An early warning method for anchor rock failure

Abstract

This application provides a failure warning method for anchored rock masses, belonging to the technical field of failure warning technology. The method includes: calculating the shear contribution of the anchor rod; constructing anchor rod contribution curves at different anchoring angles based on the anchor rod shear contribution; setting safety warnings for the anchored rock mass system based on the anchor rod contribution curves; and implementing failure warnings based on the safety warning settings. This method solves the problems of low computational efficiency and high computational costs, thereby accurately indicating the working status of the anchored rock mass and providing failure warnings.

Description

Technical Field

[0001] The present application relates to the technical field of failure warning, and in particular to a method for early warning of failure of anchored rock masses. Background Art

[0002] The research on the load transfer law at the interface of the anchoring system mainly focuses on anchor rods and anchor cables, and mainly studies the stress characteristics of anchor rods (cables) in rock and soil media, including the axial force of the anchor rod (cable), the shear stress distribution characteristics at the interface between the rod and the rock and soil, etc. This is also a hot topic of research for many scholars.

[0003] Traditionally, existing anchor (cable) design specifications assume a uniform shear stress distribution between the anchor (cable) and the rock mass when verifying the anchor's bearing capacity. However, numerous experimental studies have shown that the forces acting on the anchor in the rock mass are non-uniform, and the shear stress distribution is not uniform. Consequently, existing technologies have made numerous assumptions about the stress distribution characteristics at the anchor system interface and proposed theoretical models for the corresponding interfacial stress distribution patterns.

[0004] For example, the document "Phillips SH E. Factors affecting the design of anchorages in rock [R]. London: Cementation Research Ltd, 1970." proposed the power function distribution form of the interface shear stress in the anchoring section of the anchor rod and obtained the calculation formula for the minimum length of the anchoring section.

[0005] The document "You Chunan, Theoretical and applied research on stress transfer mechanism of anchoring system [D] Qingdao: Shandong University of Science and Technology, 2004." Based on the basic theory of elastic mechanics, the shear stress and axial force distribution models of the anchoring section interface of full-length bonded, tension-concentrated, tension-dispersed, pressure-concentrated and pressure-dispersed anchor rods (cables) were derived respectively. Systematic experiments and field test research were carried out to explore and analyze the stress transfer mechanism of the anchoring system.

[0006] The literature "Zhang Jiru, Tang Baofu. Hyperbolic function model for anchor load transfer mechanism analysis [1. Journal of Geotechnical Engineering, 2002, 24(2):188-192. " assumes that the anchor body and the rock and soil are in a coordinated deformation relationship, establishes a hyperbolic function model for anchor load transfer, and compares it with the field measured data for verification.

[0007] The literature "Jiang Zhongxin. Gaussian curve model of shear stress distribution in the anchoring section of tension-type anchor cables [J]. Chinese Journal of Geotechnical Engineering, 2001, 23(6): 696-699." summarizes and analyzes the on-site test data of tension-type anchor cables, uses a three-parameter Gaussian curve to describe the non-uniform distribution characteristics of the interface shear stress in the anchoring section of the anchor cable, and discusses the effective anchoring section length and its safety reserve.

[0008] However, when implementing anchor rock failure warning, existing technologies are difficult to accurately give the key points of normal operation and failure warning of anchor rock. Therefore, how to accurately implement anchor rock failure warning is a technical problem that urgently needs to be solved. Summary of the Invention

[0009] The present application provides a method for early warning of failure of an anchored rock mass, which is used to solve the problem of how to accurately provide key points for normal operation and failure early warning of the anchored rock mass.

[0010] This application provides an anchor rock failure early warning method, comprising:

[0011] Calculate the shear contribution of anchor bolts;

[0012] Based on the anchor rod shear contribution, construct anchor rod contribution curves at different anchoring angles;

[0013] Based on the anchor contribution curve, a safety warning setting is performed on the anchor rock system;

[0014] Failure warning is implemented based on the safety warning setting.

[0015] Furthermore, based on the anchor contribution curve, a safety warning setting is performed on the anchor rock system, including:

[0016] The anchor contribution curve presents three areas, namely, the elastic normal working area, the elastic-plastic development area, and the plastic failure area. The intersection point of the elastic normal working area and the elastic-plastic development area is the elastic critical point, and the intersection point of the elastic-plastic development area and the plastic failure area is the elastic-plastic critical point. Based on the elastic critical point and the elastic-plastic critical point, a safety warning is set for the anchoring rock system.

[0017] Furthermore, based on the first elastic critical point and the second elastoplastic critical point, a safety warning setting is performed on the anchoring rock system, specifically including:

[0018] When the shear displacement is less than the elastic critical point, it is determined that the anchored rock mass is in a safe and normal working state;

[0019] When the shear displacement is greater than the elastoplastic critical point, it is determined that the anchored rock mass is in an unstable state.

