Shearing resistance contribution calculation method and device, equipment and storage medium

Abstract

The invention provides a shear resistance contribution calculation method and device, equipment and a storage medium, and belongs to the technical field of mechanical analysis. The method comprises the steps that rectangular coordinate systems are established on the two sides of a point A in the anchor rod respectively, the anchor rod is elastically coupled with grouting or rock mass media on one side of the point A, the rock anchor rod is regarded as a semi-infinite elastic foundation beam, the lateral deformation mechanism of the anchor rod is analyzed, the section yield criterion of the anchor rod is determined, and according to the relation between the displacement of the point O in the anchor rod and the axial force, the axial force of the anchor rod is determined. Determining an axial deformation mechanism of the anchor rod; determining an axial force and a shearing force during failure based on the lateral deformation mechanism and the axial deformation mechanism of the anchor rod; and calculating the shearing resistance contribution of the anchor rod according to the axial force and the shearing force during failure. According to the method, the influence of anchoring interface stress distribution and large elastic-plastic deformation of the anchor rod can be comprehensively considered, so that the shear contribution and the potential failure risk of the deep rock anchor rod supporting system can be evaluated more accurately and comprehensively.

Description

Technical Field

[0001] The present application relates to the technical field of mechanical analysis, and in particular to a shear contribution calculation method, device, equipment and storage medium. Background Art

[0002] At present, the depth of coal mining in the world has reached 1500m, the depth of geothermal mining has exceeded 3000m, the depth of non-ferrous metal mining has exceeded 4000m, and the depth of oil and gas resource mining has reached 7500m. Deep rock mass often has various weak faults and weak structural surfaces. Therefore, in order to safely mine coal resources, it is often necessary to support the deep excavated rock mass. As one of the economical and efficient support methods, anchor support has been widely used in the field of coal mining, especially fully grouted anchor bolts, which are usually the preferred anchor bolt type for supporting or stabilizing loose rock mass in most rock slopes and underground excavations. Anchor bolts can not only transmit the tensile stress of the surrounding rock, but also provide additional shear resistance to prevent the sliding of joints or weak structural surfaces in the rock mass. Therefore, accurately evaluating the shear contribution and potential failure risk of fully grouted anchor bolts is of great significance to ensure the safety of coal mining projects.

[0003] At present, there are mainly two methods for analyzing the mechanical state of anchor joints: theoretical analytical model method and numerical modeling method. As for theoretical analytical modeling method, the existing theoretical analytical model is difficult to accurately give the key points of normal operation and failure warning of anchored rock mass; while the numerical modeling analysis method usually uses commercial finite element software for three-dimensional modeling calculation, but due to the complexity of three-dimensional finite element modeling and high computing cost, it leads to low engineering timeliness and difficulty in guiding 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] The present application provides a method, device, equipment and storage medium for calculating the shear contribution. The existing experimental, numerical and theoretical analytical methods all have their limitations and shortcomings, such as low calculation efficiency and high operation cost, and the existing theoretical analytical methods cannot accurately indicate the working state of the anchored rock mass. The present invention aims to propose a new theoretical analytical analysis method, which can comprehensively consider the influence of the anchoring interface stress distribution and the large elastic-plastic deformation of the anchor rod, so as to achieve a more accurate and comprehensive evaluation of the shear contribution and potential failure risk of the deep rock anchor support system. By solving the above technical problems, the present invention can significantly improve the efficiency and accuracy of engineering analysis, thereby providing effective technical support for ensuring safety and stability in the deep rock mining process.

[0005] In a first aspect, the present application provides a method for calculating shear contribution, comprising:

[0006] A rectangular coordinate system is established on both sides of point A in the anchor. On one side of point A, the anchor and the grouting or rock medium are elastically coupled. The rock anchor is regarded as a semi-infinite elastic foundation beam. The lateral deformation mechanism of the anchor is analyzed and the yield criterion of the anchor section is determined, which is expressed as:

[0007]

[0008] Among them, M A is the bending moment at point A, M p is the elastic limit bending moment, which is σ y is the yield strength of the anchor rod, D b is the diameter of the anchor rod, N0 is the axial force at point O in the anchor rod, N p is the yield load of the anchor rod, which is N p =σ y S, S is the cross-sectional area of ​​the anchor rod;

[0009] According to the relationship between the displacement at point O and the axial force in the anchor bolt, the axial deformation mechanism of the anchor bolt is determined;

[0010] Determining the axial force and shear force at failure based on the lateral deformation mechanism of the anchor rod and the axial deformation mechanism of the anchor rod;

