the two geometric indices, the comprehensive deformation recognition factor can be obtained. .

[0057] The above-mentioned comprehensive deformation recognition factors satisfy the following relationship: , in, To comprehensively identify deformation factors, These are the weighting coefficients of the displacement space gradient operator. Let be the modulus of the spatial gradient of the displacement. The maximum displacement gradient across the entire cross section. This is the weighting coefficient for curvature deviation. The value is the difference between the instantaneous curvature of the support structure after deformation and the initial design curvature. This represents the initial design curvature. Furthermore, the aforementioned weighting coefficients can be adjusted and determined based on indoor and field results, such as the degree of fragmentation.

[0058] The tenth step combines the comprehensive deformation identification factor with the local shear deformation weak zone to obtain the geometric deformation analysis results at any point on the support section.

[0059] In one embodiment, a critical variable is set by combining the comprehensive deformation identification factor and the base station in the local shear deformation weak area. ,when When the distortion is too large, the geometric deformation becomes unstable, thus obtaining the geometric deformation analysis results at any point on the support section.

[0060] In this embodiment, to ensure the applicability and broad applicability of the model, further degradation verification was performed, the details of which are as follows: When the tunnel is located in isotropic strata with uniformly distributed surrounding rock pressure, the support will deform uniformly. ,constant The following conditions must be met .

[0061] The curvature deviation index is as follows: , in, This is the difference between the instantaneous curvature of the support structure after deformation and the initial design curvature. Design radius for the tunnel It represents the uniform radial displacement.

[0062] Under symmetrical pressure, the curvature deviation of the entire cross section is close to zero and uniformly distributed. This embodiment can be identified as having no significant weak areas. Therefore, this embodiment proposes geometric indices that simultaneously meet the working conditions of asymmetric and symmetrical pressure surrounding rock.

[0063] 2. Obtain the evaluation result of the eccentricity at any point on the support section.

[0064] The first step is to analyze the pressure distribution data, deformation data, and the difference ratio of the resultant force of the loads on both sides of the continuous arc length coordinate system.

[0065] This embodiment divides the entire tunnel cross-section into two regions, left and right, using the centerline of the tunnel cross-section as the boundary. Simultaneously, it sets... The coordinates of the boundary to the left of the centerline of the tunnel cross-section are [values]. The coordinates of the boundary to the right of the centerline of the tunnel cross-section are given. This is data from on-site monitoring of surrounding rock pressure.

[0066] Based on the on-site surrounding rock pressure monitoring data, the difference ratio of the resultant loads on both sides can be calculated using the following formula to obtain the load asymmetry index. And satisfy the following relationship: , in, For load asymmetry index, The coordinates of the boundary to the left of the centerline of the tunnel cross-section are [values]. For on-site surrounding rock pressure monitoring data, These are the boundary coordinates to the right of the centerline of the tunnel cross section.

[0067] The above The value range is between 0 and 1. When the tunnel is in a completely symmetrical working condition; when When the value approaches 1, it indicates that the tunnel is under extreme bias pressure conditions.

[0068] The second step is to obtain the bending moment and axial force at any point on the support section based on the pressure distribution data and deformation data, and to obtain the eccentricity at any point on the support section based on the bending moment and axial force.

[0069] In this embodiment, an asymmetric load is applied to a pre-constructed mechanical model of the support structure. Simultaneously, mechanical analysis methods such as the force method and the flexibility method are used to solve for the bending moment at any point on the support section (at any point s on the support section). and axial force The above The support section is in position The bending moment caused by the asymmetric load at the point, This refers to the location of the support section. Axial force caused by load.

[0070] Further obtain the structural eccentricity This yields the ratio of bending moment to axial force, which represents the distance between the point of application of the resultant force and the neutral axis of the support. The formula for calculating the eccentricity is as follows: , in, For the support section at the location Eccentricity at the location, For the protection section at the position The bending moment caused by the asymmetric load at the point, For the support section at the location Axial force caused by load.

[0071] The third step is to derive the eccentricity to obtain the eccentric compression coefficient at any point on the support section.

[0072] In order to eliminate the influence of cross-sectional dimensions on the evaluation of eccentricity, the above-mentioned eccentricity is used in the embodiment. Divide by support thickness Normalization is performed.

[0073] The eccentric compression coefficient satisfies the following relationship: , in, The normalized eccentric compression coefficient, For the support section at the location Eccentricity at the location, For the thickness of the support structure, For the protection section at the position The bending moment caused by the asymmetric load at the point, For the support section at the location Axial force caused by load.

[0074] The fourth step involves setting evaluation criteria for the degree of eccentricity based on the tunnel support structure and the tunnel's bias characteristics.

[0075] This embodiment, referencing tunnel support structures and tunnel eccentricity characteristics, comprehensively considering concrete structure design codes and steel structure design standards, and taking into account the eccentricity characteristics of tunnels under complex geological conditions, sets the following eccentricity evaluation conditions: When the location is determined to be in a small eccentric compression zone, the cross section is under uniform compression and the support is in a safe state, corresponding to a non-weak zone; When the location is determined to be in the eccentric compression zone, tensile stress begins to appear at the edge of the section, and the support enters an unfavorable state. If the location is determined to be in a large eccentric compression zone, the point of application of the resultant force is severely deviated, and the support is very likely to cause structural instability due to tearing on one side and crushing on the other.

[0076] The embodiment illustrates the eccentricity evaluation criteria. Please refer to the attached diagram for details. Figure 4 Where X and Z are the X-axis and Z-axis in the tunnel face, respectively. This is the left boundary of the tunnel. This is the right boundary of the tunnel.

[0077] The fifth step is to obtain the eccentricity evaluation result at any point on the support section based on the eccentricity compression coefficient and the eccentricity evaluation conditions.

[0078] Based on the above calculation of the eccentric compression coefficient By combining the eccentricity evaluation conditions, the eccentricity of any part of the tunnel support structure, including the initial support, the temporary support steel structure, and the secondary lining, can be evaluated, and the corresponding eccentricity evaluation results can be obtained, providing an important basis for the safety assessment and design optimization of the tunnel structure.

[0079] 3. Obtain the toughness assessment result at any point on the support section.

