A method for analyzing anchoring reliability of a stage locking foot anchor rod in a tunnel initial support stage

Abstract

This application provides a method for analyzing the anchorage reliability of anchor bolts in the initial support stage of tunnels. The first stage does not specifically simulate the complex contact relationship between the surrounding rock, anchor bolts, and initial support. Instead, it applies constraints at the connection between the initial support and the anchor bolts to achieve a cooperative force-bearing effect. Then, a load-structure model of the initial support structure is established using numerical simulation or analytical methods. The mechanical response of the initial support structure is calculated by applying surrounding rock loads, ultimately obtaining the bending moment, shear force, and axial force at the top of the anchor bolts for reliability assessment. The second stage involves a refined model of the anchor bolt-surrounding rock system, describing the complex contact relationship between the surrounding rock and the anchor bolts. The forces calculated in the first stage are then applied to the top of the anchor bolts in the refined model. The calculation and analysis determine whether the anchor bolt-surrounding rock system will fail, thereby assessing the anchorage reliability of the anchor bolts in the initial support stage of the tunnel.

Description

Technical Field

[0001] This application relates to the field of tunnel engineering technology, and more specifically, to a method for analyzing the anchorage reliability of anchor bolts in the initial support stage of a tunnel. Background Technology

[0002] In the initial stage of tunnel excavation, before the tunnel structure is fully closed, a support system consisting of anchor bolts, auxiliary steel frames, and shotcrete is required to bear the load and prevent instability and failure of the initial support, which could lead to safety accidents. Against this backdrop, the anchoring reliability of anchor bolts under different geological conditions is crucial for the smooth implementation of tunnel engineering and requires close attention from engineering technicians. However, compared to the tunnel lining and surrounding rock system, the geometric dimensions of anchor bolts are extremely small. Currently, accurate analysis of their anchoring reliability requires the construction of complex numerical calculation models with a large number of degrees of freedom. This not only presents significant modeling difficulties but also results in excessively long calculation times. Furthermore, the accuracy of the simulation is difficult to guarantee, failing to effectively reflect the support function of the anchor bolts. Due to these limitations, the design of anchor bolts often adopts engineering analogy methods, making it difficult to guarantee design accuracy. This can lead to overly conservative anchor bolt designs in some projects, while others suffer from insufficient safety redundancy. Summary of the Invention

[0003] The purpose of this application is to provide a method for analyzing the anchorage reliability of anchor bolts in the initial support stage of tunnels, in order to solve the problems of difficult modeling and low accuracy in existing schemes.

[0004] This application provides a method for analyzing the anchoring reliability of anchor bolts in the initial support stage of a tunnel, including: Establish the initial lining unit and apply constraints to the connection between the initial lining unit and the anchor bolt to form a load structure model; Apply surrounding rock loads to the load-structure model to obtain bending moment, shear force, and axial force at the connection. Establish a detailed model of the anchor bolts and surrounding rock; The bending moment, shear force, and axial force at the connection are converted into the cross-sectional stress distribution at the top of the anchor rod; Based on the stress distribution in the cross section, a stress load is applied to the top of the anchor bolt in the refined model to obtain the anchor bolt stress and the stress in the surrounding rock. The anchoring reliability is analyzed based on the stress of the anchor bolt and the stress in the surrounding rock.

[0005] In the above technical solution, a phased analysis mode is adopted for the anchorage reliability of the anchor bolts in the initial support stage of the tunnel. The specific implementation process is as follows: In the first stage, the complex contact relationship between the surrounding rock, the anchor bolts, and the initial support is not specifically simulated. Instead, constraints are applied at the connection between the initial support and the anchor bolts to achieve the effect of cooperating with the initial support in bearing the force. Then, a load structure model of the initial support structure is established using numerical simulation or analytical methods. The mechanical response of the initial support structure is calculated by applying the surrounding rock load, and finally, the bending moment, shear force, and axial force at the top of the anchor bolts that need to be evaluated for reliability are obtained. In the second stage, the anchor bolt-surrounding rock system is finely modeled to accurately replicate the complex contact relationship between the surrounding rock and the anchor bolts. Then, the internal forces calculated in the first stage are converted into corresponding stresses and applied to the top of the anchor bolts in the fine model. The anchor bolt-surrounding rock system is analyzed to determine whether failure will occur, thereby determining the anchorage reliability of the anchor bolts in the initial support stage of the tunnel. Meanwhile, this method can realize the mechanical response calculation of the anchor bolts throughout the entire tunnel construction process after the anchor bolts are installed, thereby guiding the reasonable selection of anchor bolt design parameters.