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

[0012] In a second aspect, the present application provides a shear contribution calculation device, including: a criterion determination module, which is used to establish a rectangular coordinate system on both sides of point A in the anchor rod, and on one side of point A, the anchor rod and the grouting or rock block medium are elastically coupled, and the rock anchor rod is regarded as a semi-infinite elastic foundation beam, and the lateral deformation mechanism of the anchor rod is analyzed to determine the criterion of the anchor rod section yield, which is expressed as:

[0013]

[0014] Among them, M A is the bending moment at point A, M p is the elastic limit bending moment, which is σ y is the yield strength of the anchor rod, D b is the diameter of the anchor rod, N0 is the axial force at point O in the anchor rod, N p is the yield load of the anchor rod, which is N p =σ y S, S is the cross-sectional area of ​​the anchor rod;

[0015] The mechanism determination module is used to determine the axial deformation mechanism of the anchor bolt according to the relationship between the displacement at point O and the axial force in the anchor bolt;

[0016] A moment calculation module, used to determine the axial force and shear force at failure based on the lateral deformation mechanism of the anchor rod and the axial deformation mechanism of the anchor rod;

[0017] Contribution calculation module, used to calculate the shear contribution of the anchor based on the axial force and shear force at failure.

[0018] In a third aspect, the present application provides an electronic device, comprising: a processor and a memory; the memory is used to store instructions; the processor is used to execute the instructions in the memory, so that the electronic device executes the method described in the first aspect.

[0019] In a fourth aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are executed by a processor, they are used to implement the method described in the first aspect.

[0020] In a fifth aspect, the present application provides a computer program product, including a computer program, which implements the method described in the first aspect when executed by a processor.

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

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

[0023] 2. Comprehensive evaluation of anchor performance: The patent of this invention can not only comprehensively consider the constitutive model of anchor interface stress distribution, but also consider the influence of large elastic-plastic deformation in the local area of ​​the anchor. This makes it possible to conduct a more accurate and comprehensive evaluation of the shear contribution and failure risk of the anchor rock mass, which helps to improve the safety of coal mining projects.

[0024] 3. Versatility and practicability: The calculation method proposed in this patent has high versatility and practicability. It can be used not only in the field of coal mining, but also in other rock slopes and underground excavation projects. This versatility enables the technical solution to provide important technical support and theoretical guidance for projects in different fields.

[0025] 4. Efficient guidance of engineering construction: Compared with the existing theoretical calculation methods and numerical modeling methods, the technical solution of the present invention has higher calculation efficiency and engineering guidance. It can quickly and accurately evaluate the stability of the anchor support system, provide an important reference for engineering construction, and reduce the time and cost of engineering construction. BRIEF DESCRIPTION OF THE DRAWINGS

[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 of a coordinate system established at point A in an anchor rod is shown as an exemplary embodiment;

[0028] Figure 2 is a schematic diagram of an anchor rod interface shown in an exemplary embodiment;

[0029] Figure 3 A force analysis diagram showing an exemplary embodiment after simplifying a circular cross section into a rectangular cross section;

[0030] Figure 4 FIG. 1 is a force analysis diagram of an anchor rod at an intersection point O of the anchor rod and the connection surface before the plastic hinge point appears, shown in an exemplary embodiment;

[0031] Figure 5 The diagram is a shear stress distribution diagram of the anchoring section considering the effect of lateral displacement on the effective bonding length according to an exemplary embodiment;

[0032] Figure 6 L1, L2 are shown as an exemplary embodiment. p and L e They represent the interfacial stress distributions of the grouting crushing section, softening section, and effective bonding section respectively;

[0033] Figure 7 is a schematic diagram of a calculation process of the axial deformation of point O according to an exemplary embodiment;

[0034] Figure 8 is a schematic diagram of the OA portion of the anchor bolt as the shear displacement continues to increase according to an exemplary embodiment;

[0035] Fig. 9 An exemplary embodiment shows the relationship between anchor contribution and shear displacement when the anchor angle is 90° and the anchor diameter is 20, 25 and 40 mm;

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

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

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

[0039] Fig.13 The present invention is a block diagram of an electronic device showing an exemplary embodiment.

[0040] The above drawings have shown clear embodiments of the present application, which will be described in more detail later. These drawings and text descriptions are not intended to limit the scope of the present application in any way, but to illustrate the concept of the present application to those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0041] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application. Instead, they are merely examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0042] It should be noted that the links involved in this application and the related information in the links, platform-related information, etc. (including but not limited to data used for analysis, stored data, displayed data, etc.) are all information and data that are understood and authorized by the relevant users or fully authorized by all parties, and the collection, use, processing, transmission, provision, disclosure and application of the relevant data comply with the laws, regulations and standards of relevant countries and regions, take necessary confidentiality measures, do not violate public order and good morals, and comply with the principles of legality, legitimacy and necessity.

