A method for calculating grading of shear failure of tunnel primary support structure

Abstract

This invention discloses a calculation method for the shear failure classification of tunnel initial support structures, including: establishing a mechanical model of the tunnel initial support structure based on thin-shell theory, and obtaining the deflection expression to derive the internal force expression; analyzing the influence of the strength parameters and structural parameters of the initial support structure on the internal forces; analyzing the internal force distribution law of the initial support structure at different cross-sections; based on the analysis results, establishing a shear failure criterion for the initial support structure based on the Mohr-Coulomb strength criterion and the static equilibrium condition at any point of the initial support shell structure; proposing the concept of initial support structure failure classification; a method for selecting support parameters based on the failure threshold; and using C language to develop a shear program for the failure of any micro-element inside the shell, realizing a visual display of the failure area and failure ratio of the initial support structure, and revealing the mechanism of shear failure of the initial support structure. This invention solves the problem of quantitatively analyzing the overall stability of tunnel initial support structures from a mechanical perspective and establishing a reasonable and objective strength criterion.

Description

Technical Field

[0001] This invention relates to the field of tunnel initial support technology, and in particular to a calculation method for the shear failure classification of tunnel initial support structure. Background Technology

[0002] The initial support of a tunnel is the primary load-bearing structure, and the effective coordination between the support structure, especially the initial support, and the surrounding rock during construction is crucial to the success of the project. Reasonable prediction of the stress and plastic zone distribution in the initial support is of great significance for tunnel stability evaluation and safe support structure design. A series of scientific studies have been conducted on the failure of the initial support structure using elastic strain softening models, elastic-brittle-plastic models, and ideal elastic-plastic models, and attempts to explore the mechanism of the interaction between the surrounding rock and the support have never ceased. Among these, the convergence constraint method has long been considered one of the authoritative methods for studying the relationship between the tunnel's surrounding rock and support and for conducting optimal design of the support structure.

[0003] The selection of initial support parameters for surrounding rock is another crucial issue in tunnel construction. Support structure design methods include analytical design, load-structure method, stratum-structure method, and empirical analogy method. Among these, the engineering analogy method, based on specifications and employing the New Austrian Tunneling Method (NATM), has made significant progress and is the main method for tunnel support design in China. Domestic and international experts and scholars have conducted extensive research on the mechanical behavior and failure safety criteria of tunnel support structures, yielding rich research results and providing many useful ideas and methods for future research on engineering blasting problems. However, the geometry of the initial tunnel support structure is approximately a flat shell structure. By using the plane strain assumption to approximate the flat shell structure as a circular ring or flat arch structure, the constraint effect of the steel arch frame is ignored, failing to accurately reflect the mechanical spatial characteristics of the initial support structure, resulting in certain errors in the analysis results. Furthermore, most stability evaluation methods for tunnel support systems are based on the deformation characteristics of the support, ignoring the stress characteristics of the tunnel and failing to establish clear failure criteria from a mechanical perspective, thus exhibiting strong subjectivity. Therefore, strength analysis and corresponding strength criteria play a crucial role in revealing the failure mechanism of the initial support structure. Further in-depth analysis is still needed on how to quantitatively analyze the overall stability of the initial support structure from a mechanical perspective and establish reasonable strength criteria. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] Based on the above problems, this invention provides a calculation method for the shear failure classification of the initial support structure of a tunnel, which solves the problem of quantitatively analyzing the overall stability of the initial support structure of a tunnel from a mechanical perspective, establishing a reasonable and objective strength criterion, and providing theoretical support for the internal force distribution law of different sections of the initial support of the tunnel and the shear failure mechanism of the initial support structure.

[0006] (II) Technical Solution

[0007] To address the aforementioned technical problems, this invention provides a method for calculating the shear failure classification of the initial support structure of a tunnel, comprising the following steps:

[0008] S1. Based on the thin shell theory, establish the mechanical model of the tunnel initial support structure and the deflection expression of the initial support structure at any point under uniform load, obtain the internal force expression, analyze the influence of the strength parameters and structural parameters of the initial support structure on the internal force, and analyze the internal force distribution law of the initial support structure at different sections.

[0009] S2. Based on the analysis results, a shear failure criterion for the initial support structure is established based on the Mohr-Coulomb strength criterion and the static equilibrium condition at any point of the initial support shell structure. The concept of failure classification of the initial support structure is proposed, and a method for selecting support parameters based on the failure threshold is proposed. A shear program for the failure of any micro-element inside the shell is developed using C language to realize the intuitive display of the failure area and failure ratio of the initial support structure, and to reveal the mechanism of shear failure of the initial support structure.