[0080] In underground engineering projects such as tunnels, accurately determining the toughness of any point on the support section is crucial for ensuring the safety and stability of the engineering structure.

[0081] The first step is to obtain the energy release density of the surrounding rock based on the volume deformation, pressure distribution data, deformation data and continuous arc length coordinate system after the surrounding rock is unloaded and expanded.

[0082] This embodiment takes into account on-site surrounding rock pressure monitoring data. Radial convergence displacement is and the vector projection coefficients of the load and displacement directions Under a unit slip arc length, the influence of volumetric deformation after unloading and expansion of the surrounding rock is comprehensively analyzed. The effective work done by the surrounding rock pressure on the support is the energy release density of the surrounding rock. The formula for calculating the energy release density of the surrounding rock is as follows: , in, The energy density released by the surrounding rock. For on-site surrounding rock pressure monitoring data, For radial convergent displacement, represents the vector projection coefficients for the load and displacement directions.

[0083] The second step is to analyze the ultimate resistance energy of the support structure based on the deformation-recoverable elastic energy storage and the non-recoverable damage energy dissipation of the support structure.

[0084] This embodiment divides the energy absorption capacity of the support structure into elastic energy storage that can recover from deformation. and irreversible damage and energy consumption .

[0085] Then, the support section is set at the location. The bending moment caused by the asymmetric load at point is The elastic modulus of the material is Moment of inertia is The support section is at the location The axial force caused by the load at the point is The equivalent shear area of ​​the support section is The geometric distortion energy conversion coefficient is The modulus of the spatial gradient of displacement is The shear modulus of the support material is The feature correlation length is Furthermore, in this embodiment, the unit arc length of the support micro-element is set.

[0086] Example: Geometric distortion energy conversion coefficient It is based on the shear modulus of the support material. With equivalent shear area The analytic function can be defined by the following formula: , in, The geometric distortion energy conversion coefficient, The shear modulus of the support material. The equivalent shear area of ​​the support section. The feature correlation length.

[0087] The ultimate resistance of the support structure can satisfy the following relationship: , in, For the support structure in position Total ultimate resistance energy density at the location, For the support section at the location Elastic energy storage density at that location, For the support section at the location Damage energy density at the site For the protection section at the position The bending moment caused by the asymmetric load at the point, The elastic modulus of the material. For the moment of inertia, For the support section at the location Axial force caused by load at the point, The equivalent shear area of ​​the support section. The geometric distortion energy conversion coefficient, Let be the modulus of the spatial gradient of the displacement.

[0088] The third step is to establish a toughness saturation index analysis function based on the energy release density and ultimate resistance energy of the surrounding rock.

[0089] To quantitatively evaluate the structural toughness state under asymmetric conditions, this study derives a dimensionless toughness saturation index based on the energy release density of the surrounding rock and the ultimate resistance energy. The calculation formula is as follows: , in, The toughness saturation index, The effective work done by the surrounding rock pressure on the support per unit arc length. For the support structure in position The total ultimate resistance energy density at the location.

[0090] The fourth step is to obtain the toughness saturation index at any point on the support section using the toughness saturation index analysis function.

[0091] This embodiment determines the toughness grading threshold based on the toughness saturation index output by the toughness saturation index analysis function, and also draws a schematic diagram of the toughness grading of the tunnel support structure. Please refer to [link / reference needed]. Figure 5 .

[0092] Combination Figure 5 The toughness grading is as follows: when It is in the linear elastic tolerance zone, which corresponds to the fatigue red line of linear energy storage of the support material. This ensures that the structure is in the pure elastic energy absorption stage under normal disturbances and has sufficient energy redundancy.

[0093] when It is in the elastoplastic transition and energy dissipation region, within which the structure can consume the maximum energy. Its energy absorption potential begins to deplete, resulting in irreversible geometric damage and energy consumption, which falls within the brittle instability warning zone.

[0094] when When the energy consumption is in a saturated and weak zone, the total potential energy does not have a stable minimum point, and it is very easy for brittle bursting and collapse to occur when the unloading expansion energy of the surrounding rock is released instantaneously.

[0095] The toughness grading threshold in this embodiment is determined based on the structural reliability theory. 0.3 corresponds to the fatigue red line of linear energy storage of the support material, which can ensure that the structure does not produce cumulative damage under normal bias. 0.7 corresponds to the critical transformation factor of structural toughness-brittle evolution, which can determine the minimum energy margin for the structure to maintain mechanical balance when facing nonlinear disturbances such as unloading expansion of the surrounding rock.

[0096] The fifth step is to classify and judge the toughness saturation index at any point on the support section to obtain the toughness judgment result at any point on the support section.

[0097] Based on the toughness saturation index calculated above By comparing the toughness grading thresholds and toughness grading results with those described above, the toughness state at any point on the support section can be determined, yielding the corresponding toughness assessment result. Through these implementation steps, the toughness assessment results at any point on the tunnel support section can be systematically obtained, providing an important basis for tunnel structure safety assessment, design optimization, and maintenance decisions.

[0098] S3. In tunnel engineering, accurately identifying the weak areas of the tunnel cross-section and generating a corresponding weighted index distribution map of weak points is of great significance for guiding engineering reinforcement and support, and ensuring the safety of the tunnel structure. This embodiment constructs a multi-index collaborative judgment model based on the results of geometric deformation analysis, eccentricity evaluation, and toughness assessment, and then generates a weighted index distribution map of the weak points of the tunnel cross-section, providing a scientific and effective decision-making basis for tunnel engineering. The implementation details are as follows: Based on the above implementation details, the embodiments mainly evaluate and analyze from three dimensions: geometry, force, and energy. Based on these three dimensions and the corresponding analysis content, a tunnel structure instability evaluation index system is constructed.

[0099] The evaluation index system for tunnel structure instability includes a geometric deformation analysis index layer, an eccentricity evaluation index layer, and a toughness judgment index layer, as detailed below: The geometric deformation analysis index layer includes displacement spatial gradient and curvature deviation. These indices reflect the degree of geometric distortion of the tunnel structure, thus yielding a geometric distortion degree index. .