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

[0044] The shear contribution calculation method provided in the present application can be implemented in any electronic device with data processing capabilities, or in a shear contribution calculation system. It should be noted that the shear contribution calculation system can be deployed separately on an electronic device in any environment (for example, separately deployed on an edge server in an edge environment), or all deployed in a cloud environment, or distributedly deployed in different environments.

[0045] For example, the anti-shear contribution calculation system can be logically divided into multiple parts, each with different functions. The parts in the anti-shear contribution calculation system can be deployed in any two or three of the electronic device (located on the user side, such as the client), the edge environment, and the cloud environment. The edge environment is an environment that includes a collection of edge electronic devices that are close to the electronic device. The edge electronic devices include: edge servers, edge stations with computing power, etc. The various parts of the anti-shear contribution calculation system deployed in different environments or devices work together to realize the functions of the data processing platform.

[0046] It should be understood that the present application does not make a restrictive division on which parts of the anti-shear contribution computing system are deployed in what specific environment. In actual application, it can be adaptively deployed according to the computing power of the electronic device, the resource occupancy of the edge environment and the cloud environment, or the specific application requirements.

[0047] Aiming at 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 high operating costs, the analysis efficiency is not high, which makes it impossible to quickly analyze the operating status of the anchored rock mass.

[0049] 2. Existing theoretical calculation methods usually ignore the constitutive structure of the interface stress in the anchoring section of the anchor and the plastic deformation of the anchor metal material.

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

[0051] An embodiment of the present invention provides a method for calculating shear contribution of an anchored rock mass and for early warning of failure, the method comprising the following steps 1 to 4.

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

[0053] In the field of geotechnical engineering, in most cases, the strength of the anchor material is much higher than that of the grouting material or rock material. Therefore, when the anchor joint is subjected to shear load, the grouting material or rock medium will first undergo plastic deformation before the anchor plastic yields. Figure 1 As shown in the figure, a rectangular coordinate system is established on the left and right sides of point A. On the left side 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 Winkel foundation beam model, the elastic resistance of the elastic coupling section (x>L1) can be expressed as:

[0054] p x =kvD b (2)

[0055] In the formula, p x For grouting material compression or rock compression; is the spring stiffness of grouting or rock, a is the stiffness coefficient; σ c is the non-shrinkage compressive strength of the main grouting material or rock; v is the lateral deformation displacement of the anchor rod.

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

[0057] p u =nσ c D b (3)

[0058] Where p u is the bearing capacity of grouting (or rock); n≥1 is the bearing capacity coefficient of the main grouting body (rock); D b is the anchor rod diameter.

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

[0060]

[0061] Where, EI is the bending stiffness of the anchor, p x is the reaction force of the surrounding rock of the anchor.

[0062] By solving formula (4), we can get the general solution:

[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 unknown coefficients.

[0065] For the left side of point A, when x approaches positive infinity, the lateral deformation v(x) of the anchor rod approaches 0 infinitely, so the coefficients c3 and c4 can be obtained to be 0. Therefore, formula (4) can be simplified to

[0066] v e (x) = Ae -βx cos(βx+B) (6)

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

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

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

[0070] Among them, v′ e (x) is the first-order derivative function of the lateral displacement function of the anchor rod on the left side of point A.

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

[0072] M e (x)=-EIv e ″(x)=-2AEIβ 2 e -βx sin(βx+B) (8)

[0073] Q e (x) = EIv e ″′(x)=2AEIβ 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 on the left side of point A, v′ e ′(x) is the second-order derivative function of the lateral displacement function of the anchor rod on the left side of point A, Q e (x) is the shear force function of the anchor section on the left side of point A, v′ e "(x) is the third-order derivative function of the lateral displacement function of the anchor rod on the left side of point A.

[0075] like Figure 1 As shown, to the right of point A, the grouting (rock) is in the plastic zone. The elastic resistance can be regarded as a constant value, as shown in formula (2). Before reaching the elastic limit bending moment of the anchor section, the bending moment at point A gradually increases with the expansion of the plastic zone of the grouting (rock). 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 be subjected to tensile-flexural effects and shear loads until it breaks. Since the influence of shear effect on the lateral deformation and deflection angle of the anchor is significantly smaller than that of bending, the influence of shear deformation on the lateral behavior is not considered when analyzing the lateral deformation of the anchor. As Figure 2 As shown in the figure, however, the existence of axial tension will significantly affect the cross-sectional stress distribution of the anchor under the action of bending moment. Therefore, when analyzing the lateral deformation and deflection of the anchor, the coupling effect between axial tension and bending must be considered. According to the coupling effect between axial tension and bending, the shear force function of the anchor section on the right side of point A and the bending moment function of the anchor section on the right side of point A are determined.