[0010] Furthermore, step S1 includes:

[0011] S11. Simplify the tunnel's initial support structure into a cylindrical flat shell, construct the shell's mechanical equilibrium differential equation, and the deflection expression of the initial support structure at any point under uniformly distributed load.

[0012] Let the dimensions of the adjacent steel arch be L, the circumferential dimension be S, and the dimensionless coordinates α and β describe the position. The differential equation of shell mechanical equilibrium in terms of displacement in the orthogonal curvilinear coordinate system of the initial support structure is:

[0013]

[0014] Assuming the initial supported structure is subjected only to a load Z perpendicular to its surface (i.e., X = Y = 0), introduce a displacement function Φ(α,β), and let...

[0015]

[0016] Assuming the radial pressure at different locations on the surface of the initial support structure is a constant value, i.e., f(ξ,η)=q, integrating over the entire region yields the expression for the deflection of the initial support structure at any point under a uniformly distributed load:

[0017]

[0018] In the formula,

[0019]

[0020] R and h are the radius and thickness of the initial support structure, respectively; E and μ are the elastic modulus (MPa) and Poisson's ratio of the initial support structure, respectively; X, Y, and Z are the three components of the external load acting on the initial support structure, respectively.

[0021] S12. Determine the internal force expression of the initial support structure based on the shell mechanical equilibrium differential equation and deflection expression, reflecting the relationship between the internal force of the initial support structure and the steel frame spacing and spray layer thickness of the initial support structure.

[0022] The internal force expressions for the initial support structure are as follows:

[0023]

[0024] Simplify to

[0025]

[0026] In the formula, N1 is the axial internal force of the initial support structure, N2 is the circumferential internal force of the initial support structure, and S is the tangential internal force inside the initial support structure; Solving for the result:

[0027]

[0028] S13. By calculating the combination of different steel frame spacing and spray layer thickness, the influence of the two on the initial support structure is obtained.

[0029] S14. Analyze the variation law of internal forces in different sections of the initial support structure.

[0030] Furthermore, the influence of the steel frame spacing and spray layer thickness on the initial support structure is as follows: the steel frame spacing and spray layer thickness have no effect on the tangential internal force of the initial support structure, and the influence on the circumferential internal force and axial internal force is similar, with the influence on the axial internal force being lower than that on the circumferential internal force.

[0031] Furthermore, the variation law of internal forces on different cross sections is as follows: the axial internal force and the circumferential internal force are both zero at the model boundary and the maximum value is at the middle position, while the tangential internal force is the maximum at the axial boundary and the minimum value is at the middle position.

[0032] Furthermore, step S2 includes the following steps:

[0033] S21. Based on the static equilibrium condition at any point in the initial support shell structure and the Mohr-Coulomb criterion, construct the shear failure criterion.

[0034] Consider a small element at any point (α, β) in the initially supported shell structure and perform a force analysis. The shear force S on any inclined section of this small element is... θ and normal force N θ This can be obtained from the static equilibrium condition:

[0035]

[0036] In the formula, S θ N θ These are the shear force and normal force on the inclined section, respectively;

[0037] The shear failure criterion is:

[0038] S θ ≥S T

[0039] in

[0040]

[0041] In the formula, C, These are the cohesion and internal friction angle of the initial support structure, respectively;

[0042] S22. A method for quantifying and classifying shear failure and selecting support parameters based on the failure threshold is used. A shear program for the failure of any micro-element inside the shell is developed using C language to achieve a visual display of the failure area and failure ratio of the initial support structure.

[0043] Furthermore, step S22 includes: dividing the initial support structure into small micro-elements along the axial direction and circumferential direction; determining whether each micro-element has undergone shear failure according to the shear failure criterion; if the micro-element has failed, filling the surface of the micro-element with different colors according to the magnitude of the shear force on the failure section; if the micro-element has not failed, filling its surface with gray, and the shear force value on the section is reflected by the brightness of the grayscale image.

[0044] The proportion of the damaged areas of different colors to the total initial support structure was counted separately. The maximum shear force value corresponding to all the damaged micro-elements was divided into four parts, which correspond to the four levels of damage. Level I is the area with the highest degree of damage, corresponding to the red area in the figure. Levels II, III and IV are the next level of damage, with Level II corresponding to the orange area, Level III to the yellow area and Level IV to the blue area.