[0100] The eccentricity evaluation index layer covers asymmetric indicators and eccentric compression coefficient. The eccentric compression coefficient can reflect the eccentricity of the tunnel structure during the stress process and can preferentially reflect the stress state of the structure.

[0101] The toughness assessment index layer uses the toughness saturation index. With this as the core, the above indicators reflect the energy characteristics of the tunnel structure, namely the structure's kinetic energy buffering capacity.

[0102] From an engineering perspective, this embodiment requires that all three indicator layers be controlled within permissible ranges. Therefore, a Boolean parallel judgment logic is adopted to better align with the limit state design principles of tunnel engineering. When any point on the support structure... A zone can be identified as a weak support area if any of the following conditions are met.

[0103] A multi-index collaborative judgment model was established in the evaluation index system for tunnel structure instability, and it satisfies the following relationship: , in, Location of tunnel cross section The stability state identifier at the location. The geometric distortion index. This is the critical threshold for geometric distortion. The coefficient for eccentric compression is... The toughness saturation index; Based on the above judgment model and the evaluation index system for tunnel structure instability, it can be concluded that: Geometric Boundaries: When This indicates that the tunnel structure has excessive local distortion and linear instability, which may affect the normal use and safety of the tunnel.

[0104] Strength limit: when This indicates that the tunnel structure has entered a state of large eccentric compression, and the cross-section is at risk of crushing, requiring timely reinforcement measures.

[0105] Resilience Limit: When This means that the tunnel structure's energy is approaching saturation, posing a risk of collapse, which requires high attention and corresponding measures.

[0106] Furthermore, a weakness-weighted index is introduced.

[0107] In areas already identified as weak points, this embodiment introduces a weakness-weighted index to more accurately guide reinforcement and support during engineering. This index can achieve a three-dimensional synergistic representation of geometric deformation, stress, and energy, thereby comprehensively reflecting the overall weakness of the tunnel cross-section support structure.

[0108] The aforementioned weakness-weighted indices satisfy the following relationship: , in, For the support structure in position The overall weakness weighted index of the location, The weighting coefficient for the geometric deformation index. This is the normalized geometric distortion index. The weighting coefficients for the internal force redistribution index. This is the normalized eccentric compression coefficient. The weighting coefficients for energy dissipation indicators. This is the normalized toughness saturation index.

[0109] The above , , These refer to the normalized geometric distortion index, the eccentric compression coefficient, and the toughness saturation index, respectively. , , These are the corresponding weight coefficients, and the weight coefficients are... .

[0110] In practical engineering, the aforementioned weighting coefficients can be reasonably determined based on different geological conditions and engineering requirements. In a specific embodiment, the geological conditions of the shallowly buried fractured zone are complex, and deformation control is crucial; therefore, it is possible to improve... The value reflects the deformation control characteristics; in deeply buried high-stress zones, energy release has a significant impact on structural safety, so it can be appropriately increased. To emphasize the release of resilient energy; in significantly biased formations, eccentric compression is the main problem, which can improve... Characterizes the eccentric compression features.

[0111] The results of geometric deformation analysis, eccentricity evaluation, and toughness judgment are synergistically characterized by the weakness weighted index and multi-index collaborative judgment model, generating a weakness weighted index distribution map of the tunnel section.

[0112] The specific content of the multi-index synergistic characterization in the evaluation index system for tunnel structure instability is as follows: Force and form coordination: Abrupt changes in the spatial gradient of displacement are often a precursor to abrupt changes in bending moment. When the geometric deformation analysis results reach the warning level while the eccentricity evaluation results are still safe, the system will issue a geometric instability warning signal. It can be suggested to check the overall linear coordination of the support structure and adjust the support parameters in a timely manner to avoid structural damage due to excessive geometric deformation.

[0113] Force and energy synergy: The eccentric compression coefficient reflects the static bearing limit, while the toughness index reflects the kinetic energy buffering capacity. When the eccentricity evaluation result is close to the critical point and the toughness judgment result suddenly surges, an extremely weak area can be identified, indicating that a collapse without warning may occur, and emergency reinforcement measures need to be taken immediately.

[0114] Degradation control: When the input pressure degrades to a symmetrical and uniform distribution, all three factors synchronously regress to a low level across the entire cross-section. At this point, the decision function... Furthermore, the structure is in a global equilibrium state, indicating that the tunnel structure is in a stable state under this working condition.

[0115] Furthermore, based on the comprehensive weakness weighted index of the support structure at any location and the multi-index collaborative judgment model, the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results are collaboratively characterized. This embodiment uses data processing methods and visualization technology to generate a weakness weighted index distribution map of the tunnel section. The above distribution map can intuitively show the weakness of different locations of the tunnel section, providing engineers with a clear basis for decision-making.

[0116] Meanwhile, based on the comprehensive weakness weighted index of the support structure at any location, asymmetric support parameter adjustment instructions can be automatically generated. Therefore, in practical applications, different reinforcement measures can be taken for areas with different degrees of weakness, such as increasing support strength and adjusting support spacing, to achieve precise reinforcement and improve the safety and stability of the tunnel structure.

[0117] Through the above implementation steps, a multi-index collaborative judgment model can be constructed based on the results of geometric deformation analysis, eccentricity evaluation, and toughness judgment. The multi-index collaborative judgment model can then generate a weighted index distribution map of the weakness of the tunnel section, providing strong support for the safe construction and operation of tunnel engineering.

[0118] S4. Based on the results of geometric deformation analysis, eccentricity evaluation, and toughness assessment, and the weighted index distribution map of weakness, differentiated support decisions for tunnels are designed. The implementation details are as follows: Under complex geological conditions, the surrounding rock pressure on tunnels typically exhibits a non-uniform distribution. Existing symmetrical support methods show highly uneven reliability indices across different parts when dealing with asymmetrical loads, making it difficult to effectively ensure the safety and stability of the tunnel structure. Therefore, this implementation is based on the identification index and evaluation model of the tunnel's weak zones, using the evaluation results of the weakness weighted index as a key reference indicator to drive the spatial allocation of support parameters, thereby transforming tunnel support from passive bearing to active control. The specific implementation focuses on asymmetrical anchorage decisions for geometric deformation design, while adjusting the anchorage length and density to enhance the stability of the tunnel structure under asymmetrical loads.