[0006] Compared with the traditional engineering analogy method, this solution can more accurately analyze the anchoring reliability of anchor bolts under different surrounding rock conditions and different design parameters, reducing the waste of resources caused by overly conservative anchor bolt design or the risk of safety hazards caused by overly aggressive design.

[0007] Compared to traditional complex numerical modeling and analysis methods, this approach significantly reduces the analysis difficulty by decomposing the core problem into two sub-problems for step-by-step solution. It avoids the challenges of multi-scale modeling with large differences in the scale of substructures or subsystems, as well as complex contact modeling problems. Furthermore, the first sub-problem can be solved using numerical methods such as the finite element method or analytical methods; the second sub-problem can focus on the anchor bolt body and its surrounding small-scale rock mass, greatly reducing the scale of detailed modeling and adapting to the entire construction process after the anchor bolt installation, making the modeling of complex contact relationships easier to advance.

[0008] In some alternative implementations, a preliminary lining unit is established, and constraints are applied to the connection between the preliminary lining unit and the anchor bolt to form a load structure model, including: using beams to simulate the preliminary lining unit composed of a steel frame and shotcrete; simulating the anchor bolt by applying constraints to the connection between the preliminary lining unit and the anchor bolt; simulating the elastic resistance of the surrounding rock to the preliminary lining unit using springs that are only under compression and not tension; and simulating the supporting effect of the tunnel foundation on the cross-section of the preliminary lining when the initial support is not closed using springs that are only under compression and not tension.

[0009] In the above technical solution, beam elements are used to simulate the initial lining unit composed of steel frame and shotcrete, and finite-length piles are used to simulate anchor bolts. Both are conventional and simplified element types used in engineering, eliminating the need to construct complex solid models. At the same time, various springs are used to simulate the constraint and support of surrounding rock and foundation, avoiding the detailed depiction of the complex contact relationship between surrounding rock, initial lining and anchor bolts. This effectively reduces the degree of freedom of the model, lowers the modeling difficulty and calculation time, and meets the needs of rapid modeling and efficient analysis in the initial support stage.

[0010] In some optional implementations, a preliminary lining unit is established, and constraints are applied to the connection between the preliminary lining unit and the anchor bolt to form a load structure model, including: selecting the surrounding rock load, tunnel physical and mechanical parameters, and anchor bolt physical and mechanical parameters according to the actual engineering situation, and establishing a load structure model.

[0011] In some alternative implementations, the surrounding rock load is calculated by the surrounding rock classification according to the response specification.

[0012] In some alternative implementations, a refined model of the anchor bolt and the surrounding rock is established, including: using finite-length pile elements to simulate the anchor bolt, treating the anchor bolt as an elastic structure, and using a Mohr-Coulomb or Hoek-Brown elastoplastic model for the surrounding rock.

[0013] In some alternative implementations, a refined model of the anchor bolt and the surrounding rock is established, including: describing the mechanical response of the anchor bolt embedded in the surrounding rock formation by means of transverse and axial foundation springs distributed along the anchor bolt axis and axial foundation springs located at the lower end of the anchor bolt that are only compressed.

[0014] In some alternative implementations, the bending moment, shear force, and axial force at the connection are converted into the cross-sectional stress distribution at the top of the anchor bolt, including: calculating the cross-sectional stress distribution using material mechanics formulas based on the bending moment, shear force, and axial force at the connection.

[0015] Specifically, the construction of a detailed model of the anchor bolt and the surrounding rock includes: In this model, the anchor bolt is considered a finite-length micropile with both axial and lateral bearing capacity. To accurately describe the mechanical response of the anchor bolt embedded in the surrounding rock strata, three types of ground springs are introduced into the model: lateral and axial ground springs distributed along the anchor bolt axis (with stiffnesses of [missing information] respectively). k y and k x ) and the axial foundation spring (stiffness of ) located at the lower end of the anchor bolt and subjected only to compression. k xb ).

[0016] Due to the lateral force R y and bending momentR φ The mechanical behavior of a finite-length anchor bolt is similar to that of an elastic foundation beam subjected to lateral forces, and its lateral deformation governing equation can be expressed as:

[0017] In the formula, U y This refers to the lateral displacement of the anchor bolt. EI b The bending stiffness of the anchor bolt section is contributed by the anchor bolt body and the surrounding grouting body, and its calculation formula is as follows: .

[0018] in, E s and E g These are the elastic moduli of the steel pipe and the grouting material, respectively. k y The transverse foundation spring stiffness per unit length along the anchor bolt axis can be expressed as: k y = KD ,in K The elastic resistance coefficient of the surrounding rock; D , d , t b These are the borehole diameter, anchor bolt diameter, and steel pipe wall thickness, respectively.