[0076] Based on the relationship between the curvature and strain of the cross-section edge of the anchor rod and the first condition, a calculation formula for the cross-section curvature of the anchor rod is determined; in the calculation formula for the cross-section curvature of the anchor rod, the cross-section curvature of the anchor rod is calculated according to the bending moment of the cross-section of the anchor rod 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 tension and the moment of inertia of the anchor cross 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 (9)

[0079] Q(x)=Q o -p u (L1-x)=p u x (10)

[0080]

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

[0082] Since both shear and axial forces are in dynamic variation, determining the stress state of the anchor cross section at any given point on the OA section is a major challenge.

[0083] The deformation of the anchor rod under the tensile bending effect is simplified by the elastic-plastic deformation theory of rectangular cross-section beams. Figure 3 As shown, the circular section is simplified into a rectangular section to analyze the relationship between the curvature and the bending moment at any section of the anchor OA segment.

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

[0085] Since the cross section is still in the elastic stage, Hooke's law is strictly followed. ( σ x =Eε x ). Therefore, based on the relationship between the curvature of the edge of the anchor cross section and the strain and the first condition, the calculation formula of the anchor cross section curvature is determined; in the calculation formula of the anchor cross section curvature, the anchor cross section curvature is calculated according to the bending moment of the anchor 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 tension and the moment of inertia of the anchor cross section to the product of the bending moment of the anchor cross section at point x and the area of ​​the anchor cross section.

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

[0087]

[0088] Among them, C1 and C2 are unknown 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, It represents the special solution of the lateral displacement of the anchor bolt;

[0093] Represents the special solution part of the anchor deflection angle.

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

[0095]

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

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

[0098]

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

[0100] like Figure 4 As shown in Figure 2, before the plastic hinge appears, the anchor expression at the intersection O of the anchor and the connection surface can be obtained by equations (22) and (23). The relationship between shear displacement and lateral displacement can be obtained by the following formula:

[0101]

[0102] Among them, U0 is the shear displacement of the anchor rod at point O, v0 is the lateral component of the shear displacement of the anchor rod at point O, and θ is the anchoring angle of the anchor rod.

[0103] Point A has zero shear force and maximum bending moment, making it particularly prone to transformation into a plastic hinge. Determining the stress distribution of the cross section at point A is a considerable challenge and is difficult to achieve in theory. This is because the cross section is subject to tensile bending effects, and changes in the stress state of the cross section are related to the early loading history, while the axial force and bending moment are in a dynamic change 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 location 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 formula (1).

[0104]

[0105] Among them, M A is the bending moment at point A, M p is the elastic limit bending moment, which is 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 is the yield load of the anchor rod, which is N p =σ y S.

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

[0107] For anchor rods in shearing process, in the initial stage of shear slip failure, the axial force of the anchor rod is highly sensitive to the axial displacement. In order to analyze the relationship between the axial displacement and axial force of the anchor rod O point, Figure 5 is the shear stress distribution diagram of the anchor section considering the effect of lateral displacement on the effective bonding length, L1, L p and L e They represent the lengths of the grouting crushing section, softening section and effective bonding section respectively. Figure 6 L1, L p and L e Respectively represent the interfacial stress distribution of the grouting crushing section, softening section and effective bonding section.

[0108] for Figure 6 Determine the shear stress distribution of the effective joint section shown in (a).

[0109] for Figure 6 The shear stress distribution of the softening zone is determined in (b).

[0110] for Figure 6 The shear stress distribution of the softening zone is determined in (c).

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

[0112]

[0113] Among them, σ e is the axial stress at the junction of the effective bonding section and the softening section, σ p is the axial stress at the junction of the softening section and the grouting crushing section, σ0 is the axial stress of the anchor rod at point O, and u e is the axial extension of the effective joint section, u p is the axial elongation of the softening section, u1 is the axial elongation of the grouting crushing section, and c is the interface damage coefficient of the effective bonding section;

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

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

[0116]

[0117] like Figure 7As shown in the figure, the calculation process of the axial deformation at point O can be iteratively accumulated from the lateral deformation increment according to the geometric relationship. According to the geometric relationship between the lateral deformation and the axial deformation, the lateral displacement increment of the anchor rod in each iteration is the product of the axial deformation increment and the cosine value of the first angle divided by the sine value 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, and the lateral displacement increment of the anchor rod in each iteration is accumulated to obtain the axial displacement at point O of the anchor rod.

