Shear contribution calculation methods, apparatus, equipment and storage media

Abstract

This application provides a method, apparatus, equipment, and storage medium for calculating shear contribution, belonging to the field of mechanical analysis technology. The method includes: establishing a rectangular coordinate system on both sides of point A in the anchor bolt; on one side of point A, elastically coupling the anchor bolt and the grouting or rock block medium, treating the rock anchor bolt as a semi-infinite elastic foundation beam; analyzing the lateral deformation mechanism of the anchor bolt; determining the yield criterion of the anchor bolt section; determining the axial deformation mechanism of the anchor bolt based on the relationship between the displacement at point O and the axial force; determining the axial force and shear force at failure based on the lateral and axial deformation mechanisms; and calculating the shear contribution of the anchor bolt based on the axial force and shear force at failure. This application can comprehensively consider the stress distribution at the anchorage interface and the influence of the large elastic-plastic deformation of the anchor bolt, thereby achieving a more accurate and comprehensive assessment of the shear contribution and potential failure risk of deep rock mass anchor bolt support systems.

Description

Technical Field

[0001] This application relates to the field of mechanical analysis technology, and in particular to a method, apparatus, equipment and storage medium for calculating shear contribution. Background Technology

[0002] Currently, coal mining depths worldwide have reached 1500m, geothermal mining depths exceed 3000m, non-ferrous metal mining depths exceed 4000m, and oil and gas resource mining depths reach as high as 7500m. Deep rock masses often contain various weak faults and soft structural planes; therefore, for safe coal mining, support is often required for deep excavated rock masses. As an economical and efficient support method, rock bolt support is widely used in coal mining, especially fully grouted anchor bolts, which are usually the preferred type of anchor bolt for supporting or stabilizing loose rock masses in most rock slopes and underground excavations. Anchor bolts not only transfer tensile stress from the surrounding rock but also provide additional shear resistance, preventing slippage of joints or weak structural planes within the rock mass. Therefore, accurately assessing the shear contribution and potential failure risk of fully grouted anchor bolts is of great significance for ensuring the safety of coal mining projects.

[0003] Currently, the main methods for analyzing the mechanical state of anchored joints include theoretical analytical models and numerical modeling methods. Regarding theoretical analytical models, existing models struggle to accurately pinpoint key points for the normal operation and failure warning of anchored rock masses. Numerical modeling methods typically involve 3D modeling and calculation using commercial finite element software; however, the complexity and high computational cost of 3D finite element modeling result in low timeliness and limited guidance for engineering construction. Therefore, there is an urgent need to develop an efficient, accurate, and universal calculation method to meet the needs of the engineering field. Summary of the Invention

[0004] This application provides a method, apparatus, equipment, and storage medium for calculating shear contribution. Existing experimental, numerical, and theoretical analytical methods all have limitations and shortcomings, such as low computational efficiency and high computational costs. Furthermore, existing theoretical analytical methods cannot accurately indicate the working state of anchored rock masses. This invention aims to propose a novel theoretical analytical method that comprehensively considers the stress distribution at the anchorage interface and the influence of the anchor bolt's large elasto-plastic deformation, thereby achieving a more accurate and comprehensive assessment of the shear contribution and potential failure risk of deep rock mass anchor bolt support systems. By solving the above-mentioned technical problems, this invention can significantly improve the efficiency and accuracy of engineering analysis, thus providing effective technical support for ensuring the safety and stability of deep rock mass mining processes.

[0005] In a first aspect, this application provides a method for calculating shear contribution, including:

[0006] Establish a rectangular coordinate system on both sides of point A in the anchor bolt. On one side of point A, the anchor bolt and the grouting or rock block medium are elastically coupled. Treat the rock anchor bolt as a semi-infinite elastic foundation beam, analyze the lateral deformation mechanism of the anchor bolt, and determine the criterion for the yielding of the anchor bolt section, expressed as:

[0007]

[0008] Among them, M A Let M be the bending moment at point A. p The elastic limit bending moment is taken as [value]. σ y D represents the anchor bolt yield strength. b Let N be the diameter of the anchor bolt, N0 be the axial force at point O in the anchor bolt, and N p The yield load of the anchor bolt is N. p =σ y S, where S is the cross-sectional area of ​​the anchor bolt;

[0009] The axial deformation mechanism of the anchor rod is determined based on the relationship between the displacement at point O in the anchor rod and the axial force.

[0010] The axial force and shear force at failure are determined based on the lateral deformation mechanism and axial deformation mechanism of the anchor bolt.

[0011] The shear contribution of the anchor bolt is calculated based on the axial force and shear force at the time of failure.

[0012] Secondly, this application provides a shear contribution calculation device, comprising: a criterion determination module, used to establish a rectangular coordinate system on both sides of point A in the anchor bolt, wherein on one side of point A, the anchor bolt and the grouting or rock block medium are elastically coupled, the rock anchor bolt is regarded as a semi-infinite elastic foundation beam, the lateral deformation mechanism of the anchor bolt is analyzed, and the criterion for yielding of the anchor bolt section is determined, expressed as:

[0013]

[0014] Among them, M A Let M be the bending moment at point A. p The elastic limit bending moment is taken as [value]. σ y D represents the anchor bolt yield strength. b Let N be the diameter of the anchor bolt, N0 be the axial force at point O in the anchor bolt, and N p The yield load of the anchor bolt is N. p =σ y S, where S is the cross-sectional area of ​​the anchor bolt;

[0015] The mechanism determination module is used to determine the axial deformation mechanism of the anchor rod based on the relationship between the displacement at point O and the axial force in the anchor rod.