[0119] In one embodiment, asymmetric anchoring decisions for geometric deformation design are made based on the results of geometric deformation analysis and the weakness distribution map.

[0120] Asymmetric anchorage length design in asymmetric anchorage decision-making: Based on the results of geometric deformation analysis and the weak point distribution map, the embodiment makes asymmetric anchoring decisions for geometric deformation design. That is, by adjusting the anchoring parameters differently, the anchoring system can better adapt to the asymmetric distribution of surrounding rock pressure. Specifically, based on the weak areas identified by the geometric distortion field, the length and density of the anchor bolts are designed in a targeted manner according to the weak point weighting index to form an effective load-bearing system. This anchors the asymmetric deformation pressure in the deeper rock mass, thereby improving the overall stability of the tunnel structure.

[0121] For weak areas identified by the geometric distortion field, especially the biased side, differentiated design is required. In an optional embodiment, under biased conditions, the bedding-side anchor bolts need to pass through the potential slip line and enter the stable rock mass to provide sufficient anchoring force. This embodiment establishes an asymmetric anchoring length calculation method by considering factors such as bias angle and degree of geometric distortion, so that the anchor bolt length increases non-linearly with the degree of distortion, thereby better adapting to asymmetric deformation pressure.

[0122] Further set the standard design anchor length as At a bias tilt angle of Under operating conditions, position Differentiated anchor bolt design length at any location The calculation formula is as follows: , in, For position Differentiated anchor bolt design length at the location, The standard design anchor bolt length, This is the rock mass fracturing degree adjustment coefficient. This is the normalized geometric distortion index. This is the bias tilt angle. It is the polar angle.

[0123] Location The differentiated anchor bolt design length refers to the differentiated anchor bolt design length at any point on the support section. The unit needs to be determined according to the actual project, such as meters (m). The standard design anchor length is a basic design parameter, and the unit must be the same as the design length of the differentiated anchor. The rock mass fragmentation degree adjustment coefficient can characterize the demand for long anchor bolts. Its value range is usually determined based on engineering experience. In this embodiment, it is set between 0 and 1. The more fragmented the rock mass, the larger the value of the rock mass fragmentation degree adjustment coefficient.

[0124] The normalized geometric distortion index reflects the position The degree of geometric deformation at any point (on the support section), where the value ranges from 0 to 1.

[0125] The bias angle is an important parameter describing the asymmetric direction of the surrounding rock pressure, and its unit can be degrees (°) or radians (rad).

[0126] The polar angle at the location of the anchor bolt can determine the specific position of the anchor bolt on the tunnel cross section, and the unit is the same as the bias angle.

[0127] Asymmetric anchorage density design in asymmetric anchorage decision-making: In asymmetric biased pressure zones, the anchor spacing is not constant. In order to form an effective bearing ring, the anchor density (number of anchors per unit area) should be proportional to the weakness weighting index. That is, in areas with greater weakness, the anchor density should be increased accordingly to improve the support strength and stability of the area.

[0128] In this implementation, the standard design spacing of the anchor bolts is: ,Location Differential circumferential anchor spacing at any point (on the support section) The calculation formula is as follows: , in, For position Differential circumferential anchor spacing at the location, The standard anchor spacing is designed for this purpose. For anchor bolt density sensitivity factor, For the support structure in position The overall weakness weighted index of the location, This represents the average value of the overall cross-sectional weakness.

[0129] Location The differential circumferential anchor spacing refers to the differential circumferential anchor spacing at any point on the support section, and its unit can be determined according to the actual project. The standard design anchor spacing is a basic design parameter, and its unit should be the same as that of the differentiated circumferential anchor spacing. The anchor density sensitivity factor is used to characterize the rate at which the asymmetry of surrounding rock pressure is converted into support density. Its value range is determined based on engineering experience and can be set between 0 and 1. The stronger the asymmetry of surrounding rock pressure, the larger the value of the anchor density sensitivity factor.

[0130] support structure in location The comprehensive weakness weighted index reflects the overall weakness at different locations, and the range of values ​​is determined according to the specific calculation method.

[0131] The average cross-sectional weakness can measure the average weakness of the entire tunnel cross-section. The specific calculation formula satisfies the following relationship: , in, For the support structure in position The overall weakness weighted index of the location, The number of sampling points on the tunnel cross-section. For the first The location of each sampling point.

[0132] Furthermore, after the asymmetric anchoring design is completed and implemented, its effectiveness needs to be evaluated.

[0133] By monitoring indicators such as geometric deformation and stress-strain of the tunnel cross-section, and comparing data changes before and after implementation, the effectiveness of asymmetric anchoring decisions in improving tunnel structural stability can be evaluated. Simultaneously, by combining changes in the thinness weighted index distribution map, it can be determined whether the adjustment of anchoring parameters has led to a more uniform thinness weighted index across the entire cross-section support structure.

[0134] Next, the asymmetric anchoring parameters are dynamically adjusted based on the effect evaluation results. If the support effect in certain areas is found to be unsatisfactory, and the weakness weighted index remains high, the anchor length or density in those areas can be further increased; conversely, if the support strength in certain areas is too high, resulting in resource waste, the anchor length or density can be appropriately reduced. Through dynamic adjustment, the optimal configuration of support parameters is achieved, improving the economy and safety of tunnel engineering. To more intuitively illustrate the asymmetric anchorage length and density distribution, this embodiment includes a diagram illustrating the asymmetric anchorage length and density distribution. Please refer to the diagram for details. Figure 6 . Figure 6 The visualization shows the design of anchor bolt lengths and spacing at different locations, as well as their correspondence with geometric distortion fields and weakness weighted indices. Figure 6 It provides a clear understanding of the specific implementation methods and effects of asymmetric anchoring decisions, offering a reference for practical engineering applications.

[0135] In one embodiment, the decision on the variable cross-section stiffness of a large eccentric compression design is made based on the eccentricity evaluation results and the weakness distribution diagram.