[0020] Furthermore, implementing failure warning based on the safety warning setting includes:

[0021] When the anchored rock mass is about to become unstable, a failure warning is issued.

[0022] Furthermore, the calculation of anchor shear contribution includes:

[0023] Randomly selecting a first target point and a second target point in the anchor rod, establishing a rectangular coordinate system to the right of the first target point, with the origin of the rectangular coordinate system being the second target point, and determining a yield criterion for the anchor rod cross section based on the rectangular coordinate system;

[0024] determining the axial deformation mechanism of the anchor bolt according to the relationship between the displacement of the second target point and the axial force;

[0025] Determining the axial force and shear force at failure based on the anchor rod lateral deformation mechanism and the anchor rod axial deformation mechanism;

[0026] The shear contribution of the anchor is calculated based on the axial force and shear force at failure.

[0027] Furthermore, the yield criterion of the anchor section is expressed as:

[0028]

[0029] Among them, M A is the bending moment at the first target point, 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 of the second target point 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.

[0030] Furthermore, based on the relationship between the displacement of the second target point in the anchor bolt and the axial force, the axial deformation mechanism of the anchor bolt is determined, which specifically includes:

[0031] Establishing a shear stress distribution diagram of the anchor section that takes into account the effect of lateral displacement on the effective bonding length, wherein the shear stress distribution diagram of the anchor section includes a grouting crushing section, a softening section, and an effective bonding section;

[0032] For the effective bonding section, the shear stress is expressed as:

[0033]

[0034] Where: s p is the shear stress at the proximal end, s′ pis the shear stress at the far end, c is the interface failure coefficient, L e is the effective binding segment length;

[0035] For the softening stage, the shear stress distribution is expressed as:

[0036]

[0037] Where Δ=s p -μp u ;μp u represents the static friction force of the grouting crushing section, μ represents the friction coefficient, L p Indicates the length of the softening section;

[0038] For the grouting and crushing section, the shear stress distribution is expressed as:

[0039] τ1(x)=μp u (4)

[0040] Based on the shear stress distribution of each segment, the axial stress of the anchor point x0, L1 and the second target point is obtained by integrating Equations (5)-(7), and L is obtained by Equations (8)-(10). e 、L p And the axial deformation of L1:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] 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 the second target point, 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;

[0048] The axial displacement of the first target point on the anchor is expressed as:

[0049] u0=u e +u p +u1 (11)

[0050] Substituting formulas (5)-(10) into formula (11) and rearranging them, we obtain:

[0051]

[0052] Where: ξ=4L e c+L p c+L p represents the anchoring effect coefficient;

[0053] represents the interface damage effect coefficient;

[0054] represents the friction effect coefficient;

[0055] Before the plastic hinge appears, the relationship between the axial force and axial displacement of the second target point on the anchor rod is expressed as formula (13):

[0056]

[0057] According to the geometric relationship between lateral deformation and axial deformation, the relationship between the anchor bolt lateral displacement increment and axial deformation increment in each iteration is shown in Equation (14). The total axial deformation of the second target point is obtained by Equation (15):

[0058]

[0059] u0=ΣΔu i (15)

[0060] Among them, △u i represents the anchor rod lateral displacement increment, △v0 represents the axial deformation increment, ω 0(i) It represents the deflection angle of the anchor rod at the second target point calculated in the i-th iteration, and u0 represents the axial displacement of the anchor rod at the second target point.

[0061] Furthermore, determining the axial force and shear force at failure based on the anchor rod lateral deformation mechanism and the anchor rod axial deformation mechanism specifically includes:

[0062] After the plastic hinge of the anchor rod is formed, the bending moment of the first target point reaches the maximum allowable limit, and a partial anchor rod is formed from the first target point to the second target point. The length of the partial anchor rod begins to rotate around the first target point and continuously lengthens. The length of the partial anchor rod rotates around the first target point and is accompanied by continuous elongation. After each iteration, the length of the partial anchor rod, the increment of the deflection angle, the deflection angle, and the total shear displacement are expressed by the following formula:

[0063]

[0064]

[0065]

[0066] U0=U oe +iΔU (19)

[0067] Among them, w oe The shear displacement of the second target point of the anchor bolt after the rotation angle and plastic hinge 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 the anchor deflection angle at the second target point during the i-1th iteration calculation, w op is the anchor rod deflection angle at the second target point, U0 is the anchor rod shear displacement at the second target point, i is the i-th iteration calculation, U oe is the ultimate shear displacement of the anchor in the elastic stage;