[0016] The torque calculation module is used to determine the axial force and shear force at failure based on the lateral deformation mechanism and axial deformation mechanism of the anchor bolt.

[0017] The contribution calculation module is used to calculate the shear contribution of the anchor bolt based on the axial force and shear force at the time of failure.

[0018] Thirdly, this application provides an electronic device, which includes: a processor and a memory; the memory is used to store instructions; the processor is used to execute the instructions in the memory, causing the electronic device to perform the method as described in the first aspect.

[0019] Fourthly, this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the method described in the first aspect.

[0020] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the method described in the first aspect.

[0021] The shear contribution calculation method, apparatus, equipment, and storage medium provided in this application have the following technical advantages:

[0022] 1. Simple and efficient calculation: Compared to complex three-dimensional finite element numerical simulation, the calculation method proposed in this patent is simple and easy to implement, with high computational and analytical efficiency. This means that the shear contribution and potential failure risk of anchored rock masses can be quickly and accurately assessed, providing real-time technical support for engineering projects.

[0023] 2. Comprehensive evaluation of anchor bolt performance: This invention not only comprehensively considers the constitutive model of stress distribution at the anchorage interface, but also the influence of large elasto-plastic deformation in local areas of the anchor bolt. This makes it possible to conduct a more accurate and comprehensive assessment of the shear contribution and failure risk of the anchor bolt rock mass, which helps to improve the safety of coal mining engineering.

[0024] 3. Versatility and Practicality: The calculation method proposed in this invention patent has high versatility and practicality. It can be applied not only in coal mining but also in other rock slope and underground excavation projects. This versatility enables the technical solution to provide important technical support and theoretical guidance for engineering projects in various fields.

[0025] 4. Highly Efficient Engineering Guidance: Compared with existing theoretical calculation methods and numerical modeling methods, the technical solution of this invention has higher computational efficiency and engineering guidance. It can quickly and accurately assess the stability of the anchor bolt support system, providing important reference for engineering construction, while reducing the time and cost of engineering construction. Attached Figure Description

[0026] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0027] Figure 1 A schematic diagram illustrating a coordinate system established at point A in an anchor bolt, as shown in an exemplary embodiment;

[0028] Figure 2 A schematic diagram of an anchor bolt interface shown in an exemplary embodiment;

[0029] Figure 3 A force analysis diagram showing the simplification of a circular cross-section to a rectangular cross-section as an exemplary embodiment is shown.

[0030] Figure 4 An exemplary embodiment shows the force analysis diagram of the anchor bolt at the intersection point O of the anchor bolt and the connecting surface before the plastic hinge point appears;

[0031] Figure 5 An exemplary embodiment shows the shear stress distribution of the anchorage section considering the effect of lateral displacement on the effective bond length.

[0032] Figure 6 L1, L shown in an exemplary embodiment p and L e These represent the interfacial stress distributions in the grouting fracture section, softened section, and effective bonding section, respectively.

[0033] Figure 7 A schematic diagram illustrating the calculation process of axial deformation at point O, as shown in an exemplary embodiment;

[0034] Figure 8 This is a schematic diagram illustrating the OA portion of the anchor bolt as the shear displacement continues to increase, as shown in an exemplary embodiment.

[0035] Figure 9 The relationship between anchor contribution and shear displacement is shown as an exemplary embodiment when the anchoring angle is 90° and the anchor diameter is 20, 25 and 40 mm.

[0036] Figure 10 The relationship between anchor contribution and shear displacement is shown as an exemplary embodiment when the anchoring angle is 60° and the anchor diameter is 20 and 25 mm.

[0037] Figure 11 The relationship between anchor contribution and shear displacement is shown as an exemplary embodiment when the anchoring angle is 45° and the anchor diameter is 25mm.

[0038] Figure 12 A structural diagram of a shear contribution calculation device is shown as an exemplary embodiment;

[0039] Figure 13 A block diagram illustrating an electronic device as an exemplary embodiment.

[0040] The accompanying drawings have illustrated specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0041] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0042] It should be noted that the links involved in this application, as well as the related information and platform information contained therein (including but not limited to data used for analysis, stored data, and displayed data), are all information and data that have been understood and authorized by the relevant users or have been fully authorized by all parties. Furthermore, the collection, use, processing, transmission, provision, disclosure, and application of the relevant data have all complied with the laws, regulations, and standards of the relevant countries and regions, taken necessary confidentiality measures, and have not violated public order and good morals, and have conformed to the principles of legality, legitimacy, and necessity.

[0043] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will be described below with reference to the accompanying drawings.

[0044] The shear contribution calculation method provided in this application can be implemented on any electronic device with data processing capabilities, or it can be a shear contribution calculation system. It should be noted that the shear contribution calculation system can be deployed independently on an electronic device in any environment (e.g., deployed independently on an edge server in an edge environment), deployed entirely in a cloud environment, or distributed across different environments.

[0045] For example, a shear contribution computing system can be logically divided into multiple parts, each with different functions. These parts can be deployed in any two or three of the following environments: electronic devices (located on the user side, such as clients), edge environments, and cloud environments. An edge environment comprises a collection of edge electronic devices located close to the electronic devices, including edge servers and edge stations with computing power. The various parts of the shear contribution computing system deployed in different environments or devices work together to realize the functions of a data processing platform.

[0046] It should be understood that this application does not restrict the specific deployment environment of which parts of the antishear contribution computing system are deployed. In practical applications, the deployment can be adapted according to the computing power of electronic devices, the resource availability of edge and cloud environments, or specific application requirements.