[0045] This invention also discloses a calculation system for the shear failure classification of tunnel initial support structures based on shell theory, comprising: at least one processor and at least one memory communicatively connected to the processor, wherein: the memory stores program instructions executable by the processor, and the processor can execute the calculation method for the shear failure classification of tunnel initial support structures by calling the program instructions.

[0046] The present invention also discloses a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the calculation method for the shear failure classification of the tunnel initial support structure.

[0047] (III) Beneficial Effects

[0048] The above-described technical solution of the present invention has the following advantages:

[0049] (1) This invention establishes a mechanical model of the tunnel initial support structure reflecting deformation characteristics through thin shell theory, obtains the deformation and internal force expressions, analyzes the internal force distribution law, and then establishes a shear failure criterion for the initial support structure based on the Mohr-Coulomb strength criterion, and classifies the failure of the initial support structure accordingly. The support parameters are selected and optimized according to the failure threshold. The failure area and failure ratio of the initial support structure are displayed intuitively using C language. The overall stability of the tunnel initial support structure is analyzed from a mechanical perspective. A reasonable and objective strength criterion is established from a mechanical perspective. The failure area and failure ratio of the initial support structure are displayed intuitively through classification. This provides theoretical support for the internal force distribution law of different sections of the tunnel initial support and the shear failure mechanism of the initial support structure.

[0050] (2) The present invention can set the total failure ratio threshold according to the actual situation, and then select the corresponding initial support structure parameters according to the threshold. It can also combine different thresholds with the failure ratio of each level to make more accurate parameter selection. Furthermore, the intuitive display of the failure area and failure ratio of the graded and initial support structure strengthens the support, which is conducive to ensuring the safety and stability of the tunnel initial support structure. Attached Figure Description

[0051] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings:

[0052] Figure 1 This is a schematic diagram of the standard cross-sectional layout of a tunnel according to an embodiment of the present invention;

[0053] Figure 2 This is a schematic diagram of the initial support structure mechanical model according to an embodiment of the present invention;

[0054] Figure 3 This is a cross-sectional force diagram of the initial support structure according to an embodiment of the present invention;

[0055] Figure 4 This is a schematic diagram illustrating the influence of the steel frame spacing on the internal forces of the initial support structure according to an embodiment of the present invention.

[0056] Figure 5 This is a schematic diagram illustrating the influence of the spray layer thickness on the internal forces of the initial support structure according to an embodiment of the present invention.

[0057] Figure 6 This is a schematic diagram illustrating the variation of axial internal forces at different cross-sections in an embodiment of the present invention.

[0058] Figure 7 This is a schematic diagram illustrating the variation of circumferential internal forces at different cross-sections in an embodiment of the present invention.

[0059] Figure 8 This is a schematic diagram illustrating the variation of tangential internal forces at different cross-sections in an embodiment of the present invention.

[0060] Figure 9 This is a schematic diagram of the force analysis of the micro-element of the initial support structure according to an embodiment of the present invention;

[0061] Figure 10 This is a schematic diagram illustrating the maximum shear stress distribution of the initial support structure according to an embodiment of the present invention.

[0062] Figure 11 This is a schematic diagram of the failure classification of the initial support structure under different support parameters in an embodiment of the present invention (Class V surrounding rock);

[0063] Figure 12 This is a schematic diagram of the tunnel monitoring section layout according to an embodiment of the present invention;

[0064] Figure 13 This is a schematic diagram of the initial support pressure monitoring according to an embodiment of the present invention;

[0065] Figure 14 This is a schematic diagram comparing the theoretical and measured values ​​of the initial support structure deformation in an embodiment of the present invention. Detailed Implementation

[0066] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0067] This invention provides a calculation method for the shear failure classification of the initial support structure of a tunnel. A mechanical model of the initial support structure is established using thin-shell theory to obtain expressions for deformation and internal forces. Subsequently, based on the Mohr-Coulomb strength criterion, a shear failure criterion for the initial support structure is established, and the concept of initial support structure failure classification is proposed. The failure area and failure ratio of the initial support structure are displayed intuitively using C language, revealing the mechanism of shear failure in the initial support structure. This embodiment takes the Dongmachang No. 1 Tunnel on the Huali Expressway as an example, selecting a standard cross-section outside the influence range of the Chenghai-Binchuan active fault for deformation and stress analysis. The tunnel is 5205m long, located west of Yongsheng County, Lijiang City, Yunnan Province, east of Chenghai Lake, with a relatively steep terrain slope. The tunnel site belongs to a tectonic erosion block high mountain landform, with the main strata consisting of mudstone, silty mudstone, sandstone, quartz sandstone, conglomerate, limestone, and dolomitic limestone, mainly classified as Class III to V. The design follows the New Austrian Tunneling Method (NATM) and adopts the engineering analogy method, using a composite lining support type.