[0019] The general solution of equation (1) can be expressed as:

[0020] In the formula, C 1 C 4 is an undetermined coefficient that needs to be determined through boundary conditions; and The root of the characteristic equation of equation (2) is given by , where i It is the imaginary unit.

[0021] Meanwhile, the external force boundary conditions at both ends of the anchor bolt are:

[0022] In the formula, M and Q The bending moment and shear force of the anchor bolt are respectively, which can be further expressed by its lateral displacement as follows:

[0023] By combining equations (2) to (4), we can obtain:

[0024] In the formula, F=[ R φ , R y , 0, 0] T C represents the lateral external force vector at both ends of the anchor bolt; C 1, C 2, C 3, C 4] T S is the vector of undetermined coefficients; S is the relationship matrix between the transverse external force vector F and the vector of undetermined coefficients C, specifically in the form of: .

[0025] On the other hand, the displacement boundary conditions at both ends of the anchor bolt satisfy the following equation:

[0026] In the formula, u y and u φ These represent the lateral displacement and rotation angle of the upper end of the anchor bolt, respectively. and These represent the lateral displacement and rotation angle of the lower end of the anchor bolt, respectively.

[0027] Substituting equation (2) into equation (6) and rewriting the result in matrix form, we can further obtain the following equation:

[0028] In the formula, U=[ u φ , u y , u φ-end , u y-end ] T It is a vector consisting of the lateral displacement and rotation angle at both ends of the anchor bolt; .

[0029] By combining equations (5) and (7) to eliminate the undetermined coefficient vector C, the relationship between the external force F and the displacement U can be obtained as follows:

[0030] In the formula, K h =SB 1 This is the correlation stiffness matrix between the lateral force and the lateral displacement at the end of a finite-length anchor bolt.

[0031] Rewriting equation (8) in block matrix form and expanding it, we get:

[0032] In the formula, F1=[ R φ , R y ] T And F2=[0, 0] T These are the external load vectors at the upper and lower ends of the anchor bolt, respectively; U1=[ u φ , uy ] T and U2=[ u φ-end , u y-end ] T These are the displacement vectors of the upper and lower ends of the anchor bolt, respectively. This is a block matrix with a corresponding dimension of 2×2.

[0033] According to equation (10), U2 can be obtained as follows:

[0034] Substituting equation (3-15) into equation (3-13), F1 can be further expressed as:

[0035] In the formula, Let be the lateral stiffness matrix of a finite-length anchor bolt.

[0036] Subsequently, the focus was placed on the axial force at the upper end of the finite-length anchor bolt. R x Axial response under load. Based on the mechanical mechanism of axial force on a pile, the governing equation for the axial deformation of the anchor bolt can be expressed as:

[0037] In the formula, U x This refers to the axial displacement of the anchor bolt. EA b The compressive stiffness of the anchor bolt is calculated using the following formula: , k x The axial foundation spring stiffness per unit length along the anchor bolt axis can be expressed as: k x =(2π / 3 + 4π / 3) χ ) G

[38] ,in G The shear modulus of the surrounding rock. χ ( χ ≥3) is a coefficient characterizing the size of the disturbed rock mass region.

[0038] Based on equation (13), the axial displacement of the anchor bolt can be further expressed as:

[0039] In the formula, D 1 and D 2 is an undetermined coefficient that needs to be determined through boundary conditions; It is the root of the characteristic equation of equation (14).

[0040] Furthermore, the axial force of the anchor bolt is the first derivative of the axial displacement with respect to the axial coordinate:

[0041] Based on equations (14) and (15), the vector of axial force and axial displacement at the upper and lower ends of the anchor bolt can be obtained by including... D 1 and D The vector of undetermined coefficients of 2 is represented as:

[0042] In the formula, and These are the axial force vector and axial displacement vector of the anchor bolt, respectively. For inclusion D 1 and D The vector of undetermined coefficients for 2. The coefficient matrices Q and T are respectively: , .

[0043] After eliminating the undetermined coefficient vector D by combining equations (16) and (17), we can obtain:

[0044] In the formula, This is the correlation stiffness matrix between the axial force and the axial displacement at the end of a finite-length anchor bolt.

[0045] Rewriting equation (18) in block form and expanding it, we get:

[0046] In the formula, For matrix The corresponding element.