[0047] To address the following problems existing in the prior art:

[0048] 1. Based on three-dimensional finite element numerical simulation: Due to the complexity of three-dimensional finite element modeling and the high operating cost, the analysis efficiency is not high, which makes it impossible to quickly analyze the operating status of anchored rock mass.

[0049] 2. Existing theoretical calculation methods usually neglect the constitutive stress at the interface of the anchorage section and the plastic deformation of the anchor metal material.

[0050] 3. Existing methods are not accurate enough to meet engineering requirements.

[0051] This invention provides a method for calculating the shear contribution of anchored rock mass and for early warning of failure, which includes the following steps 1 to 4.

[0052] Step 1: Determine the lateral deformation mechanism of the anchor bolt.

[0053] In geotechnical engineering, the strength of anchor materials is often much higher than that of grouting materials or rock materials. Therefore, when the anchor joint is subjected to shear loads, the grouting material or rock medium will undergo plastic deformation before the anchor material plastically yields. For example... Figure 1 As shown, a rectangular coordinate system is established on both the left and right sides of point A. To the left of point A, the rock anchor and the grouting (or rock block) medium are elastically coupled, and the rock anchor can be regarded as a semi-infinite elastic foundation beam. According to the Winkler foundation beam model, the elastic resistance of the elastically coupled segment (x>L1) can be expressed as:

[0054] p x =kvD b (2)

[0055] In the formula, p x For grouting material to resist compressive stress or rock to resist compressive stress; σ represents the spring stiffness of the grout or rock, where α is the stiffness coefficient; c ν is the non-shrink compressive strength of the main grouting material or rock; v is the lateral deformation displacement of the anchor bolt.

[0056] To the right of point A, the grouting (or rock) medium exceeds its ultimate elastic strain and transitions into the plastic zone. At this point, the elastic resistance depends on the bearing capacity of the grouting (or rock), and can be expressed by the following formula:

[0057] p u =nσ c D b (3)

[0058] In the formula p u The bearing capacity of the grout (or rock); n≥1 is the bearing capacity coefficient of the main grouting body (rock); D b The diameter is the anchor bolt.

[0059] According to the Winkel elastic foundation beam model, the lateral deformation of the anchor rod on the left side of point A satisfies the differential equation represented by formula (4).

[0060]

[0061] Where EI is the bending stiffness of the anchor rod, p x This represents the reaction force of the surrounding rock for the anchor bolt.

[0062] By solving formula (4), the general solution can be obtained as follows:

[0063] v(x) = e -βx (c1cosβx+c2sinβx)+e βx (c3cosβx+c4sinβx) (5)

[0064] in, 1 / β represents the characteristic length of the beam; c1, c2, c3, and c4 are undetermined coefficients.

[0065] To the left of point A, as x approaches positive infinity, the lateral deformation v(x) of the anchor rod approaches 0 infinitely, therefore the coefficients c3 and c4 can be calculated to be 0. Thus, formula (4) can be simplified to...

[0066] v e (x)=A'e -βx cos(βx+B) (6)

[0067] Among them, v e (x) is the lateral displacement function of the anchor rod to the left of point A, and A' and B are undetermined coefficients.

[0068] By differentiating formula (6), the deflection angle function of the anchor rod can be expressed as:

[0069] w e (x)=v e ′(x)=-A'βe -βx [cos(βx+B)+sin(βx+B)] (7)

[0070] Among them, v' e (x) is the first derivative of the lateral displacement function of the anchor bolt to the left of point A.

[0071] According to the Euler-Bernoulli beam theory, the relationship between bending moment and shear force can be derived as follows:

[0072] M e (x)=-EIv e "(x)=-2A'EIβ 2 e -βx sin(βx+B) (8)

[0073] Q e (x)=EIv e "′(x)=2A'EIβ 3 e -βx [cos(βx+B)-sin(βx+B)] (9)

[0074] Among them, M e (x) is the bending moment function of the anchor section to the left of point A, v' e '(x) is the second derivative of the lateral displacement function of the anchor bolt to the left of point A, Q e (x) represents the shear force function at the anchor section to the left of point A, v' e "(x) is the third derivative of the lateral displacement function of the anchor rod to the left of point A.

[0075] like Figure 1 As shown, to the right of point A, the grout (rock) is in the plastic zone. The elastic resistance can be considered as a constant value, as shown in equation (2). Before reaching the elastic limit moment of the anchor section, the bending moment at point A gradually increases as the plastic zone of the grout (rock) expands. Generally, when shear displacement occurs at the joint connection, the anchor will undergo overall deformation under the action of axial tension, shear force, and bending moment. Therefore, for the anchor cross-section, it will bear the tensile-flexural effect and shear load until fracture. Since the effect of shear on the lateral deformation and deflection angle of the anchor is significantly less than that of bending, the effect of shear deformation on lateral behavior is not considered when analyzing the lateral deformation of the anchor. Figure 2 As shown, however, the presence of axial tension significantly affects the stress distribution of the anchor bolt section under bending moment. Therefore, when analyzing the lateral deformation and deflection of the anchor bolt, the coupling effect between axial tension and bending must be considered. Based on the coupling effect between axial tension and bending, the shear force function and bending moment function of the anchor bolt section to the right of point A are determined.

[0076] Based on the relationship between the curvature and strain of the anchor bolt cross-section edge and the first condition, a formula for calculating the curvature of the anchor bolt cross-section is determined; in the formula for calculating the curvature of the anchor bolt cross-section, the curvature of the anchor bolt cross-section is calculated based on the bending moment of the anchor bolt cross-section at point x and the position of the neutral layer.