[0136] In underground engineering structures such as tunnels, due to complex geological conditions and uneven load distribution, the structure is subjected to large eccentric compression. Large eccentric compression can lead to significant local bending moments, ultimately causing structural failure. Traditional uniform cross-section support designs are insufficient to effectively address situations with large local eccentric compression, and these weak points affect the structure's safety and stability. Therefore, this embodiment proposes a variable cross-section stiffness decision for large eccentric compression design based on eccentricity evaluation results and a weak point distribution map. By adjusting the stiffness of the support cross-section, the structure can better adapt to large eccentric compression conditions, improving its overall performance.

[0137] Based on the eccentricity evaluation results and the weak point distribution map, this embodiment identifies weak areas in the structure that are significantly affected by large eccentric compression. Then, it focuses on adjusting the flexural modulus of the cross-sections in these weak areas. By differentially distributing the cross-sectional stiffness, the support structure can more rationally distribute internal forces under large eccentric compression, reducing local stress concentration and improving the structure's load-bearing capacity. This ensures that under the ultimate state of large eccentric compression, the stress in each part of the support structure does not exceed the allowable stress of the material, preventing structural failure. Simultaneously, by optimizing the cross-sectional stiffness distribution, the overall stability and safety of the structure are improved, and engineering costs are reduced.

[0138] Based on the weak zones identified by the eccentric compression coefficient in the eccentricity evaluation results, in order to adjust the flexural modulus of the section so that the minimum flexural modulus required by the support structure satisfies the limit state of large eccentric compression, a differentiated stiffness distribution equation for the support structure is derived, which satisfies the following relationship: , in, For position The moment of inertia of the differentiated cross section at the location, For the standard design section moment of inertia, The cross-sectional strengthening sensitivity coefficient, The coefficient for eccentric compression is given.

[0139] The eccentric compression coefficient is an important indicator for measuring the degree of eccentric compression on a structure; therefore, in this implementation, it is defined as the eccentricity. Distance from the core of the cross section The ratio, i.e. The larger the eccentric compression coefficient mentioned above, the more significant the effect of eccentric compression on the structure.

[0140] The moment of inertia of a cross section is a geometric quantity reflecting the bending resistance of the cross section, and it is related to the shape and size of the cross section. In this embodiment, it is used... Indicates position Differential section moment of inertia at any point (of the support section), This represents the moment of inertia of the standard design section.

[0141] The differential stiffness distribution equation shows that when the eccentric compression coefficient Once the small eccentricity limit (0.2) is exceeded, the support stiffness will increase exponentially. The above design method can accurately counteract sudden changes in local bending moment and improve the load-bearing capacity of the structure under large eccentric compression.

[0142] The section hardening sensitivity coefficient is an adaptive parameter based on the edge stress non-limit criterion. It reflects the sensitivity of section stiffness to the eccentric compression coefficient, and its value can be obtained by considering the most unfavorable eccentricity. With the allowable stress of the material The mapping equation is determined dynamically, and its calculation formula is as follows: , in, The cross-sectional strengthening sensitivity coefficient, To design the maximum permissible eccentric compression coefficient, This represents the design value of the maximum bending moment at the location section. This is the distance from the edge of the compression zone of the cross section to the neutral axis. The allowable stress of the material, The moment of inertia for the standard design section.

[0143] The design value of the maximum bending moment at a cross-section is the maximum bending moment that the cross-section may withstand, which can be calculated considering various load combinations. .

[0144] The stress distribution on a cross section is mainly related to the shape and size of the cross section.

[0145] Allowable stress of material It is determined based on the mechanical properties of the materials and design requirements. Under normal use conditions, the stress of the structure should not exceed this value.

[0146] The differentiated moment of inertia can be calculated based on the variable cross-section stiffness decision. Therefore, a variable cross-section support structure can be designed. In application, an asymmetric variable cross-section steel frame can be used, such as welding stiffeners on the eccentrically loaded side, to achieve differentiated distribution of cross-sectional stiffness. During the design process, the feasibility and economy of constructing the variable cross-section support structure must be ensured. Simultaneously, the designed variable cross-section support structure needs to undergo mechanical analysis and verification to check whether it meets the limit state requirements for large eccentric compression and the structural safety requirements. If the verification results do not meet the requirements, the design parameters can be adjusted and optimized, and the calculation and design can be repeated until the requirements are met.

[0147] In practical engineering applications, various parameters should be rationally determined based on specific geological conditions, load conditions, and design requirements. The variable cross-section stiffness decision-making and support structure design should be strictly carried out according to the above implementation steps. Simultaneously, quality control and monitoring during construction should be strengthened to ensure the construction quality and safety of the variable cross-section support structure. Ultimately, the variable cross-section stiffness decision-making for large eccentric compression design should be achieved based on the eccentricity evaluation results and weak point distribution diagram, effectively improving the bearing capacity and stability of underground engineering structures such as tunnels under large eccentric compression conditions.

[0148] In one embodiment, an asymmetric buffer layer design decision is made based on the resilience assessment results and the weakness distribution map for energy risk.

[0149] During the excavation and support of underground engineering projects such as tunnels and roadways, the surrounding rock will generate expansion energy due to unloading. If the energy release is not effectively buffered and controlled, it may lead to serious accidents such as structural collapse and crushing. Traditional uniform buffer layer design is difficult to effectively address the differences in energy risk in different areas. Therefore, this embodiment proposes a method for making decisions on the design of asymmetric buffer layers based on toughness assessment results and weak point distribution maps. By accurately identifying weak areas and rationally arranging the thickness of the buffer layer, the toughness and safety of the structure under energy impact can be improved.

[0150] Based on the toughness assessment results and the weakness distribution map, this embodiment identifies weak areas with high energy risk in the structure. For these weak areas, an energy-absorbing layer is used to mitigate the expansion energy generated by the unloading of the surrounding rock. By establishing the relationship between the thickness of the buffer layer and the energy density released by the surrounding rock, the structural bearing capacity, and the performance of the buffer material, an asymmetric arrangement of the buffer layer thickness is achieved, enabling the buffer layer to absorb and disperse energy more effectively.

[0151] Based on the weak areas identified by the toughness saturation index in the toughness assessment results, in order to mitigate the unloading expansion energy through an energy-absorbing layer, a differentiated deformation space or buffer layer thickness is reserved between the fractured rock mass and the initial support. Energy density should be released from the surrounding rock. The driver is used, and the calculation formula is as follows: , in, To differentiate the deformation space or buffer layer thickness, The energy density released by the surrounding rock. The energy threshold corresponding to the structural bearing capacity. This is the equivalent compressive strength of the cushioning material.