[0047] Meanwhile, by performing a force analysis on the axial foundation spring at the lower end of the anchor bolt, the relationship between its axial force and its stress state can be obtained as follows:

[0048] In the formula, k xb The formula for calculating the stiffness of the foundation spring at the lower end of the anchor bolt, which is only subjected to axial compression, is as follows: , in K The elastic resistance coefficient of the surrounding rock. A b Let be the cross-sectional area of ​​the anchor bolt. Clearly, the anchor bolt's mechanical response exhibits nonlinear characteristics when subjected only to the axially compressed foundation spring.

[0049] Furthermore, the displacement and force boundary conditions at the upper end of the anchor bolt can be expressed as follows:

[0050] Based on equations (19) to (22), axial external force R x With axial displacement u x The relationship can be represented as:

[0051] In the formula, This refers to the axial stiffness of the anchor bolt.

[0052] Combining the lateral and axial mechanical behaviors, the governing equations for a finite-length anchor bolt can be expressed as:

[0053] In the formula, F=[ R x , R y , R φ ] T Let U be the external force vector, then U = [ u x , u y , u φ ] T Let K be the displacement vector. b Let be the complete stiffness matrix of the anchor bolt in the local coordinate system, and its expression is:

[0054] In addition, the design parameters of the anchor bolts include: the physical and mechanical parameters of the anchor bolts themselves (axial length, outer diameter of the steel pipe, wall thickness, diameter of the grouting ring) and the location, angle and number of anchor bolts. All of the above parameters are program variables and can be quantitatively calculated.

[0055] In some optional implementations, the anchorage reliability is analyzed based on the anchorage stress and the stress in the surrounding rock, including: if the anchorage stress is greater than the yield limit or the stress in the surrounding rock reaches the strength failure condition, the anchorage reliability does not meet the reliability requirements; if the anchorage stress is less than or equal to the yield limit and the stress in the surrounding rock does not reach the strength failure condition, the anchorage reliability meets the reliability requirements.

[0056] In the above technical solution, if the stress of the anchor bolt in the calculation analysis exceeds the yield strength or the stress in the surrounding rock reaches the strength failure condition, the anchor bolt design lacks sufficient anchoring reliability and requires reinforcement design. Conversely, if the stress of the anchor bolt in the calculation analysis is less than or equal to the yield strength and the stress in the surrounding rock has not yet reached the strength failure condition, the anchor bolt design has good anchoring reliability and can be applied in practice. Furthermore, this calculation method can calculate the mechanical response of the anchor bolt at all construction stages after installation, determine the anchoring reliability at each stage, and is suitable for the entire process of anchor bolt mechanical calculation.

[0057] An electronic device provided in this application includes a processor and a memory, wherein the memory stores machine-readable instructions executable by the processor, and the machine-readable instructions, when executed by the processor, perform any of the methods described above.

[0058] This application provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of any of the methods described above. Attached Figure Description

[0059] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 A flowchart illustrating the steps of a method for analyzing the anchorage reliability of a locking anchor bolt during the initial support stage of a tunnel, as provided in this application embodiment; Figure 2 This is a schematic diagram of the load structure model provided in the embodiments of this application; Figure 3 This is a schematic diagram of a load-bearing structural model provided in another embodiment of this application; Figure 4 A detailed model diagram provided for an embodiment of this application; Figure 5 This application illustrates one possible structure of an electronic device provided in an embodiment of the present application. Detailed Implementation

[0061] The technical solutions in the embodiments of this application will now be described with reference to the accompanying drawings.

[0062] Please refer to Figure 1 , Figure 1 A flowchart illustrating the steps of a method for analyzing the anchorage reliability of anchor bolts in the initial support stage of a tunnel, provided in this application embodiment, includes: Step S1: Establish the initial lining unit and apply constraints to the connection between the initial lining unit and the anchor bolt to form a load structure model; Step S2: Apply surrounding rock load to the load structure model to obtain the bending moment, shear force and axial force at the connection. Step S3: Establish a detailed model of the anchor bolt and surrounding rock; Step S4: Convert the bending moment, shear force, and axial force at the connection point into the stress distribution of the cross section at the top of the anchor rod; Step S5: Based on the stress distribution of the cross section, apply a stress load to the top of the anchor bolt in the refined model to obtain the anchor bolt stress and the stress in the surrounding rock. Step S6: Analyze the anchoring reliability based on the stress of the anchor bolt and the stress in the surrounding rock.