[0068] The calculation method for the shear failure classification of the tunnel's initial support structure includes the following steps:

[0069] S1. Based on the thin shell theory, establish the mechanical model of the tunnel initial support structure and the deflection expression of the initial support structure at any point under uniform load, obtain the internal force expression, analyze the influence of the strength parameters and structural parameters of the initial support structure on the internal force, and analyze the internal force distribution law of the initial support structure at different sections.

[0070] S11. Simplify the tunnel's initial support structure into a cylindrical flat shell, construct the shell's mechanical equilibrium differential equation, and the deflection expression of the initial support structure at any point under uniformly distributed load.

[0071] The initial support structure of the tunnel is simplified into a cylindrical flat shell, such as... Figure 1 As shown, taking two adjacent steel frames and the shotcrete layer in between as the research object, let the size of the adjacent steel arch be L, the circumferential dimension be S, and the dimensionless coordinates α, β describing the position be as follows: Figure 2 As shown, the differential equation of shell mechanical equilibrium in terms of displacement in the orthogonal curvilinear coordinate system of the initial support structure is:

[0072]

[0073] Assuming the initial supported structure is subjected only to a load Z perpendicular to its surface (i.e., X = Y = 0), introduce a displacement function Φ(α,β), and let...

[0074]

[0075] Assuming the radial pressure at different locations on the surface of the initial support structure is a constant value, i.e., f(ξ,η)=q, integrating over the entire region yields the expression for the deflection of the initial support structure at any point under a uniformly distributed load:

[0076]

[0077] In the formula,

[0078]

[0079] R and h represent the radius and thickness of the initial support structure, respectively; E and μ represent the elastic modulus (MPa) and Poisson's ratio of the initial support structure, respectively; X, Y, and Z represent the three components of the external load acting on the initial support structure, respectively.

[0080] S12. Determine the internal force expression of the initial support structure based on the shell mechanical equilibrium differential equation and deflection expression, reflecting the relationship between the internal force of the initial support structure and the steel frame spacing and spray layer thickness of the initial support structure.

[0081] Substituting the deflection expressions (3) and (4) of the initial support structure into the geometric and physical equations, the stress expression within the initial support structure can be determined. Then, based on the synthesis of the normal internal forces N1, N2 and the shear force S, the internal force expression of the initial support structure is obtained as follows:

[0082]

[0083] Based on the relationship between the displacement function Φ(α,β) and the displacements u,v,w in equation (2), the above equation can be further simplified to:

[0084]

[0085] In the formula, N1 is the axial internal force of the initial support structure, N2 is the circumferential internal force of the initial support structure, and S is the tangential internal force inside the initial support structure.

[0086] Substituting the displacement function in expression (4) into equation (6), we obtain the expressions for the normal internal forces (N1, N2) and tangential internal forces (S) of the initial support structure:

[0087]

[0088] Equation (7) reflects the relationship between the internal forces of the initial support structure and the steel frame spacing and spray layer thickness of the initial support structure. By calculating different combinations of steel frame spacing and spray layer thickness, the influence of the two on the initial support structure can be obtained.

[0089] S13. By calculating the combination of different steel frame spacing and spray layer thickness, the influence of the two on the initial support structure is obtained.

[0090] Figure 4 The influence of the spacing of the steel frame on the internal forces of the initial support structure shows that the tangential internal force is always zero at the midpoint of the initial support structure. The circumferential and axial internal forces exhibit the same trend, showing an increasing rate of change as the steel frame spacing increases, but the axial internal force increases less with the steel frame spacing. When the steel frame spacing increases from 60cm to 100cm, the circumferential internal force increases exponentially, but the increment is small; when it exceeds 120cm, the circumferential internal force of the initial support structure begins to increase rapidly.

[0091] Figure 5 The study reflects the influence of spray coating thickness on the internal forces of the initial support structure. It shows that the spray coating thickness has no effect on the tangential internal force. The influence on the circumferential and axial internal forces follows the same pattern, exhibiting a decreasing trend with a gradually decreasing rate of change. However, the axial internal force decreases slightly with increasing spray coating thickness. When the spray coating thickness decreases to below 20 cm, the circumferential internal force of the initial support increases rapidly, which will lead to cracking or even failure of the initial support structure.