[0152] Based on the implementation details, the aforementioned toughness saturation index is an important indicator for measuring a structure's ability to resist damage under energy impact. It comprehensively considers factors such as the structure's material properties, geometry, and stress state, and can be used to determine whether a structure has entered a toughness-weak zone. When the toughness saturation index reaches a certain threshold, it indicates that the structure's toughness in that region is insufficient, and corresponding strengthening measures need to be taken.

[0153] The energy density released by the surrounding rock refers to the energy released per unit volume of surrounding rock during the unloading process, which is related to the physical and mechanical properties of the surrounding rock, stress state, excavation method, and other factors.

[0154] The energy threshold corresponding to the structural bearing capacity refers to the maximum energy that the structure can withstand under normal working conditions. When the energy released by the surrounding rock exceeds this threshold, the structure may be damaged. This threshold is related to factors such as the material strength, cross-sectional dimensions, and support method of the structure.

[0155] The equivalent compressive strength of a buffer material refers to the maximum stress that the buffer material can withstand during compression. It reflects the energy absorption capacity of the buffer material. Since different types of buffer materials have different equivalent compressive strengths, selecting a suitable buffer material is of great importance for achieving effective energy buffering.

[0156] Differential deformation space or buffer layer thickness refers to the thickness of the space or buffer layer reserved between the fractured rock mass and the initial support for absorbing energy. The thickness is mainly determined by calculation based on the energy density released by the surrounding rock, the structural bearing capacity, and the performance of the buffer material. Different thickness values ​​can be used in different areas to achieve asymmetrical arrangement.

[0157] The above It is a parameter used to determine whether a structure has entered a region of weak toughness. This indicates that the structure has entered a region of weak toughness, requiring corresponding measures to enhance its toughness. At this point, it is necessary to calculate the excess energy and convert it into the compressive displacement demand of the buffer layer. The aforementioned excess energy... It can be represented as follows: , Furthermore, based on the mechanical properties of the cushioning material, the compressive displacement of the cushioning layer... With excess energy and the equivalent compressive strength of the cushioning material There is a relationship between them, which can be calculated using relevant mechanical models. On the non-biased side, the energy release is relatively small, so the value is 0; on the biased peak side, according to the calculation results, an asymmetric energy buffer zone with a thickness of 10-20cm is formed, which effectively prevents structural collapse and crushing.

[0158] In one embodiment, based on the calculated buffer layer thickness By combining the weakness distribution diagram, the asymmetric arrangement scheme of the buffer layer can be determined. On the bias peak side, a thicker buffer layer is set according to the calculation results to form an asymmetric energy buffer band; on the non-bias side, the thickness of the buffer layer can be appropriately reduced or set to 0. At the same time, detailed buffer layer design drawings can be drawn according to the asymmetric arrangement scheme, clarifying the size, shape, and position parameters of the buffer layer.

[0159] In practical engineering applications, it is necessary to rationally determine various parameters based on specific geological conditions, engineering requirements, and the energy release characteristics of the surrounding rock, and strictly follow the above implementation steps for the decision-making, design, and construction of the asymmetric buffer layer. Simultaneously, it is crucial to strengthen quality control and monitoring and evaluation during construction to ensure that the buffer layer can effectively buffer energy and improve the safety and stability of the structure.

[0160] Differentiated tunnel support is achieved through asymmetric anchoring decisions, variable cross-section stiffness decisions, and asymmetric buffer layer decisions.

[0161] In tunnel engineering, due to complex geological conditions and construction disturbances, tunnels are often under asymmetrical pressure. This asymmetrical pressure leads to uneven stress on the tunnel structure and the emergence of weak areas. If traditional symmetrical support methods are used directly, they cannot effectively cope with the complex stress conditions, thereby affecting the safety and stability of the tunnel. The embodiment realizes differentiated support for the tunnel through asymmetrical anchoring decisions, variable cross-section stiffness decisions, and asymmetrical buffer layer decisions, so as to better adapt to asymmetrical pressure conditions and improve the support effect of the tunnel.

[0162] This implementation of a tunnel weak zone identification and differentiated support method based on asymmetric load evolution ensures that the structure has sufficient stiffness to resist deformation while possessing a certain degree of toughness to absorb and dissipate energy, thus preventing brittle failure of the structure.

[0163] In an optional embodiment, the specific implementation steps of the tunnel weak zone identification and differentiated support method are as follows: First, real-time displacement field data and surrounding rock pressure data of the tunnel cross section are collected using monitoring equipment. The displacement field data can be obtained by displacement sensors placed on the tunnel lining, while the surrounding rock pressure data can be monitored by pressure cells and other equipment.

[0164] Then, calibrate two key parameters simultaneously. and The above The parameters that can reflect the degree of damage to the surrounding rock are related to the physical and mechanical properties and stress state of the surrounding rock. Their values ​​can be determined by analyzing the acoustic emission and electromagnetic radiation signals of the surrounding rock. It is a parameter related to the surrounding rock pressure and can be calibrated based on the measured surrounding rock pressure data.

[0165] The multi-indicator collaborative judgment model is obtained This function comprehensively considers multiple factors such as displacement, stress, and energy of the tunnel cross-section, and can effectively determine whether each location on the entire tunnel cross-section is a weak zone. Furthermore, the multi-index collaborative judgment model can be determined based on actual engineering conditions and theoretical analysis, which can be expressed as... Through the decision function Determine the location of the entire cross-section when When the value reaches or exceeds the preset Boolean threshold, the corresponding arc length interval is marked as a weak area. The weak area may be a geometrically distorted segment, a large eccentrically compressed segment, or a high-energy accumulation segment, etc.

[0166] Next, we proceeded with differentiated design.