[0118] Establishing a shear stress distribution diagram of the anchoring section considering the influence of the lateral displacement on the effective bonding length, wherein the shear stress distribution diagram of the anchoring section includes a grouting crushing section, a softening section and an effective bonding section;

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

[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 means that the anchor at point A has reached the capacity to resist the additional bending moment. Figure 8 As shown in the figure, with the continuous increase of shear displacement, the OA part of the anchor can only elongate and rotate around point A.

[0121] After the plastic hinge of the anchor is formed, the bending moment at point A reaches the maximum allowable limit. The length of the anchor OA part begins to rotate around point A and continuously lengthens. Subsequently, the length of the OA part rotates around point A and continues to elongate. After each iteration, the length of the OA part, the increment of the deflection angle, the deflection angle, and the total shear displacement can be expressed by the following formula.

[0122]

[0123] U0=U oe +iΔU (26)

[0124] Among them, w oe The shear displacement of the anchor point O after the rotation angle and plastic hinge point are formed is the shear displacement increment of each iteration, L 1(i) is the length of the rock crushing section calculated for the i-th iteration, △U is the anchor shear displacement increment, L 1(i-1) Calculate the length of the rock crushing section for the i-1th iteration, △w op(i) is the increment of anchor deflection angle at point O during the i-1th iteration calculation, w op is the anchor rod deflection angle at point O, U0 is the anchor rod shear displacement at point O, i is the i-th iteration calculation, U oe is the ultimate shear displacement of the anchor in the elastic stage.

[0125] Since the OA segment reaches a yield state under tension, bending and shearing, it is reasonable to consider that the metal material of the OA segment enters the strain hardening stage. After yielding, the analysis of the axial force of the anchor bolt is approximated by the metal strain hardening model. The natural logarithm of the first ratio is divided by the natural logarithm of the second ratio to obtain the strain hardening index m. The first ratio is the ratio of the axial stress at failure to the axial yield stress at yielding, and the second ratio is the ratio of the axial strain at failure to the axial yield strain at yielding; the strength coefficient is calculated based on the product of the elastic modulus and the exponential function of the axial yield strain, and the exponent of the exponential function of the axial yield strain is 1-m.

[0126] The interaction point O between the anchor rod and the shear sliding surface is taken as the failure point, and the relationship between the shear force and the axial force at the failure point O is expressed as the sum of the square of the third ratio and the square of the fourth ratio being 1, wherein 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 rod;

[0127] Where N 0(n) is the axial force at failure, Q0 is the shear force at failure, N f =σ f S, represents the plastic limit tension of the anchor rod, Indicates the plastic limit tensile force of the anchor rod.

[0128] In order 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 is formed, the shear force at point O remains unchanged. However, due to the stretching of the plastic section OA, the shear force at point O may increase slightly with the stretching of the plastic section. Therefore, the interaction point O between the anchor and the shear sliding surface is used as the failure point.

[0130] Anchor failure usually occurs at the interaction point O between the anchor 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 square of the third ratio and the square of the fourth ratio is 1, wherein 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.

[0131] Step 4: Calculation of anchor shear contribution.

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

[0133] The resultant force of axial force and shear force is taken as the square difference of the sum of the square of shear force at failure and the square of axial tension force at failure;

[0134] The inverse tangent 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 tension at failure;

[0135] The cosine value and sine value 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 anchoring angle of the anchor rod minus the loading angle and the deflection angle between the shear force and the axial force;

[0136] The total shear contribution of the anchor bolt is the sum 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] An embodiment of the present invention also provides an application of the shear contribution calculation method described in any of the above embodiments. Specifically, based on the anchor shear contribution calculated by the method described in the above embodiments, an anchor contribution curve under different anchoring angles is constructed; and failure warning is achieved based on the anchor contribution curve.

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

[0139] The basic parameters of the test in this embodiment are as follows: anchor length, anchor Young's modulus, anchor Young's modulus in the strain hardening stage, anchor yield stress, anchor ultimate stress and anchor failure strain. Table 1 lists the detailed parameters of each set of results, including anchor diameter, rock uniaxial compressive strength and joint friction angle. In addition, 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 ) Table 1 Test parameters

[0140]

[0141]

[0142] The comparison between the experimental data and the calculated results is shown in Fig. 9 , 10, 11, Fig. 9 The relationship between anchor contribution and shear displacement when the anchor angle is 90° and the anchor diameter is 20, 25 and 40 mm. Fig.10The relationship between anchor contribution and shear displacement when the anchor angle is 60° and the anchor diameter is 20 and 25 mm. Fig.11 The relationship between anchor contribution and shear displacement when the anchor angle is 45° and the anchor diameter is 25 mm. The method proposed in this application can accurately describe the mechanical response of the anchor under shear of the anchored rock mass, and can accurately capture its mechanical characteristics at different anchor angles, especially the inflection point of the anchor contribution along the shear displacement curve. Based on this analysis model calculation method, an effective safety assessment can be conducted on the mechanical state of the anchored rock joints, thereby providing effective reference guidance for engineering safety warning.