[0092] In summary, the spacing between the steel frames and the thickness of the spray layer have no effect on the tangential internal force of the initial support structure, but have the same effect on the circumferential and axial internal forces, with the axial internal force remaining at a relatively low level. As can be seen from equation (7), the coefficient part of the circumferential stress expression does not include the structural parameter λ, and λ = L / S. Since L is much smaller than S, the circumferential internal force is much greater than the axial internal force. Because the circumferential and axial internal forces gradually increase with the spacing between the steel frames, it indicates that establishing a plane strain model to analyze the internal forces of the initial support structure has limitations.

[0093] S14. Analyze the variation law of internal forces in different sections of the initial support structure;

[0094] Figures 6 to 8 This reflects the variation of internal forces on different cross sections and axial sections. From Figure 6 It can be seen that the axial internal forces at different cross-sections are symmetrically distributed, with the largest values ​​at the middle position. At the boundary (β=0°), the axial stress is zero. As the cross-section moves towards the middle position, the axial internal force shows a trend of first increasing and then decreasing. The axial internal force reaches its peak at β=40°, and then the direction of the internal force changes at β=80°, gradually increasing towards the center line of the shell. The distribution trend of the axial internal force is consistent across different cross-sections. The internal force is zero at the axial boundary, increases rapidly towards the tunnel center, and the peak value is larger closer to the axial center line, but the growth rate gradually decreases, then rapidly decreases to near zero, and fluctuates around zero.

[0095] Figure 7 This describes the variation trend of circumferential internal forces at different axial and cross-sectional sections. The values ​​of these internal forces are significantly higher than those of the axial internal forces, consistent with previous conclusions. At different axial sections, the circumferential internal forces exhibit a parabolic distribution, symmetrically along the axial centerline, with minimal variation in force values ​​between different sections, and the direction of the internal forces remains unchanged. At different cross-sections, the circumferential internal forces are zero at the axial boundaries, then rapidly increase, fluctuating around a certain value. The closer to the axial centerline, the larger the peak value of the circumferential internal forces, but the rate of increase gradually decreases, reaching its maximum at the centerline.

[0096] Figure 8 The data reflects the changing trends of tangential internal forces at different axial sections and cross sections, with overall values ​​being relatively small. At different axial sections, stress directions change, with the inflection point located at the axial centerline. At different cross sections, the tangential internal forces reach their peak at the two arch abutments and exhibit an anti-symmetrical distribution. The tangential internal forces at the arch abutments are greater than those at the axial centerline, decreasing to zero at the centerline. Since the tangential internal forces at the boundaries are significantly higher than at other locations, it indicates that the arch abutment support should be strengthened during construction to prevent shear failure of the initial support structure at the arch abutments.

[0097] In summary, the above analysis shows that both axial and circumferential internal forces are zero at the model boundaries, but are relatively large in the middle. The tangential internal force is largest at the axial boundaries and relatively small in the middle. The tangential internal force is the resultant of shear stress along the shell thickness direction, with high tangential internal forces appearing at the arch foot, consistent with existing research. The variation trend of internal forces at different cross-sections cannot be obtained using commonly used plane strain models. Our results also indicate that the axial and circumferential internal forces are largest at the axis centerline; neglecting this factor makes it difficult to reveal the deformation and failure mechanism of the initial support structure.

[0098] S2. Based on the analysis results, a shear failure criterion for the initial support structure is established based on the Mohr-Coulomb strength criterion and the static equilibrium condition at any point of the initial support shell structure. The concept of failure classification of the initial support structure is proposed, and a method for selecting support parameters based on the failure threshold is proposed. A shear program for the failure of any micro-element inside the shell is developed using C language to realize the intuitive display of the failure area and failure ratio of the initial support structure, and to reveal the mechanism of shear failure of the initial support structure.

[0099] S21. Based on the static equilibrium condition at any point in the initial support shell structure and the Mohr-Coulomb criterion, construct the shear failure criterion.

[0100] Perform a force analysis on a small element at any point (α, β) in the initial support shell structure, such as... Figure 9 As shown, the shear force S on any inclined section of this infinitesimal element is... θ and normal force N θ This can be obtained from the static equilibrium condition:

[0101]

[0102] In the formula, S θ N θ These are the shear force and normal force on the inclined section, respectively.

[0103] The initially supported structure is subjected to external surrounding rock pressure, and the failure mode is compression-shear. According to the Mohr-Coulomb criterion, when the initially supported structure fails in shear, the internal shear force must overcome not only the cohesion of the rock but also the normal internal force N. θ The additional shear force generated. In this paper, the shear force generated by cohesion and the shear force generated by normal internal forces are collectively referred to as shear force, denoted as S. T Then the shear failure criterion at any point of the initial support structure can be expressed as:

[0104] S θ ≥S T (9)

[0105] in

[0106]

[0107] In the formula, C, These represent the cohesion and internal friction angle of the initial support structure, respectively.