[0063] In this embodiment, a phased analysis mode is adopted for the anchorage reliability of the anchor bolts in the initial support stage of the tunnel. The specific implementation process is as follows: In the first stage, the complex contact relationship between the surrounding rock, the anchor bolts, and the initial support is not specifically simulated. Instead, constraints are applied at the connection between the initial support and the anchor bolts to achieve the effect of cooperating with the initial support in bearing the force. Then, a load structure model of the initial support structure is established using numerical simulation or analytical methods. The mechanical response of the initial support structure is calculated by applying the surrounding rock load, and finally, the bending moment, shear force, and axial force at the top of the anchor bolts that need to be evaluated for reliability are obtained. In the second stage, the anchor bolt-surrounding rock system is finely modeled to accurately replicate the complex contact relationship between the surrounding rock and the anchor bolts. Then, the internal forces calculated in the first stage are converted into corresponding stresses and applied to the top of the anchor bolts in the fine model. By calculating and analyzing whether the anchor bolt-surrounding rock system will fail, the anchorage reliability of the anchor bolts in the initial support stage of the tunnel is determined. Meanwhile, this method can realize the mechanical response calculation of the anchor bolts throughout the entire tunnel construction process after the anchor bolts are installed, thereby guiding the reasonable selection of anchor bolt design parameters.

[0064] Compared with the traditional engineering analogy method, this solution can more accurately analyze the anchoring reliability of anchor bolts under different surrounding rock conditions and different design parameters, reducing the waste of resources caused by overly conservative anchor bolt design or the risk of safety hazards caused by overly aggressive design.

[0065] Compared to traditional complex numerical modeling and analysis methods, this approach significantly reduces the analysis difficulty by decomposing the core problem into two sub-problems for step-by-step solution. It avoids the challenges of multi-scale modeling with large differences in the scale of substructures or subsystems, as well as complex contact modeling problems. Furthermore, the first sub-problem can be solved using numerical methods such as the finite element method or analytical methods; the second sub-problem can focus on the anchor bolt body and its surrounding small-scale rock mass, greatly reducing the scale of detailed modeling and adapting to the entire construction process after the anchor bolt installation, making the modeling of complex contact relationships easier to advance.

[0066] In some alternative implementations, please refer to Figure 2 and Figure 3 A preliminary lining unit is established, and constraints are applied to the connection between the preliminary lining unit and the anchor bolt to form a load-bearing structural model, including: Beams were used to simulate the initial lining unit composed of a steel frame and shotcrete. The locking anchor is simulated by applying constraints at the connection between the initial lining unit and the locking anchor. The elastic resistance of the surrounding rock to the initial lining unit is simulated using a spring that is only under compression and not under tension; The supporting effect of the tunnel foundation on the cross section of the initial lining when the initial support is not closed is simulated using springs that are only under compression and not tension.

[0067] In this embodiment, beam elements are used to simulate the initial lining unit composed of steel frame and shotcrete, and finite-length piles are used to simulate anchor bolts. Both are conventional and simplified element types used in engineering, eliminating the need to construct complex solid models. At the same time, various springs are used to simulate the constraint and support of surrounding rock and foundation, avoiding the detailed depiction of the complex contact relationship between surrounding rock, initial lining and anchor bolts. This effectively reduces the degree of freedom of the model, lowers the modeling difficulty and calculation time, and meets the needs of rapid modeling and efficient analysis in the initial support stage.

[0068] In some alternative implementations, an initial lining unit is established, and constraints are applied to the connection between the initial lining unit and the anchor bolts to form a load-bearing structural model, including: Based on the actual engineering conditions, the surrounding rock load, tunnel physical and mechanical parameters, and anchor bolt physical and mechanical parameters are selected to establish a load structure model.

[0069] In some alternative implementations, the surrounding rock load is calculated by the surrounding rock classification according to the response specification.

[0070] In some alternative implementations, please refer to Figure 4 Establish a detailed model of the anchor bolt and surrounding rock, including: Finite-length pile elements are used to simulate the anchor bolts, which are considered as elastic structures. The surrounding rock is modeled using the Mohr-Coulomb or Hoek-Brown elastoplastic model.

[0071] In some alternative implementations, a detailed model of the anchor bolt and surrounding rock is created, including: The mechanical response of the anchor bolt embedded in the surrounding rock formation is described by the transverse and axial foundation springs distributed along the anchor bolt axis and the axial foundation spring located at the lower end of the anchor bolt that is only compressed.

[0072] In some alternative implementations, the bending moment, shear force, and axial force at the connection are converted into the stress distribution of the cross-section at the top of the anchor bolt, including: The stress distribution across the cross section is calculated using formulas from mechanics of materials based on the bending moment, shear force, and axial force at the connection.