[0167] Geometric Distortion Segment Support Design: Based on the Equation for Calculating Asymmetric Anchorage Length Determine the length distribution of asymmetric long and short anchors and the circumferential spacing function. Determine the anchor bolt density; based on and Based on the output results, an asymmetric long and short anchor bolt and quincunx reinforcement scheme was formulated. In locations with large geometric distortion, longer anchor bolts were used and the arrangement density was increased to enhance the support effect; in relatively stable locations, shorter anchor bolts were used and the arrangement density was appropriately reduced.

[0168] Support design for eccentrically compressed sections: For eccentrically compressed sections, a differentiated stiffness distribution equation is used. Get location The equation, which considers factors such as the eccentric compression coefficient, surrounding rock pressure, and structural dimensions, effectively analyzes the relationship between the support structure dimensions and the degree of eccentric compression. Based on... The output results determine the dimensions of the variable cross-section support structure. In locations with greater eccentric compression, the cross-sectional dimensions of the support structure are increased to improve its load-bearing capacity; in locations with less eccentric compression, the cross-sectional dimensions are appropriately reduced to save materials and lower costs.

[0169] Support design for high-energy accumulation sections: For high-energy accumulation sections, calculations are performed based on the energy density released by the surrounding rock. The range and energy magnitude of the high-energy accumulation area are determined through theoretical analysis or numerical simulation. Based on the calculated energy magnitude, an asymmetric energy-absorbing buffer layer is laid. On the load peak side, i.e., where energy release is greater, a thicker buffer layer is laid to absorb and dissipate energy. On the location where energy release is less, a thinner buffer layer is laid or no buffer layer is laid.

[0170] Then, the aforementioned differentiated design schemes were subjected to degradation verification.

[0171] When the external environment returns to a uniform pressure field, the relevant parameters will change as follows: Displacement space gradient At this time, the spatial gradient of displacement The value approaches 0, indicating that the displacement distribution of the tunnel tends to be uniform.

[0172] Eccentricity coefficient The value tends to a constant (small eccentricity or no eccentricity), indicating that the degree of eccentricity of the tunnel under pressure decreases.

[0173] The energy saturation index is homogenized across the entire cross section, meaning that the energy state at each location tends to be consistent.

[0174] Therefore, it can be concluded that under uniform pressure field conditions, the determination function... Outputting non-weak areas indicates that under the above conditions, there are no obvious weak areas in the tunnel, and differentiated support methods are not required.

[0175] This embodiment refers to the symmetrical design concept and conventional symmetrical equal-strength support design of railway tunnel design specifications or highway tunnel design specifications. It further illustrates that the identification of weak areas in tunnels under asymmetrical load evolution and the differentiated support method have advantages in dealing with eccentric load conditions. At the same time, it has good upward compatibility with conventional conditions and can flexibly adjust the support scheme according to different working conditions.

[0176] For the decision-making process and detailed information regarding the differentiated support method for tunnels under asymmetric compression in this embodiment, please refer to Table 1.

[0177] Table 1. Decision Table for Differentiated Support Methods in Tunnels under Symmetrical Compression. In the field of tunnel engineering, tunnel excavation often faces the problem of instability caused by eccentric pressure due to various factors such as initial stress field and geological structure. This paper proposes a multi-index collaborative judgment and decision-making method for weak areas of tunnel support based on asymmetric load evolution: first, the asymmetric load field is inverted, and the displacement space gradient operator is extracted (…). ), eccentric compression coefficient ( ), toughness saturation index ( Three key indicators are used; then, Boolean logic decision functions are used to identify weak areas in the cross section, and risk classification is carried out in combination with the weakness weighted index; finally, based on the principle of energy allocation on demand and stiffness-toughness matching, the support structure is driven to carry out asymmetric design in reverse. The method of this embodiment realizes the effective transformation from traditional equal strength design to asymmetric targeted support, improves the structural safety of the biased side, and reduces the input of ineffective materials on the non-biased side.

[0178] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for identifying and differentiating supporting of weak areas of a tunnel based on asymmetric load evolution, characterized in that, Includes the following steps: Collect pressure distribution data and deformation data of the tunnel cross section, and construct a continuous arc length coordinate system along the neutral axis of the support structure based on the pressure distribution data and the deformation data; Based on the pressure distribution data, the deformation data, and the continuous arc length coordinate system, the geometry, stress, and energy state of the tunnel section are analyzed, and the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section are obtained. Based on the geometric deformation analysis results, the eccentricity evaluation results, and the toughness judgment results, a multi-index collaborative judgment model is constructed, and a weighted index distribution map of the weakness of the tunnel section is generated through the multi-index collaborative judgment model. Based on the geometric deformation analysis results, the eccentricity evaluation results, and the toughness judgment results, as well as the weakness weighted index distribution map, a differentiated support decision for the tunnel is designed.

2. The tunnel weak zone identification and differential support method based on asymmetric load evolution of claim 1, wherein, The step of analyzing the geometry, stress, and energy state of the tunnel cross-section based on the pressure distribution data, the deformation data, and the continuous arc length coordinate system, and obtaining the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section, includes: The relationship between the geometric linear deformation and spatial position of the support structure is analyzed based on the continuous arc length coordinate system. Based on the aforementioned relationship, the pressure distribution data, and the deformation data, a displacement space gradient operator analysis formula is constructed. The displacement space gradient at any point on the support section is obtained using the displacement space gradient operator analysis formula. Obtain the ultimate shear strain of the support material, and determine the displacement space gradient threshold by referring to the ultimate shear strain of the support material; The local shear deformation weak zone is determined by the displacement spatial gradient threshold and the displacement spatial gradient.

3. The tunnel weak zone identification and differential support method based on asymmetric load evolution of claim 2, wherein, The step of analyzing the geometry, stress, and energy state of the tunnel cross-section based on the pressure distribution data, the deformation data, and the continuous arc length coordinate system, and obtaining the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section, includes: Determine the initial design curvature of the support structure; Instantaneous curvature is obtained by inversion analysis based on the continuous arc length coordinate system and the initial design curvature. A curvature deviation analysis function is constructed based on the initial design curvature and the instantaneous curvature; The difference between the instantaneous curvature of the support structure after deformation and the initial design curvature is obtained through the curvature deviation analysis function. A coupled analysis is performed on the displacement spatial gradient and the difference to obtain a comprehensive deformation identification factor; By combining the comprehensive deformation identification factor with the local shear deformation weak zone, the geometric deformation analysis results at any point on the support section are obtained.