[0143] Fig.12 1 is a structural diagram of a shear contribution calculation device shown in an exemplary embodiment. The shear contribution calculation device 1200 includes:

[0144] The criterion determination module 1210 is used to establish a rectangular coordinate system on both sides of point A in the anchor rod. On one side of point A, the anchor rod and the grouting or rock medium are elastically coupled. The rock anchor rod is regarded as a semi-infinite elastic foundation beam, and the lateral deformation mechanism of the anchor rod is analyzed to determine the criterion for the yield of the anchor rod section, which is expressed as:

[0145]

[0146] Among them, M A is the bending moment at point A, M p is the elastic limit bending moment, which is σ y is the yield strength of the anchor rod, D b is the diameter of the anchor rod, N0 is the axial force at point O in the anchor rod, N p is the yield load of the anchor rod, which is N p =σ y S, S is the cross-sectional area of ​​the anchor rod;

[0147] The mechanism determination module 1220 is used to determine the axial deformation mechanism of the anchor rod according to the relationship between the displacement at point O in the anchor rod and the axial force;

[0148] A moment calculation module 1230, for determining the axial force and shear force at failure based on the anchor lateral deformation mechanism and the anchor axial deformation mechanism;

[0149] The contribution calculation module 1240 is used to calculate the shear contribution of the anchor rod according to the axial force and shear force at the time of failure.

[0150] 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 effects are similar, and this embodiment will not be repeated here.

[0151] Fig.13is a block diagram of an electronic device according to an exemplary embodiment. 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; exemplarily, 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.

[0152] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), etc. A general-purpose processor may be a microprocessor or any conventional processor, etc. The steps of the method disclosed in the present application may be directly implemented as being executed by a hardware processor, or may be implemented by a combination of hardware and software modules in the processor.

[0153] The present application provides a computer-readable storage medium, on which computer-executable instructions are stored; when the computer-executable instructions are executed by a processor, they are used to implement a shear contribution calculation method as described in any of the above embodiments.

[0154] An embodiment of the present application provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the above-mentioned shear contribution calculation method is implemented.

[0155] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the invention disclosed herein. The present application is intended to cover any modification, use or adaptation of the present application, which follows the general principles of the present application and includes common knowledge or customary techniques in the art that are not disclosed in the present application. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the following claims.

[0156] It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A method for calculating shear contribution, characterized in that: include: A rectangular coordinate system is established on both sides of point A in the anchor. On one side of point A, the anchor and the grouting or rock medium are elastically coupled. The rock anchor is regarded as a semi-infinite elastic foundation beam. The lateral deformation mechanism of the anchor is analyzed and the yield criterion of the anchor section is determined, which is expressed as: Among them, M A is the bending moment at point A, M p is the elastic limit bending moment, which is σ y is the yield strength of the anchor rod, D b is the diameter of the anchor rod, N0 is the axial force at point O in the anchor rod, N p is the yield load of the anchor rod, which is N p =σ y S, S is the cross-sectional area of ​​the anchor rod; According to the relationship between the displacement at point O and the axial force in the anchor bolt, the axial deformation mechanism of the anchor bolt is determined; Determining the axial force and shear force at failure based on the lateral deformation mechanism of the anchor rod and the axial deformation mechanism of the anchor rod; The shear contribution of the anchor is calculated based on the axial force and shear force at failure.