[0108] According to the theoretical calculation results of equation (8), the shear stress of the inclined section of the infinitesimal element is related to the azimuth angle of the section. The results are obtained by using a C language program. Figure 10 The maximum shear stress distribution pattern in the entire initial-support shell structure is shown, with units of (S). θ / Pa).

[0109] from Figure 10 It can be seen that in the entire initial support shell structure, the maximum shear stress is mainly distributed symmetrically at the arch feet on both sides. The area with the highest concentration of shear stress is at the steel frame support location at the model boundary, where the maximum shear stress can reach 1.6 MPa, which is a dangerous location for shear failure. Near the arch crown, the shear stress is almost zero, and there is no risk of shear failure and instability. There is a low shear stress zone in the initial support structure between the steel frames. When strengthening the arch foot support, the focus should be on using anchor bolts at the steel frame to enhance its shear resistance and ensure the stability of the shell structure.

[0110] S22. A method for quantitatively classifying shear failure and selecting support parameters based on the failure threshold is used. A shear program for the failure of any micro-element inside the shell is developed using C language to achieve a visual display of the failure area and failure ratio of the initial support structure.

[0111] The ratio of the number of micro-elements that undergo shear failure to the total number of micro-elements is defined as the failure ratio of the initial support structure. To quantitatively study the failure ratio of the initial support structure under different support parameters, a program was developed in C language to study the failure state of any micro-element within the initial support structure. The initial support structure is divided into small micro-elements along the axial and circumferential directions. Shear failure criteria are used to determine whether each micro-element undergoes shear failure. If a micro-element fails, its surface is filled with a different color according to the magnitude of the shear force at the failure section; if the micro-element does not fail, its surface is filled with gray, and the shear force value at the section is reflected by the brightness of the grayscale image.

[0112] The proportion of damaged areas of different colors relative to the total initial support structure was statistically analyzed to achieve a quantitative classification of the initial support structure's failure. The maximum shear force values ​​corresponding to all failed micro-elements were divided into four parts, each corresponding to one of the four failure levels. Level I represents the highest degree of damage, corresponding to the red area in the diagram. Levels II, III, and IV represent the next highest degrees of damage, with Level II corresponding to the orange area, Level III to the yellow area, and Level IV to the blue area. Figure 11 As shown.

[0113] In engineering applications, the total failure ratio threshold can be set according to the actual situation, and then the corresponding initial support structure parameters can be selected based on the threshold; alternatively, different thresholds can be set in combination with the failure ratios at each level to achieve more precise parameter selection.

[0114] The failure analysis of the initial support structure is as follows:

[0115] The initial support structure is divided into 160×270 small micro-elements. Figure 11 The failure classification of the initial support structure in Class V surrounding rock under different support parameters is presented. It can be seen that the failure area of ​​the initial support structure exhibits a symmetrical pattern, with the most severe damage concentrated at the arch foot. The initial support structure with a steel frame spacing of 80cm and a shotcrete thickness of 15cm shows a significantly larger failure area and degree of damage than the initial support structure with a shotcrete thickness of 20cm. When the shotcrete thickness is 20cm, as the steel frame spacing increases (90cm, 100cm), the failure area of ​​the initial support structure does not increase significantly, but the degree of damage increases considerably. Table 1 shows the failure ratios of each level of the initial support structure under different support parameters.

[0116] Table 1. Failure rates of each stage of the initial support structure under different support parameters.

[0117]

[0118]

[0119] Note: The failure ratio was calculated based on confining pressure q = 1 MPa, the initial support structure's C25 concrete cohesion C = 2.58 MPa, and the internal friction angle...

[0120] The overall failure pattern is that the failure ratios at each level and the total failure ratio increase with increasing steel frame spacing and decrease with increasing spray coating thickness. When the steel frame spacing is 60cm, the total failure ratio of the support structure does not exceed 10% when the spray coating thickness varies from 15 to 30cm. When the spacing is 70cm and the spray coating thickness is 15cm, the total failure ratio of the initial support structure exceeds 10%. If 10% is taken as the threshold for the total failure ratio, Table 1 shows that the critical spray coating thicknesses for the total failure ratio of the initial support structure not exceeding the threshold are 20cm, 25cm, 30cm, and 30cm, respectively, when the steel frame spacing is 80cm, 90cm, 100cm, and 110cm. When the steel frame spacing exceeds 120cm, even with a spray coating thickness of 30cm, the corresponding failure ratio of the initial support structure exceeds 10%.