[0073] Specifically, the construction of a detailed model of the anchor bolt and the surrounding rock includes: In this model, the anchor bolt is considered a finite-length micropile with both axial and lateral bearing capacity. To accurately describe the mechanical response of the anchor bolt embedded in the surrounding rock strata, three types of ground springs are introduced into the model: lateral and axial ground springs distributed along the anchor bolt axis (with stiffnesses of [missing information] respectively). k y and k x ) and the axial foundation spring (stiffness of ) located at the lower end of the anchor bolt and subjected only to compression. k xb ).

[0074] Due to the lateral force R y and bending moment R φ The mechanical behavior of a finite-length anchor bolt is similar to that of an elastic foundation beam subjected to lateral forces, and its lateral deformation governing equation can be expressed as:

[0075] In the formula, U y This refers to the lateral displacement of the anchor bolt. EI b The bending stiffness of the anchor bolt section is contributed by the anchor bolt body and the surrounding grouting body, and its calculation formula is as follows: .

[0076] in, E s and E g These are the elastic moduli of the steel pipe and the grouting material, respectively. k y The transverse foundation spring stiffness per unit length along the anchor bolt axis can be expressed as: k y = KD ,in KThe elastic resistance coefficient of the surrounding rock; D , d , t b These are the borehole diameter, anchor bolt diameter, and steel pipe wall thickness, respectively.

[0077] The general solution of equation (1) can be expressed as:

[0078] In the formula, C 1 C 4 is an undetermined coefficient that needs to be determined through boundary conditions; and The root of the characteristic equation of equation (2) is given by , where i It is the imaginary unit.

[0079] Meanwhile, the external force boundary conditions at both ends of the anchor bolt are:

[0080] In the formula, M and Q The bending moment and shear force of the anchor bolt are respectively, which can be further expressed by its lateral displacement as follows:

[0081] By combining equations (2) to (4), we can obtain:

[0082] In the formula, F=[ R φ , R y , 0, 0] T C represents the lateral external force vector at both ends of the anchor bolt; C 1, C 2, C 3, C 4] T S is the vector of undetermined coefficients; S is the relationship matrix between the transverse external force vector F and the vector of undetermined coefficients C, specifically in the form of: .

[0083] On the other hand, the displacement boundary conditions at both ends of the anchor bolt satisfy the following equation:

[0084] In the formula, u y and u φ These represent the lateral displacement and rotation angle of the upper end of the anchor bolt, respectively. and These represent the lateral displacement and rotation angle of the lower end of the anchor bolt, respectively.

[0085] Substituting equation (2) into equation (6) and rewriting the result in matrix form, we can further obtain the following equation:

[0086] In the formula, U=[ u φ , u y , u φ-end , u y-end ] T It is a vector consisting of the lateral displacement and rotation angle at both ends of the anchor bolt; .

[0087] By combining equations (5) and (7) to eliminate the undetermined coefficient vector C, the relationship between the external force F and the displacement U can be obtained as follows:

[0088] In the formula, K h =SB 1 This is the correlation stiffness matrix between the lateral force and the lateral displacement at the end of a finite-length anchor bolt.

[0089] Rewriting equation (8) in block matrix form and expanding it, we get:

[0090] In the formula, F1=[ R φ , R y ] T And F2=[0, 0] T These are the external load vectors at the upper and lower ends of the anchor bolt, respectively; U1=[ u φ , uy ] T and U2=[ u φ-end , u y-end ] T These are the displacement vectors of the upper and lower ends of the anchor bolt, respectively. This is a block matrix with a corresponding dimension of 2×2.

[0091] According to equation (10), U2 can be obtained as follows:

[0092] Substituting equation (3-15) into equation (3-13), F1 can be further expressed as:

[0093] In the formula, Let be the lateral stiffness matrix of a finite-length anchor bolt.

[0094] Subsequently, the focus was placed on the axial force at the upper end of the finite-length anchor bolt. R x Axial response under load. Based on the mechanical mechanism of axial force on a pile, the governing equation for the axial deformation of the anchor bolt can be expressed as:

[0095] In the formula, U x This refers to the axial displacement of the anchor bolt. EA b The compressive stiffness of the anchor bolt is calculated using the following formula: , k x The axial foundation spring stiffness per unit length along the anchor bolt axis can be expressed as: k x =(2π / 3 + 4π / 3) χ ) G

[38] ,in G The shear modulus of the surrounding rock. χ ( χ ≥3) is a coefficient characterizing the size of the disturbed rock mass region.

[0096] Based on equation (13), the axial displacement of the anchor bolt can be further expressed as:

[0097] In the formula, D 1 and D 2 is an undetermined coefficient that needs to be determined through boundary conditions; It is the root of the characteristic equation of equation (14).