[0077] The position of the neutral layer is the ratio of the product of the axial tensile force and the moment of inertia of the anchor section to the product of the bending moment of the anchor cross section at point x and the area of ​​the anchor cross section.

[0078] Q o =p u L1

[0079] Q(x) = Q o -p u (L1-x)=p u x

[0080]

[0081] Where Q0 is the anchor shear force at point O, p u Let L1 be the ultimate bearing capacity of the surrounding rock, L1 be the length of the rock plastic section, Q(x) be the shear force function of the anchor section to the right of point A, and M(x) be the bending moment function of the anchor section to the right of point A.

[0082] Since both shear force and axial force are dynamically changing, determining the stress state of the anchor section at any given point on the OA section is a major challenge.

[0083] The deformation of the anchor bolt under tensile bending effect is simplified by the elastoplastic deformation theory of a rectangular cross-section beam. For example... Figure 3 As shown, the circular cross-section is simplified to a rectangular cross-section to analyze the relationship between curvature and bending moment at any cross-section of the anchor bolt segment OA.

[0084] When the sum of the stress in the outermost fiber on the tension side of the anchor bolt cross-section and the cross-sectional stress generated by the axial tensile force is less than a set value, the upper fiber of the anchor bolt cross-section satisfies the first condition; wherein, the first condition is that the sum of the stress in the outermost fiber on the tension side of the anchor bolt cross-section and the cross-sectional stress generated by the axial tensile force is equal to the stress at the edge of the anchor bolt cross-section. For example, the set value can be σ. s M is the bending moment at the anchor bolt cross-section at point x; N is the axial tensile force; S is the area of ​​the anchor bolt cross-section; σ(x) is the stress at the edge of the anchor bolt cross-section; σ M σ represents the stress in the outermost fiber of the anchor bolt section on the tension side; N I represents the cross-sectional stress generated under axial tensile force; I represents the moment of inertia of the anchor bolt cross-section.

[0085] Since the cross-section is still in the elastic stage, it strictly conforms to Hooke's Law. σ x =Eε x Therefore, based on the relationship between the curvature and strain of the anchor bolt cross-section edge and the first condition, a formula for calculating the curvature of the anchor bolt cross-section is determined. In this formula, the curvature is calculated based on the bending moment of the anchor bolt cross-section at point x and the position of the neutral layer. The position of the neutral layer is the ratio of the product of the axial tensile force and the moment of inertia of the anchor bolt cross-section to the product of the bending moment of the anchor bolt cross-section at point x and the area of ​​the anchor bolt cross-section.

[0086] Therefore, under elastic conditions, the relationship between curvature and the distance x from point A of the anchor rod can be approximately represented by formula (16). By integrating the formula for calculating the curvature of the anchor rod cross section, the deflection angle and lateral displacement function of the anchor rod can be obtained as follows:

[0087]

[0088] Where C1 and C2 are undetermined coefficients.

[0089] Rearranging the above formula, we get:

[0090] w(x) = w p (x)+C1 (10)

[0091] v(x)=v p (x)+C1x+C2 (11)

[0092] in, This represents the particular solution of the lateral displacement of the anchor bolt;

[0093] This represents the particular solution of the anchor bolt deflection angle.

[0094] Substituting the boundary conditions for shear force, bending moment, displacement, and deflection angle at point A, we get:

[0095]

[0096] Among them, M e (0) is the bending moment of the anchor section to the left of point A, M p (0) represents the bending moment at the anchor section to the right of point A, Q. e (0) represents the anchor shear force at point A, Q p (L1) represents the anchor shear force at point O, w e (0) represents the lateral deflection angle of the anchor bolt at the left side of point A, w p (0) is the lateral deflection angle of the anchor bolt at the right side of point A, v e (0) represents the lateral displacement of the anchor bolt to the left of point A, v p(0) represents the lateral displacement of the anchor bolt to the right of point A.

[0097] Therefore, the deflection angle and lateral displacement at point O can be obtained by the following formula:

[0098]

[0099] Among them, w p (L1) represents the anchor bolt deflection angle at point O, v p (L1) represents the lateral displacement of the anchor rod at point O.

[0100] like Figure 4 As shown, before the plastic hinge point appears, the anchor bolt expression at the intersection point O of the anchor bolt and the connecting surface can be obtained from equations (22) and (23). The relationship between shear displacement and lateral displacement can be obtained from the following formula:

[0101]

[0102] Where U0 is the shear displacement of the anchor at point O, v0 is the lateral component of the shear displacement of the anchor at point O, and θ is the anchorage angle of the anchor.

[0103] Point A has zero shear force and maximum bending moment, making it particularly prone to transforming into a plastic hinge point. Determining the stress distribution of the cross-section at point A is a considerable challenge and is theoretically difficult to achieve. This is because the cross-section is affected by tensile-bending effects, and the change in the stress state of the cross-section is related to the early loading history, while the axial force and bending moment are in a dynamic process. When the stress of the outermost fiber reaches the yield stress of the material, a large portion of the stress on the cross-section at the plastic hinge point is still below the yield stress, indicating that the entire cross-section has not yet met the plastic condition. Therefore, the calculation method proposed in this paper provides a criterion for determining the yield of the entire anchor section, as shown in Equation (1).

[0104]

[0105] Among them, M A Let M be the bending moment at point A. p The elastic limit bending moment is taken as [value]. N0 is the axial force at point O (for simplicity, the axial force at point O is approximately equal to the axial force at point A), N p The yield load of the anchor bolt is N. p =σ y S.

[0106] Step 2, the mechanism of axial deformation of anchor bolts.