[0121] The theoretical and measured values ​​are verified below:

[0122] During tunnel construction, monitoring was conducted on the Class V surrounding rock section (chainage ZK71+050) and the Class IV surrounding rock section (chainage ZK75+210), which are outside the influence of the F4 fault. Theoretical and measured values ​​were compared. Initial support pressure was monitored using a double-diaphragm pressure cell; the cross-sectional layout is shown in [reference needed]. Figure 12 The initial support pressure monitoring points and measured values ​​are as follows: Figure 13 As shown in Table 2, Figure 13 The left figure in the diagram is a schematic diagram of the arrangement of the initial support pressure monitoring points. Figure 13 The right figure shows the monitoring value of the initial support pressure at section ZK71+050.

[0123] Table 2. Monitoring data of initial support pressure at sections ZK71+050 and ZK75+210

[0124]

[0125] When determining the support parameters, the total failure rate threshold of the initial support structure was set to 10%. During the design phase, the appropriate shotcrete thickness was selected based on the steel frame spacing to ensure that the failure rate corresponding to the optimal support structure was less than the set threshold. Monitoring section ZK71+050 is located in a Class V surrounding rock section, with a tunnel excavation radius of 6.7m, a steel frame spacing of 80cm, and a shotcrete thickness of 25cm. Monitoring section ZK75+210 is located in a Class IV surrounding rock section, with a tunnel excavation radius of 6.5m, a steel frame spacing of 80cm, and a shotcrete thickness of 22cm.

[0126] According to the deformation calculation formula (Equation 5), the theoretical deformation values ​​of the initial support structure under different support parameters can be calculated. Figure 14 The pressure values ​​in the theoretical calculations were taken as the average of seven monitoring points on the monitoring section. The average surrounding rock pressure for Class IV confining pressure was 0.817 MPa, and for Class V confining rock it was 1.251 MPa. A comparison between the theoretical and measured values ​​shows that, except for the significant difference in deformation values ​​between the two sides of the cross-section, the values ​​at other points are basically consistent. This indicates that the initial support structure model established in this paper based on the thin shell structure can basically reflect the deformation characteristics of the initial support structure.

[0127] Finally, it should be noted that the above calculation method can be converted into software program instructions. This can be implemented using a computing system including a processor and memory, or using computer instructions stored in a non-transitory computer-readable storage medium. The integrated unit implemented as a software functional unit can be stored in a computer-readable storage medium. This software functional unit, stored in a storage medium, includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0128] In summary, the above-mentioned calculation method for the shear failure classification of tunnel initial support structures has the following beneficial effects: This invention establishes a mechanical model of the tunnel initial support structure reflecting deformation characteristics through thin-shell theory, obtains the expressions for deformation and internal forces, analyzes the distribution law of internal forces, and then establishes a shear failure criterion for the initial support structure based on the Mohr-Coulomb strength criterion, and classifies the failure of the initial support structure accordingly. Support parameters are selected and optimized based on the failure threshold, and the failure area and failure ratio of the initial support structure are displayed intuitively using C language. The overall stability of the tunnel initial support structure is analyzed from a mechanical perspective, a reasonable and objective strength criterion is established from a mechanical perspective, and the classification and the failure area and failure ratio of the initial support structure are displayed intuitively, providing theoretical support for the distribution law of internal forces at different sections of the tunnel initial support and the shear failure mechanism of the initial support structure.