[0098] Furthermore, the axial force of the anchor bolt is the first derivative of the axial displacement with respect to the axial coordinate:

[0099] Based on equations (14) and (15), the vector of axial force and axial displacement at the upper and lower ends of the anchor bolt can be obtained by including... D 1 and D The vector of undetermined coefficients of 2 is represented as:

[0100] In the formula, and These are the axial force vector and axial displacement vector of the anchor bolt, respectively. For inclusion D 1 and D The vector of undetermined coefficients for 2. The coefficient matrices Q and T are respectively: , .

[0101] After eliminating the undetermined coefficient vector D by combining equations (16) and (17), we can obtain:

[0102] In the formula, This is the correlation stiffness matrix between the axial force and the axial displacement at the end of a finite-length anchor bolt.

[0103] Rewriting equation (18) in block form and expanding it, we get:

[0104] In the formula, For matrix The corresponding element.

[0105] Meanwhile, by performing a force analysis on the axial foundation spring at the lower end of the anchor bolt, the relationship between its axial force and its stress state can be obtained as follows:

[0106] In the formula, k xb The formula for calculating the stiffness of the foundation spring at the lower end of the anchor bolt, which is only subjected to axial compression, is as follows: , in K The elastic resistance coefficient of the surrounding rock. A b Let be the cross-sectional area of ​​the anchor bolt. Clearly, the anchor bolt's mechanical response exhibits nonlinear characteristics when subjected only to the axially compressed foundation spring.

[0107] Furthermore, the displacement and force boundary conditions at the upper end of the anchor bolt can be expressed as follows:

[0108] Based on equations (19) to (22), axial external force R x With axial displacement u x The relationship can be represented as:

[0109] In the formula, This refers to the axial stiffness of the anchor bolt.

[0110] Combining the lateral and axial mechanical behaviors, the governing equations for a finite-length anchor bolt can be expressed as:

[0111] In the formula, F=[ R x , R y , R φ ] T Let U be the external force vector, then U = [ u x , u y , u φ ] T Let K be the displacement vector. b Let be the complete stiffness matrix of the anchor bolt in the local coordinate system, and its expression is:

[0112] In addition, the design parameters of the anchor bolts include: the physical and mechanical parameters of the anchor bolts themselves (axial length, outer diameter of the steel pipe, wall thickness, diameter of the grouting ring) and the location, angle and number of anchor bolts. All of the above parameters are program variables and can be quantitatively calculated.

[0113] In some alternative implementations, the anchorage reliability is analyzed based on the anchor bolt stress and the stress in the surrounding rock, including: If the stress of the anchor bolt exceeds the yield limit or the stress in the surrounding rock reaches the strength failure condition, the anchoring reliability does not meet the reliability requirements. If the stress of the anchor bolt is less than or equal to the yield strength and the stress in the surrounding rock does not reach the strength failure condition, then the anchoring reliability meets the reliability requirements.

[0114] In this embodiment, if the stress of the anchor bolt in the calculation analysis exceeds the yield strength or the stress in the surrounding rock reaches the strength failure condition, the anchor bolt design lacks sufficient anchoring reliability and requires reinforcement design. Conversely, if the stress of the anchor bolt in the calculation analysis is less than or equal to the yield strength and the stress in the surrounding rock has not yet reached the strength failure condition, the anchor bolt design has good anchoring reliability and can be applied in practice. Furthermore, this calculation method can calculate the mechanical response of the anchor bolt at all construction stages after installation, determine the anchoring reliability at each stage, and adapt to the mechanical calculation of the anchor bolt throughout the entire process.

[0115] Figure 5 This illustration shows a possible structure of an electronic device provided in an embodiment of this application. (Refer to...) Figure 5The electronic device includes a processor, memory, and a communication interface, which are interconnected and communicate with each other via a communication bus and / or other forms of connection mechanism (not shown).

[0116] The memory includes one or more (only one is shown in the figure), which can be, but is not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc. The processor and other possible components can access the memory to read and / or write data to it.

[0117] The processor comprises one or more (only one is shown in the figure), which can be an integrated circuit chip with signal processing capabilities. The aforementioned processor can be a general-purpose processor, including a Central Processing Unit (CPU), a Microcontroller Unit (MCU), a Network Processor (NP), or other conventional processors; it can also be a special-purpose processor, including a Neural-network Processing Unit (NPU), a Graphics Processing Unit (GPU), a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. Furthermore, when there are multiple processors, some can be general-purpose processors, and others can be special-purpose processors.