[0107] For anchor bolts undergoing shearing, in the initial stage of shear slip failure, the axial force of the anchor bolt is highly sensitive to the axial displacement. To analyze the relationship between the axial displacement and axial force at point O of the anchor bolt, Figure 5 The shear stress distribution diagram of the anchorage section considering the effect of lateral displacement on the effective bond length, L1, L p and L e These represent the lengths of the grouting breakup section, the softening section, and the effective bonding section, respectively. Figure 6 For L1, L p and L e These represent the interfacial stress distributions in the grouting fracture section, softened section, and effective bonding section, respectively.

[0108] for Figure 6 The effective joint segment shown in (a) is used to determine its shear stress distribution.

[0109] for Figure 6 The shear stress distribution of the softened section shown in (b) is determined.

[0110] for Figure 6 The shear stress distribution of the softened section shown in (c) is determined.

[0111] Based on the shear stress distribution of the effective bonding section, softened section, and grouting fracture section, the axial stresses at points x0, L1, and O on the anchor rod are obtained by integrating equations (16)-(18), and L is obtained by equations (19)-(21). e L p Axial deformation of L1:

[0112]

[0113] Where, σ e To effectively control the axial stress at the junction of the bonding section and the softened section, σ p The axial stress is at the junction of the softened section and the grouting and breaking section, σ0 is the axial stress of the anchor bolt at point O, and u e To effectively combine the axial elongation of the segment, u p denoted as axial elongation of the softened section, u1 as axial elongation of the grouting and breaking section, and c as the interface damage coefficient of the effective bonding section.

[0114] Therefore, the axial displacement of point A on the anchor bolt is the sum of the axial elongation of the effective joint section, the axial elongation of the softened section, and the axial elongation of the grouting and breaking section. The axial stress of the anchor bolt at point O is calculated based on the axial displacement of point A on the anchor bolt and equations (16)-(18).

[0115] Before the plastic hinge point appears, the relationship between the axial force and axial displacement at point O on the anchor bolt can be expressed as formula (22).

[0116]

[0117] like Figure 7As shown, the calculation process of the axial deformation at point O can be iteratively accumulated from the lateral deformation increment based on the geometric relationship. According to the geometric relationship between lateral deformation and axial deformation, the lateral displacement increment of the anchor rod in each iteration is the product of the axial deformation increment and the cosine of the first angle, divided by the sine of the anchor rod anchoring angle, where the first angle is the anchor rod anchoring angle minus the anchor rod deflection angle at point O calculated in the i-th iteration. By accumulating the lateral displacement increment of the anchor rod in each iteration, the axial displacement at point O of the anchor rod is obtained.

[0118] An anchorage section shear stress distribution diagram considering the influence of lateral displacement on the effective bonding length is established. The anchorage section shear stress distribution diagram includes the grouting fracture section, the softened section, and the effective bonding section.

[0119] Step 3: Determine the deformation mechanism after the anchor bolt yields.

[0120] As the shear displacement increases, the axial force and shear force at point O also increase accordingly. Once the axial force or shear force reaches the limit defined by formula (25), it indicates that the anchor at point A has reached its capacity to resist additional bending moments. Figure 8 As shown, with the continuous increase of shear displacement, the OA part of the anchor bolt can only elongate and rotate around point A.

[0121] After the plastic hinge point of the anchor bolt is formed, the bending moment at point A reaches its maximum allowable limit. The length of the anchor bolt OA section begins to rotate around point A and continuously elongates. Subsequently, the length of the OA section rotates around point A, accompanied by continuous elongation. After each iteration, the length of the OA section, the increment of the deflection angle, the deflection angle, and the total shear displacement can be expressed by the following formulas.

[0122]

[0123] U0=U oe +iΔU (26)

[0124] Among them, w oe L is the deflection angle of the anchor bolt at point O after the rotation angle and plastic hinge point are formed. 1(i) For the i-th iteration, the length of the rock fracture section is calculated, ΔU is the increment of the anchor bolt shear displacement, and L is the length of the rock fracture section. 1(i-1) To calculate the length of the rock fracture segment in the (i-1)th iteration, Δw op(i) w represents the increment of the anchor bolt deflection angle at point O during the (i-1)th iteration. op Let U be the anchor bolt deflection angle at point O, U0 be the anchor bolt shear displacement at point O, and i be the value of the i-th iteration calculation. oe This represents the ultimate shear displacement during the elastic stage of the anchor bolt.

[0125] Since segment OA reaches the yield state under tension, bending, and shear, it is reasonable to consider that the metallic material in segment OA enters the strain hardening stage. After yielding, the analysis of the axial force of the anchor bolt is approximated using a metallic strain hardening model. The strain hardening exponent m is obtained by dividing the natural logarithm of the first ratio by the natural logarithm of the second ratio. The first ratio is the ratio of the axial stress at failure to the axial yield stress at yield, and the second ratio is the ratio of the axial strain at failure to the axial yield strain at yield. The strength coefficient is calculated by multiplying the elastic modulus by an exponential function of the axial yield strain, where the exponent of the exponential function of the axial yield strain is 1-m.

[0126] The interaction point O between the anchor bolt and the shear sliding surface is taken as the failure point. The relationship between the shear force and the axial force at the failure point O is expressed as the sum of the squares of the third ratio and the fourth ratio, which is 1. The third ratio is the ratio of the axial force at failure to the shear force at failure, and the fourth ratio is the ratio of the shear force at failure to the plastic limit tensile force of the anchor bolt.

[0127] Where N 0(n) The axial force at failure is N, and Q0 is the shear force at failure. f =σ f S represents the plastic ultimate tensile force of the anchor bolt. This indicates the plastic limit tensile force of the anchor bolt.