4. The tunnel weak zone identification and differential support method based on asymmetric load evolution of claim 3, wherein, The coupled analysis of the displacement spatial gradient and the difference to obtain the comprehensive deformation identification factor includes: The comprehensive deformation recognition factor satisfies the following relationship: ， wherein, is a comprehensive deformation identification factor, is a weight coefficient of the displacement space gradient operator, is a modulus of the displacement space gradient, is a full-face maximum displacement gradient, is a weight coefficient of the curvature deviation, is a difference between the instantaneous curvature of the support structure after deformation and the initial design curvature, is the initial design curvature.

5. The method for identifying weak zones and providing differentiated support in tunnels based on asymmetric load evolution according to claim 1, characterized in that, The step of analyzing the geometry, stress, and energy state of the tunnel cross-section based on the pressure distribution data, the deformation data, and the continuous arc length coordinate system, and obtaining the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section, includes: Based on the pressure distribution data, the deformation data analysis, and the difference ratio of the resultant loads on both sides of the continuous arc length coordinate system; Based on the pressure distribution data and the deformation data, the bending moment and axial force at any point on the support section are obtained; The eccentricity at any point on the support section is obtained based on the bending moment and the axial force. The eccentricity is derived to obtain the eccentric compression coefficient at any point on the support section; The evaluation criteria for the degree of eccentricity are set with reference to the tunnel support structure and the tunnel bias characteristics. The eccentricity evaluation result at any point on the support section is obtained based on the eccentricity compression coefficient and the eccentricity evaluation conditions.

6. The method for identifying weak zones and providing differentiated support in tunnels based on asymmetric load evolution according to claim 5, characterized in that, The derivation of the eccentricity to obtain the eccentric compression coefficient at any point on the support section includes: The eccentricity satisfies the following relationship: ， in, For the support section at the location Eccentricity at the location, For the protection section at the position The bending moment caused by the asymmetric load at the point, For the support section at the location Axial force caused by load at the point; The eccentric compression coefficient satisfies the following relationship: ， in, The normalized eccentric compression coefficient, For the support section at the location Eccentricity at the location, For the thickness of the support structure, For the protection section at the position The bending moment caused by the asymmetric load at the point, For the support section at the location Axial force caused by load.

7. The method for identifying weak zones and providing differentiated support in tunnels based on asymmetric load evolution according to claim 1, characterized in that, The step of analyzing the geometry, stress, and energy state of the tunnel cross-section based on the pressure distribution data, the deformation data, and the continuous arc length coordinate system, and obtaining the geometric deformation analysis results, eccentricity evaluation results, and toughness judgment results at any point of the support section, includes: The energy release density of the surrounding rock is obtained based on the volumetric deformation after unloading and expansion of the surrounding rock, the pressure distribution data, the deformation data, and the continuous arc length coordinate system. Analysis of the ultimate resistance energy of the support structure based on the deformation-recoverable elastic energy storage and non-recoverable damage energy dissipation of the support structure; A toughness saturation index analysis function is established based on the energy release density of the surrounding rock and the ultimate resistance energy. The toughness saturation index at any point on the support section can be obtained through the toughness saturation index analysis function. The toughness saturation index at any point on the support section is graded to obtain the toughness judgment result at any point on the support section.

8. The method for identifying weak zones and providing differentiated support in tunnels based on asymmetric load evolution according to claim 7, characterized in that, The ultimate resistance energy of the support structure, based on the deformation-recoverable elastic energy storage and non-recoverable damage energy dissipation analysis of the support structure, includes: The ultimate resistance energy satisfies the following relationship: ， in, For the support structure in position Total ultimate resistance energy density at the location, For the support section at the location Elastic energy storage density at that location, For the support section at the location Damage energy density at the site For the protection section at the position The bending moment caused by the asymmetric load at the point, The elastic modulus of the material. For the moment of inertia, For the support section at the location Axial force caused by load at the point, The equivalent shear area of ​​the support section. The geometric distortion energy conversion coefficient, Let be the modulus of the spatial gradient of the displacement.

9. The method for identifying weak zones and providing differentiated support in tunnels based on asymmetric load evolution according to claim 1, characterized in that, The step of constructing a multi-index collaborative judgment model based on the geometric deformation analysis results, the eccentricity evaluation results, and the toughness judgment results, and generating a weighted index distribution map of the weak point of the tunnel section through the multi-index collaborative judgment model includes: Introduce a weakness-weighted index; Based on the aforementioned weakness weighted index and the multi-index collaborative judgment model, the geometric deformation analysis results, the eccentricity evaluation results, and the toughness judgment results are collaboratively characterized to generate a weakness weighted index distribution map of the tunnel section. The multi-indicator collaborative judgment model satisfies the following relationship: ， in, Location of tunnel cross section The stability state identifier at the location. The geometric distortion index. This is the critical threshold for geometric distortion. The coefficient for eccentric compression is... The toughness saturation index; The multi-indicator collaborative judgment model satisfies the following relationship: ， in, For the support structure in position The comprehensive weakness weighted index of the location, The weighting coefficient for the geometric deformation index. This is the normalized geometric distortion index. The weighting coefficients for the internal force redistribution index. This is the normalized eccentric compression coefficient. The weighting coefficients for energy dissipation indicators. This is the normalized toughness saturation index.

10. The method for identifying weak zones and providing differentiated support in tunnels based on asymmetric load evolution according to claim 1, characterized in that, The design of differentiated tunnel support decisions based on the geometric deformation analysis results, the eccentricity evaluation results, the toughness judgment results, and the weakness weighted index distribution map includes: Based on the geometric deformation analysis results and the weakness distribution diagram, make asymmetric anchorage decisions for geometric deformation design; Decisions on the variable cross-section stiffness of the large eccentric compression design are made based on the eccentricity evaluation results and the weakness distribution diagram. Based on the toughness assessment results and the weakness distribution map, a decision is made on designing an asymmetric buffer layer for energy risk. Differentiated tunnel support is achieved through the asymmetric anchoring decision, the variable cross-section stiffness decision, and the asymmetric buffer layer decision.

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