2. The method according to claim 1, characterized in that Analyze the lateral deformation mechanism of the anchor and determine the criteria for the yield of the anchor section, including: According to the Winkel foundation beam model, the elastic resistance of the elastic coupling section is expressed as: p x =kvD b (2) In the formula, p x For grouting material compression or rock compression; is the spring stiffness of grouting or rock, a is the stiffness coefficient; σ c is the non-shrinkage compressive strength of the main grouting material or rock; v is the lateral deformation displacement of the anchor; On the right side of point A, when the grouting or rock medium exceeds the ultimate elastic strain and transitions to the plastic zone, the elastic resistance depends on the bearing capacity of the grouting or rock, which is expressed by the following formula: p u nσ c D b (3) Where p u is the bearing capacity of grouting or rock; n≥1 is the bearing capacity coefficient of the main grouting body or rock; D b is the anchor diameter; 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 expressed by formula (4): Where, EI is the bending stiffness of the anchor, p x is the surrounding rock reaction force of the anchor; By solving formula (4), the lateral deformation 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 unknown coefficients. When coefficients c3 and c4 are 0, formula (5) is simplified to: v e (x)=Ae -βx cos(βx+B) (6) Among them, v e (x) is the lateral displacement function of the anchor rod on the left side of point A, and A and B are unknown coefficients; By deriving formula (5), the deflection angle function of the anchor rod is determined as follows: w e (x)=v e ′(x)=-Aβe -βx [cos(βx+B)+sin(βx+B)] (7) Among them, v′ e (x) is the first-order derivative function of the lateral displacement function of the anchor rod on the left side of point A; According to the Euler-Bernoulli beam theory, the relationship between bending moment and shear force is determined as: M e (x)=-EIv e ″(x)=-2AEIβ 2 e -βx sin(βx+B) (8) Q e (x)=EIv e ″′(x)=2AEIβ 3 e -βx [cos(βx+B)-sin(βx+B)] (9) Among them, M e (x) is the bending moment function of the anchor section on the left side of point A, v′ e ′(x) is the second-order derivative function of the lateral displacement function of the anchor rod on the left side of point A, Q e (x) is the shear force function of the anchor section on the left side of point A, v′ e "(x) is the third-order derivative function of the lateral displacement function of the anchor rod on the left side of point A; According to the coupling effect between axial tension and bending, the shear force function of the anchor section on the right side of point A and the bending moment function of the anchor section on the right side of point A are determined; When the sum of the stress of the outermost fiber layer on the tension side of the anchor cross section and the cross-sectional stress generated by the axial tension is less than a set value, the upper fiber of the anchor cross section meets the first condition; wherein the first condition is that the sum of the stress of the outermost fiber layer on the tension side of the anchor cross section and the cross-sectional stress generated by the axial tension is equal to the stress at the edge of the anchor cross section; Based on the relationship between the curvature and strain of the cross-section edge of the anchor rod and the first condition, a calculation formula for the cross-section curvature of the anchor rod is determined; in the calculation formula for the cross-section curvature of the anchor rod, the cross-section curvature of the anchor rod is calculated according to the bending moment of the cross-section of the anchor rod 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 tension and the moment of inertia of the anchor cross section to the product of the bending moment of the anchor cross section at point x and the area of ​​the anchor cross section; Integrating the calculation formula of the cross-sectional curvature of the anchor rod to obtain the deflection angle and lateral displacement function of the anchor rod; w(x)=w p (x)+C1 (10) v(x)=v p (x)+C1x+C2 (11) in, It represents the special solution of the lateral displacement of the anchor bolt; It represents the special solution part of the anchor deflection angle; Substituting the boundary conditions of shear force, bending moment, displacement and deflection angle at point A into the equation: Among them, M e (0) Bending moment of the anchor section on the left side of point A, M p (0) Bending moment of the anchor section on the right side of point A, Q e (0) is the anchor shear force at point A, Q p (L1) is the anchor shear force at point O, w e (0) is the lateral displacement of the anchor rod on the left side of point A, w p (0) is the lateral displacement of the anchor rod on the right side of point A, v e (0) is the lateral deflection angle of the anchor rod on the left side of point A, v p (0) is the lateral deflection angle of the anchor rod on the right side of point A; The deflection angle and lateral displacement of point O are obtained by the following formula: Among them, w p (L1) is the anchor bolt deflection displacement at point O, v p (L1) is the anchor deflection angle at point O; The relationship between shear displacement and lateral displacement is given by the following formula: Among them, U0 is the shear displacement of the anchor rod at point O, v0 is the lateral component of the shear displacement of the anchor rod at point O, and θ is the anchoring angle of the anchor rod.

3. The method according to claim 2, characterized in that According to the relationship between the displacement at point O and the axial force in the anchor bolt, the axial deformation mechanism of the anchor bolt is determined, including: Establishing a shear stress distribution diagram of the anchoring section considering the influence of the lateral displacement on the effective bonding length, wherein the shear stress distribution diagram of the anchoring section includes a grouting crushing section, a softening section and an effective bonding section; Based on the shear stress distribution of the effective bonding section, softening section and grouting crushing section, the axial stresses of points x0, L1 and O on the anchor are obtained by integrating equations (16)-(18), and L is obtained by equations (19)-(21). e , L p And the axial deformation of L1: Among them, σ e is the axial stress at the junction of the effective bonding section and the softening section, σ p is the axial stress at the junction of the softening section and the grouting crushing section, σ0 is the axial stress of the anchor rod at point O, u e is the axial extension of the effective joint section, u p is the axial elongation of the softening section, u1 is the axial elongation of the grouting crushing section, and c is the interface damage coefficient of the effective bonding section; The axial displacement of point A on the anchor is the sum of the axial elongation of the effective bonding section, the axial elongation of the softening section, and the axial elongation of the grouting and crushing section; The axial stress of the anchor at point O is calculated based on the axial displacement of point A on the anchor and equations (16)-(18); Before the plastic hinge appears, the relationship between the axial force and axial displacement at point O on the anchor is expressed as: 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 value of the first angle divided by the sine value 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. The lateral displacement increment of the anchor rod in each iteration is accumulated to obtain the axial displacement at point O of the anchor rod.