[0118] The communication interface includes one or more (only one is shown in the figure), which can be used to communicate directly or indirectly with other devices to exchange data. The communication interface may include interfaces for wired and / or wireless communication.

[0119] One or more computer program instructions may be stored in the memory, and the processor may read and execute these computer program instructions to implement the methods provided in the embodiments of this application.

[0120] Understandable. Figure 5 The structure shown is for illustrative purposes only; the electronic device may also include structures that are more complex than those shown. Figure 5 The more or fewer components shown, or having the same Figure 5 The different structures shown. Figure 5 The components shown can be implemented using hardware, software, or a combination thereof. Electronic devices may be physical devices, such as PCs, laptops, tablets, mobile phones, servers, embedded devices, etc., or they may be virtual devices, such as virtual machines, virtualized containers, etc. Furthermore, electronic devices are not limited to a single device; they can also be a combination of multiple devices or a cluster of a large number of devices.

[0121] This application provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of any of the methods described above.

[0122] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Additionally, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some communication interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.

[0123] Furthermore, the units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0124] Furthermore, the functional modules in the various embodiments of this application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0125] In this document, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, without necessarily requiring or implying any such actual relationship or order between these entities or operations.

[0126] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for analyzing the reliability of anchorage of locking anchor bolts in the initial support stage of tunnels, characterized in that, include: Establish the initial lining unit and apply constraints to the connection between the initial lining unit and the anchor bolt to form a load structure model; Apply surrounding rock load to the load structure model to obtain the bending moment, shear force and axial force at the connection. Establish a detailed model of the anchor bolts and surrounding rock; The bending moment, shear force, and axial force at the connection are converted into the cross-sectional stress distribution at the top of the anchor bolt; Based on the stress distribution of the cross section, a stress load is applied to the top of the anchor bolt in the refined model to obtain the anchor bolt stress and the stress in the surrounding rock. The anchoring reliability is analyzed based on the stress of the anchor bolt and the stress in the surrounding rock.

2. The method as described in claim 1, characterized in that, The process of establishing the initial lining unit and applying constraints to the connection between the initial lining unit and the anchor bolt to form a load-bearing structural model includes: Beams were used to simulate the initial lining unit composed of a steel frame and shotcrete. The locking anchor bolt is simulated by applying constraints to the corresponding nodes; The elastic resistance of the surrounding rock to the initial lining unit is simulated using a spring that is only under compression and not under tension; The supporting effect of the tunnel foundation on the cross section of the initial lining when the initial support is not closed is simulated using springs that are only under compression and not tension.

3. The method as described in claim 1, characterized in that, The process of establishing the initial lining unit and applying constraints to the connection between the initial lining unit and the anchor bolt to form a load-bearing structural model includes: Based on the actual engineering conditions, the surrounding rock load, tunnel physical and mechanical parameters, and anchor bolt physical and mechanical parameters are selected to establish the load structure model.

4. The method as described in claim 1, characterized in that, The surrounding rock load is calculated according to the response specification based on the surrounding rock classification.

5. The method as described in claim 1, characterized in that, The establishment of a detailed model of the anchor bolt and surrounding rock includes: Finite-length pile elements are used to simulate the anchor bolts, which are considered as elastic structures. The surrounding rock is modeled using the Mohr-Coulomb or Hoek-Brown elastoplastic model.

6. The method as described in claim 1, characterized in that, The establishment of a detailed model of the anchor bolt and surrounding rock includes: The mechanical response of the anchor bolt embedded in the surrounding rock formation is described by the transverse and axial foundation springs distributed along the anchor bolt axis and the axial foundation spring located at the lower end of the anchor bolt that is only compressed.

7. The method as described in claim 1, characterized in that, The process of converting the bending moment, shear force, and axial force at the connection point into the cross-sectional stress distribution at the top of the anchor bolt includes: The stress distribution of the cross section is calculated using material mechanics formulas based on the bending moment, shear force, and axial force at the connection.

8. The method as described in claim 1, characterized in that, The analysis of anchorage reliability based on the stress of the anchor bolt and the stress in the surrounding rock includes: If the stress of the anchor bolt exceeds the yield limit or the stress in the surrounding rock reaches the strength failure condition, the anchoring reliability does not meet the reliability requirements. If the stress of the anchor bolt is less than or equal to the yield strength and the stress in the surrounding rock does not reach the strength failure condition, then the anchoring reliability meets the reliability requirements.

9. An electronic device, characterized in that, include: A processor and a memory, the memory storing machine-readable instructions executable by the processor, which, when executed by the processor, perform the method as described in any one of claims 1-8.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method described in any one of claims 1-8.

Images