[0129] 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 it; although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A calculation method for the shear failure classification of the initial support structure of a tunnel, characterized in that, Includes the following steps: S1. Based on the thin shell theory, establish the mechanical model of the tunnel initial support structure and the deflection expression of the initial support structure at any point under uniform load, obtain the internal force expression, analyze the influence of the strength parameters and structural parameters of the initial support structure on the internal force, and analyze the internal force distribution law of the initial support structure at different sections. S2. Based on the analysis results, a shear failure criterion for the initial support structure is established based on the Mohr-Coulomb strength criterion and the static equilibrium condition at any point of the initial support shell structure. The concept of failure classification of the initial support structure is proposed, and a method for selecting support parameters based on the failure threshold is proposed. A shear program for the failure of any micro-element inside the shell is developed using C language to realize the intuitive display of the failure area and failure ratio of the initial support structure, and to reveal the mechanism of shear failure of the initial support structure. Step S2 includes the following steps: S21. Based on the static equilibrium condition at any point in the initial support shell structure and the Mohr-Coulomb criterion, construct the shear failure criterion. Consider a small element at any point (α, β) in the initially supported shell structure and perform a force analysis. The shear force S on any inclined section of this small element is... θ and normal force N θ This can be obtained from the static equilibrium condition: In the formula, N1 is the axial internal force of the initial support structure, N2 is the circumferential internal force of the initial support structure, and S... θ N θ These are the shear force and normal force on the inclined section, respectively; The shear failure criterion is: S θ ≥S T in In the formula, , respectively, represent the cohesion and internal friction angle of the initial support structure, and h is the thickness of the initial support structure; S22. A method for quantitatively classifying shear failure and selecting support parameters based on the failure threshold is used. A shear program for the failure of any micro-element inside the shell is developed using C language to achieve a visual display of the failure area and failure ratio of the initial support structure. Step S22 includes: dividing the initial support structure into small micro-elements along the axial direction and circumferential direction; determining whether each micro-element has undergone shear failure according to the shear failure criterion; if the micro-element has failed, filling the surface of the micro-element with different colors according to the magnitude of the shear force on the failure section; if the micro-element has not failed, filling its surface with gray, and the shear force value on the section is reflected by the brightness of the grayscale image. The proportion of the damaged areas of different colors to the total initial support structure was counted separately. The maximum shear force value corresponding to all the damaged micro-elements was divided into four parts, which correspond to the four levels of damage. Level I is the area with the highest degree of damage, corresponding to the red area in the figure. Levels II, III and IV are the next level of damage, with Level II corresponding to the orange area, Level III to the yellow area and Level IV to the blue area.

2. The calculation method for the shear failure classification of the initial support structure of a tunnel according to claim 1, characterized in that, Step S1 includes: S11. Simplify the tunnel's initial support structure into a cylindrical flat shell, construct the shell's mechanical equilibrium differential equation, and the deflection expression of the initial support structure at any point under uniformly distributed load. Let the dimensions of the adjacent steel arch be L, the circumferential dimension be S, and the dimensionless coordinates α and β describe the position. The differential equation of shell mechanical equilibrium in terms of displacement in the orthogonal curvilinear coordinate system of the initial support structure is: Assuming the initial supported structure is subjected only to a load Z perpendicular to its surface, i.e., X = Y = 0, introduce a displacement function Φ(α,β), and let... Assuming the radial pressure at different locations on the surface of the initial support structure is a constant value, i.e., f(ξ,η)=q, integrating over the entire region yields the expression for the deflection of the initial support structure at any point under a uniformly distributed load: In the formula, R and h are the radius and thickness of the initial support structure, respectively; E and μ are the elastic modulus and Poisson's ratio of the initial support structure, respectively; X, Y, and Z are the three components of the external load acting on the initial support structure, respectively. S12. Determine the internal force expression of the initial support structure based on the shell mechanical equilibrium differential equation and deflection expression, reflecting the relationship between the internal force of the initial support structure and the steel frame spacing and spray layer thickness of the initial support structure. The internal force expressions for the initial support structure are as follows: Simplify to In the formula, N1 is the axial internal force of the initial support structure, N2 is the circumferential internal force of the initial support structure, and S is the tangential internal force inside the initial support structure; Solving for the result: S13. By calculating the combination of different steel frame spacing and spray layer thickness, the influence of the two on the initial support structure is obtained. S14. Analyze the variation law of internal forces in different sections of the initial support structure.

3. The calculation method for the shear failure classification of the initial support structure of a tunnel according to claim 2, characterized in that, The influence of the steel frame spacing and spray layer thickness on the initial support structure is as follows: the steel frame spacing and spray layer thickness have no effect on the tangential internal force of the initial support structure, and the influence on the circumferential internal force and axial internal force has the same trend, with the influence on the axial internal force being lower than that on the circumferential internal force.

4. The calculation method for the shear failure classification of the initial support structure of a tunnel according to claim 3, characterized in that, The variation law of internal forces on different cross sections is as follows: the axial internal force and the circumferential internal force are both zero at the model boundary and the value is the largest at the middle position, while the tangential internal force is the largest at the axial boundary and the value is the smallest at the middle position.

5. A calculation system for the shear failure classification of tunnel initial support structures based on shell theory, characterized in that, include: At least one processor and at least one memory communicatively connected to the processor, wherein: the memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the calculation method for shear failure grading of tunnel initial support structure as described in any one of claims 1-4.

6. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to execute the calculation method for the shear failure classification of the tunnel initial support structure as described in any one of claims 1-4.

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