[0128] To minimize the error in each iteration, the derivative of the metal strain hardening model is calculated when calculating the axial force of the anchor bolt. The axial force is approximated by accumulating the product of each local incremental strain and the tangent modulus.

[0129] After the plastic hinge point is formed, the shear force at point O remains constant. However, due to the tension of the plastic section OA, the shear force at point O may increase slightly with the tension of the plastic section. Therefore, the interaction point O between the anchor and the shear sliding surface is considered the failure point.

[0130] Anchor bolt failure typically occurs at the interaction point O between the anchor bolt and the shear sliding surface. According to the Von-Mises failure criterion, the relationship between the shear force and the axial force at the failure point O can be expressed as the sum of the squares of the third ratio and the fourth ratio being 1, where the third ratio is the ratio of the axial force at failure to the shear force at failure, and the fourth ratio is the ratio of the shear force at failure to the plastic ultimate tensile force of the anchor bolt.

[0131] Step 4: Calculate the shear contribution of the anchor bolt.

[0132] like Figure 8 As shown, the shear contribution of the anchor bolt is calculated through the following steps:

[0133] The resultant force of the axial force and the shear force is the sum of the squares of the shear force at failure and the squares of the axial tensile force at failure.

[0134] The arctangent function value of the fifth ratio is used as the loading angle between the shear force and the axial force; wherein, the fifth ratio is the ratio of the shear force at failure to the axial tensile force at failure;

[0135] The cosine and sine values ​​of the second angle are used as the axial force parallel to the shear plane and the shear force perpendicular to the shear plane, respectively; wherein, the second angle is the anchorage angle of the anchor bolt minus the loading angle and deflection angle between the shear force and the axial force;

[0136] The total shear resistance contribution of the anchor bolt is the sum of the products of the axial force parallel to the shear plane and the shear force perpendicular to the shear plane multiplied by the tangent of the joint friction angle.

[0137] This invention also provides an application of the shear contribution calculation method described in any of the above embodiments. Specifically, based on the shear contribution of the anchor bolt calculated by the method described in the above embodiments, anchor bolt contribution curves under different anchorage angles are constructed; and failure early warning is realized based on the anchor bolt contribution curves.

[0138] The application of shear contribution calculation methods in failure early warning is taken as a specific example. The following embodiments of the present invention will verify the feasibility and progressiveness of this application with specific examples.

[0139] The basic parameters for the experiment in this embodiment are as follows: anchor length, anchor Young's modulus, anchor Young's modulus during the strain hardening stage, anchor yield stress, anchor ultimate stress, and anchor failure strain. Table 1 lists the detailed parameters for each set of results, including anchor diameter, uniaxial compressive strength of rock, and joint friction angle. Furthermore, the parameter values ​​in the formula are as follows: a = 1000, n = 1, μ = 0.25, L p =2.5D b L e =LL p -L1, (in )

[0140] Table 1 Experimental parameters

[0141]

[0142]

[0143] The experimental data and calculation results are compared as follows: Figure 9 As shown in 10 and 11, Figure 9 The relationship between anchor bolt contribution and shear displacement is shown for anchoring angles of 90° and anchor bolt diameters of 20, 25, and 40 mm. Figure 10The relationship between anchor bolt contribution and shear displacement is shown for anchoring angles of 60° and anchor bolt diameters of 20 and 25 mm. Figure 11 This paper describes the relationship between anchor contribution and shear displacement when the anchoring angle is 45° and the anchor diameter is 25mm. The method proposed in this application can accurately describe the mechanical response of anchors under shear in anchored rock mass, and can accurately capture its mechanical characteristics for different anchoring angles, especially the inflection point of the anchor contribution versus shear displacement curve. Based on this analytical model and calculation method, a safety assessment of the joint mechanical state of anchored rock mass can be effectively carried out, thus providing effective reference guidance for engineering safety early warning.

[0144] Figure 12 This is an exemplary embodiment illustrating a shear contribution calculation device structure diagram. The shear contribution calculation device 1200 includes:

[0145] The criterion determination module 1210 is used to establish a rectangular coordinate system on both sides of point A in the anchor bolt. On one side of point A, the anchor bolt and the grouting or rock block medium are elastically coupled. The rock anchor bolt is regarded as a semi-infinite elastic foundation beam. The lateral deformation mechanism of the anchor bolt is analyzed, and the criterion for the yielding of the anchor bolt section is determined, expressed as:

[0146]

[0147] Among them, M A Let M be the bending moment at point A. p The elastic limit bending moment is taken as [value]. σ y D represents the anchor bolt yield strength. b Let N be the diameter of the anchor bolt, N0 be the axial force at point O in the anchor bolt, and N p The yield load of the anchor bolt is N. p =σ y S, where S is the cross-sectional area of ​​the anchor bolt;

[0148] The mechanism determination module 1220 is used to determine the axial deformation mechanism of the anchor rod based on the relationship between the displacement at point O in the anchor rod and the axial force.

[0149] The torque calculation module 1230 is used to determine the axial force and shear force at failure based on the lateral deformation mechanism and axial deformation mechanism of the anchor bolt.

[0150] The contribution calculation module 1240 is used to calculate the shear contribution of the anchor bolt based on the axial force and shear force at failure.

[0151] The shear contribution calculation device provided in this embodiment can be used to execute the above-mentioned shear contribution calculation method. Its implementation principle and technical effect are similar, and will not be described again in this embodiment.