4. The method according to claim 3, characterized in that The axial force and shear force at failure are determined based on the lateral deformation mechanism and axial deformation mechanism of the anchor rod, specifically including: As the shear displacement continues to increase, the OA portion of the anchor elongates and rotates around point A; After the plastic hinge of the anchor is formed, the bending moment at point A reaches the maximum allowable limit, and the length of the OA part of the anchor begins to rotate around point A and continuously lengthen. The length of the OA part rotates around point A and is accompanied by continuous elongation. After each iteration, the length of the OA part, the increment of the deflection angle, the deflection angle, and the total shear displacement are expressed by the following formula: U0=U oe +iΔU (26) Among them, w oe The shear displacement of the anchor point O after the rotation angle and plastic hinge point are formed is the shear displacement increment of each iteration, L 1(i) is the length of the rock crushing section calculated for the i-th iteration, △U is the anchor shear displacement increment, L 1(i-1) Calculate the length of the rock crushing section for the i-1th iteration, △w op(i) is the increment of anchor deflection angle at point O during the i-1th iteration calculation, w op is the anchor rod deflection angle at point O, U0 is the anchor rod shear displacement at point O, i is the i-th iteration calculation, U oe is the ultimate shear displacement of the anchor in the elastic stage; After yielding, the analysis of the axial force of the anchor rod is approximated by the metal strain hardening model, and the natural logarithm of the first ratio is divided by the natural logarithm of the second ratio to obtain the strain hardening index m, the first ratio is the ratio of the axial stress at failure to the axial yield stress at yielding, and the second ratio is the ratio of the axial strain at failure to the axial yield strain at yielding; the strength coefficient is calculated according to the product of the elastic modulus and the exponential function of the axial yield strain, and the exponent of the exponential function of the axial yield strain is 1-m; The axial force is calculated by accumulating the product of each local incremental strain and the tangent modulus; The interaction point O between the anchor rod and the shear sliding surface is taken as the failure point, and the relationship between the shear force and the axial force at the failure point O is expressed as the sum of the square of the third ratio and the square of the fourth ratio being 1, wherein 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 rod; Where N 0(n) is the axial force at failure, Q0 is the shear force at failure, N f =σ f S, represents the plastic limit tension of the anchor rod, Indicates the plastic limit tensile force of the anchor rod.

5. The method according to claim 4, characterized in that The shear contribution of the anchor is calculated based on the axial force and shear force at failure, including: The resultant force of axial force and shear force is taken as the square difference of the sum of the square of shear force at failure and the square of axial tension force at failure; The inverse tangent 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 tension at failure; The cosine value and sine value 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 anchoring angle of the anchor rod minus the loading angle and the deflection angle between the shear force and the axial force; The total shear contribution of the anchor bolt is the sum 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.

6. A shear contribution calculation device, 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. On one side of point A, the anchor and the grouting or rock medium are elastically coupled. The rock anchor is regarded as a semi-infinite elastic foundation beam, and the lateral deformation mechanism of the anchor is analyzed to determine the criterion for the yield of the anchor section, which is expressed as: Among them, M A is the bending moment at point A, M p is the elastic limit bending moment, which is σ y is the yield strength of the anchor rod, D b is the diameter of the anchor rod, N0 is the axial force at point O in the anchor rod, N p is the yield load of the anchor rod, which is N p =σ y S, S is the cross-sectional area of ​​the anchor rod; The mechanism determination module is used to determine the axial deformation mechanism of the anchor bolt according to the relationship between the displacement at point O and the axial force in the anchor bolt; A moment calculation module, used to determine the axial force and shear force at failure based on the lateral deformation mechanism of the anchor rod and the axial deformation mechanism of the anchor rod; Contribution calculation module, used to calculate the shear contribution of the anchor based on the axial force and shear force at failure.

7. An electronic device, characterized in that: The electronic device comprises: a processor and a memory; the memory is used to store instructions; the processor is used to execute the instructions in the memory, so that the electronic device executes the method as claimed in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, which are used to implement the method according to any one of claims 1 to 5 when executed by a processor.

9. A computer program product, characterized in that The invention comprises a computer program, which implements the method according to any one of claims 1 to 5 when being executed by a processor.

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