[0152] Figure 13This is a block diagram illustrating an electronic device according to an exemplary embodiment. Please refer to [link / reference]. Figure 5 The electronic device 130 may include a processor 131 and a memory 132, wherein the processor 131 and the memory 132 can communicate; for example, the processor 131 and the memory 132 communicate via a communication bus 133, the memory 132 is used to store computer execution instructions, and the processor 131 is used to call the computer execution instructions in the memory to execute the shear contribution calculation method shown in any of the above method embodiments.

[0153] The aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this application can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0154] This application provides a computer-readable storage medium storing computer-executable instructions; when executed by a processor, the computer-executable instructions are used to implement the shear contribution calculation method as described in any of the above embodiments.

[0155] This application provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-described shear contribution calculation method.

[0156] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the following claims.

[0157] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for calculating shear contribution, characterized in that, include: Establish a rectangular coordinate system on both sides of point A in the anchor bolt. On one side of point A, the anchor bolt and the grouting or rock medium are elastically coupled, and the rock anchor bolt is regarded as a semi-infinite elastic foundation beam. On the other side of point A, the grouting or rock medium exceeds the ultimate elastic strain and transitions to plasticity. Analyze the lateral deformation mechanism of the anchor bolt and determine the criterion for the yielding of the anchor bolt section, expressed as: Among them, M A Let M be the bending moment at point A. p The elastic limit bending moment is taken as [value]. σ y D represents the anchor bolt yield strength. b Let N be the diameter of the anchor bolt, N0 be the axial force at point O in the anchor bolt, and N p The yield load of the anchor bolt is N. p =σ y S, where S is the cross-sectional area of ​​the anchor bolt; The axial deformation mechanism of the anchor rod is determined based on the relationship between the displacement at point O in the anchor rod and the axial force; wherein, point O is the intersection of the anchor rod and the connecting surface. The axial force and shear force at failure are determined based on the lateral deformation mechanism and axial deformation mechanism of the anchor bolt. The shear contribution of the anchor bolt is calculated based on the axial force and shear force at failure, specifically including: The square root of the sum of the square of the shear force at failure and the square of the axial tensile force at failure is taken as the resultant force of the axial force and the shear force. The arctangent function value of the fifth ratio is used as the loading angle between the shear force and the axial force; wherein, the fifth ratio is the ratio of the shear force at failure to the axial tensile force at failure; The cosine and sine values ​​of the second angle are multiplied by the resultant forces of the axial force and shear force, respectively, to form the axial force parallel to the shear plane and the shear force perpendicular to the shear plane; wherein, the second angle is the anchorage angle of the anchor bolt minus the loading angle and deflection angle between the shear force and the axial force; The total shear resistance contribution of the anchor bolt is the sum of the products of the axial force parallel to the shear plane and the shear force perpendicular to the shear plane multiplied by the tangent of the joint friction angle.

2. The method according to claim 1, characterized in that, Analyze the lateral deformation mechanism of anchor bolts and determine the yield criterion for anchor bolt sections, specifically including: According to the Winkler foundation beam model, the elastic resistance of the elastically coupled segment is expressed as: p x =kvD b (2) In the formula, p x For grouting material to resist compressive stress or rock to resist compressive stress; σ represents the spring stiffness of the grout or rock, where α is the stiffness coefficient; c ν is the non-shrink compressive strength of the main grouting material or rock; v is the lateral deformation displacement of the anchor bolt. To the right of point A, when the grouting or rock medium exceeds its ultimate elastic strain and transitions to the plastic zone, the elastic resistance depends on the bearing capacity of the grouting or rock, and is expressed by the following formula: p u nσ c D b (3) In the formula, p u The bearing capacity of the grout or rock; n≥1 is the bearing capacity coefficient of the main grout or rock; D b The diameter of the anchor bolt; According to the Winkler elastic foundation beam model, the lateral deformation of the anchor rod to the left of point A satisfies the differential equation expressed by formula (4): Where EI is the bending stiffness of the anchor rod; By solving formula (4), the lateral displacement function of the anchor rod is obtained as follows: v(x)=e -βx (c1cosβx+c2sinβx)+e βx (c3cosβx+c4sinβx) (5) in, 1 / β represents the characteristic length of the beam; c1, c2, c3, and c4 are undetermined coefficients; When the coefficients c3 and c4 are 0, formula (5) simplifies to: v e (x)=A'e -βx cos(βx+B) (6) Among them, v e (x) is the lateral displacement function of the anchor bolt to the left of point A, and A' and B are undetermined coefficients; By differentiating formula (6), the deflection angle function of the anchor rod is determined as follows: w e (x)=v′ e (x)=-A'βe -βx [cos(βx+B)+sin(βx+B)] (7) Among them, v' e (x) is the first derivative of the lateral displacement function of the anchor bolt to the left of point A; Based on the Euler-Bernoulli beam theory, determine the relationship between bending moment and shear force: M e (x)=-EIv″ e (x)=-2A'EIβ 2 e -βx sin(βx+B) (8) Q e (x)=EIv″′ e (x)=2AEIβ 3 and -βx [cos(βx+B)-sin(βx+B)] (9) Among them, M e (x) is the bending moment function of the anchor section to the left of point A, v″ e (x) is the second derivative of the lateral displacement function of the anchor bolt to the left of point A, Q. e (x) represents the shear force function of the anchor section to the left of point A, v″′ e (x) is the third derivative of the lateral displacement function of the anchor bolt to the left of point A; Based on the coupling effect between axial tension and bending, determine the shear force function and bending moment function of the anchor section to the right of point A; When the sum of the stress in the outermost fiber on the tension side of the anchor bolt cross section and the cross section stress generated by the axial tensile force is less than a set value, the upper fiber of the anchor bolt cross section satisfies the first condition; wherein, the first condition is that the sum of the stress in the outermost fiber on the tension side of the anchor bolt cross section and the cross section stress generated by the axial tensile force is equal to the stress at the edge of the anchor bolt cross section. Based on the relationship between the curvature and strain of the anchor bolt cross-section edge and the first condition, a formula for calculating the curvature of the anchor bolt cross-section is determined; in the formula for calculating the curvature of the anchor bolt cross-section, the curvature of the anchor bolt cross-section is calculated based on the bending moment of the anchor bolt cross-section at point x and the position of the neutral layer. The position of the neutral layer is the ratio of the product of the axial tensile force and the moment of inertia of the anchor section to the product of the bending moment of the anchor cross section at point x and the area of ​​the anchor cross section. By integrating the formula for calculating the curvature of the anchor bolt cross section, the deflection angle and lateral displacement function of the anchor bolt are obtained; w(x)=w p (x)+C1 (10) v(x)=v p (x)+C1x+C2 (11) Where C1 and C2 are undetermined coefficients. This represents the particular solution of the lateral displacement of the anchor bolt; This represents the particular solution of the anchor bolt deflection angle; Substituting the boundary conditions for shear force, bending moment, displacement, and deflection angle at point A, we obtain: Where Q0 is the anchor shear force at point O, and M e (0) is the bending moment of the anchor section to the left of point A, M p (0) represents the bending moment at the anchor section to the right of point A, Q. e (0) represents the anchor shear force at point A, Q p (L1) represents the anchor shear force at point O, w e (0) represents the lateral deflection angle of the anchor bolt at the left side of point A, w p (0) is the lateral deflection angle of the anchor bolt at the right side of point A, v e (0) represents the lateral displacement of the anchor bolt to the left of point A, v p (0) represents the lateral displacement of the anchor bolt to the right of point A; The deflection angle and lateral displacement at point O are obtained by the following formulas: Among them, w p (L1) represents the anchor bolt deflection angle at point O, v p (L1) represents the lateral displacement of the anchor bolt at point O; The relationship between shear displacement and lateral displacement is derived from the following formula: Where U0 is the shear displacement of the anchor at point O, v0 is the lateral component of the shear displacement of the anchor at point O, and θ is the anchorage angle of the anchor.

3. The method according to claim 2, characterized in that, Based on the relationship between the displacement at point O in the anchor bolt and the axial force, the axial deformation mechanism of the anchor bolt is determined, specifically including: An anchorage section shear stress distribution diagram considering the influence of lateral displacement on the effective bonding length is established. The anchorage section shear stress distribution diagram includes the grouting fracture section, the softened section, and the effective bonding section. Based on the shear stress distribution of the effective bonding section, softened section, and grouting fracture section, the axial stresses at points x0, L1, and O on the anchor rod are obtained by integrating equations (16)-(18), and L is obtained by equations (19)-(21). e L p Axial deformation of L1: Where, σ e To effectively control the axial stress at the junction of the bonding section and the softened section, σ p The axial stress is at the junction of the softened section and the grouting and breaking section, σ0 is the axial stress of the anchor bolt at point O, and u e To effectively combine the axial elongation of the segment, u p denoted as axial elongation of the softened section, u1 as axial elongation of the grouting and breaking section, and c as the interface damage coefficient of the effective bonding section. The axial displacement of point A on the anchor bolt is the sum of the axial elongation of the effective joint section, the axial elongation of the softened section, and the axial elongation of the grouting and breaking section; Calculate the axial stress of the anchor at point O based on the axial displacement of point A on the anchor and equations (16)-(18); Before the plastic hinge point appears, the relationship between the axial force and axial displacement at point O on the anchor bolt is expressed as: Based on the geometric relationship between lateral deformation and axial deformation, the lateral displacement increment of the anchor rod in each iteration is the product of the axial deformation increment and the cosine of the first angle, divided by the sine of the anchor rod anchoring angle. The first angle is the anchor rod anchoring angle minus the anchor rod deflection angle at point O calculated in the i-th iteration. The axial displacement at point O of the anchor rod is obtained by accumulating the lateral displacement increment of the anchor rod in each iteration.

4. A shear contribution calculation device, based on the method of any one of claims 1 to 3, characterized in that, include: The criterion determination module is used to establish a rectangular coordinate system on both sides of point A in the anchor bolt. On one side of point A, the anchor bolt and the grouting or rock block medium are elastically coupled. The rock anchor bolt is regarded as a semi-infinite elastic foundation beam. The lateral deformation mechanism of the anchor bolt is analyzed, and the criterion for the yielding of the anchor bolt section is determined, expressed as: Among them, M A Let M be the bending moment at point A. p The elastic limit bending moment is taken as [value]. σ y D represents the anchor bolt yield strength. b Let N be the diameter of the anchor bolt, N0 be the axial force at point O in the anchor bolt, and N p The yield load of the anchor bolt is N. p =σ y S, where S is the cross-sectional area of ​​the anchor bolt; The mechanism determination module is used to determine the axial deformation mechanism of the anchor rod based on the relationship between the displacement at point O and the axial force in the anchor rod. The torque calculation module is used to determine the axial force and shear force at failure based on the lateral deformation mechanism and axial deformation mechanism of the anchor bolt. The contribution calculation module is used to calculate the shear contribution of the anchor bolt based on the axial force and shear force at the time of failure.

5. An electronic device, characterized in that, The electronic device includes: a processor and a memory; the memory is used to store instructions; the processor is used to execute the instructions in the memory, causing the electronic device to perform the method as described in any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1 to 3.

7. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the method as described in any one of claims 1 to 3.

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