[0068] After yielding, the analysis of the axial force of the anchor bolt is approximated by the metal strain hardening model, as shown in Equation (20). At the beginning of the plastic hinge, the corresponding axial stress is equivalent to the yield stress, expressed as σ e , the axial strain at yield is expressed as Axial stress σ corresponding to ultimate failure u As shown in Equation (21), the axial strain at failure is expressed as ε u , the fitting process of strength coefficient and strain hardening exponent in metal strain hardening model is shown in Equations (22) and (23):

[0069] σ=Kε m (20)

[0070]

[0071]

[0072]

[0073] Where: σ is the stress on the material, Q e is the shear force at the second target point of the anchor bolt after the plastic hinge is formed, σ0 is the yield stress, K is the strength coefficient, ε For strain, m is the strain hardening exponent;

[0074] The axial force is approximated by accumulating the product of each local incremental strain and the tangent modulus; the iterative steps are shown in formulas (25)-(28). If the axial force N0 exceeds the yield tensile force Ny , then the calculation of the anchor axial force increment is transferred from formula (27) to formula (29):

[0075]

[0076] N 0(i+1) =N 0(i) +ΔN 0(i) (28)

[0077] ΔN 0(i) =E′Δε (29)

[0078] The shear force at the second target point is expressed as

[0079] Q0=p u L 1(i+1) (30)

[0080] The interaction point between the anchor 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:

[0081]

[0082] 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.

[0083] Furthermore, the shear contribution of the anchor bolt is calculated based on the axial force and shear force at failure, including:

[0084] The resultant of the axial force and the shear force is calculated using the following formula:

[0085]

[0086] Where R0 is the resultant force of axial force and shear force;

[0087] The loading angle between the shear force and the axial force is calculated using the following formula:

[0088]

[0089] Where γ0 is the loading angle between the shear force and the axial force;

[0090] The axial force and shear force parallel to and perpendicular to the shear plane are calculated using the following formulas:

[0091] R ot =R0cos(θ-γ0-w0) (34)

[0092] R on =R0sin(θ-γ0-w0) (35)

[0093] Where R ot and R on are the axial force and shear force parallel to and perpendicular to the shear plane, respectively,

[0094] The total shear contribution of the anchor is calculated using the following formula:

[0095]

[0096] Where T is the total contribution of anchor rod to shear resistance, is the joint friction angle.

[0097] The anchor rock failure early warning method provided in this application not only comprehensively considers the constitutive model of the stress distribution at the anchor interface, but also the influence of large elastic-plastic deformation in the local area of ​​the anchor. This enables a more accurate and comprehensive assessment of the shear contribution and failure risk of the anchor rock mass, helping to improve the safety of coal mining projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] 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.

[0099] Figure 1 This is an implementation scenario diagram shown for an exemplary embodiment;

[0100] Figure 2 This is a flow chart of an anchor rock failure early warning method according to an exemplary embodiment;

[0101] Figure 3 The figure is a flowchart showing the calculation of anchor contribution in a method for early warning of anchor rock failure, as shown in an exemplary embodiment.

[0102] Figure 4 FIG. 1 is a graph showing anchor rod contribution curves at different anchoring angles according to an exemplary embodiment.

[0103] The above drawings illustrate specific embodiments of the present application, which will be described in more detail below. These drawings and the textual description are not intended to limit the scope of the present application in any way, but rather to illustrate the concepts of the present application to those skilled in the art by reference to specific embodiments. DETAILED DESCRIPTION

[0104] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. In the following description, when referring to the drawings, identical numerals in different figures represent identical or similar elements, unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present application, as detailed in the appended claims.

[0105] 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.

[0106] The following specific embodiments describe in detail the technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems. 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.

[0107] The anchor rock failure warning method provided in this application can be implemented on any electronic device with data processing capabilities, or it can be an anchor rock failure warning system. It should be noted that the anchor rock failure warning system can be deployed individually on an electronic device in any environment (for example, individually on an edge server in an edge environment), or it can be deployed entirely in a cloud environment, or it can be deployed in a distributed manner in different environments.

[0108] For example, the anchor rock failure warning system can be logically divided into multiple parts, each with different functions. The various parts of the anchor rock failure warning 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 anchor rock failure warning system deployed in different environments or devices work together to realize the functions of the data processing platform.

[0109] It should be understood that this application does not restrictively divide which parts of the anchor rock failure warning system are deployed in what specific environment. In actual application, it can be adaptively deployed according to the computing power of electronic equipment, the resource availability of edge environment and cloud environment, or specific application requirements.

[0110] like Figure 1 This is an implementation scenario diagram showing an exemplary embodiment. The anchor rock failure warning system corresponding to the implementation scenario includes a computing terminal 10 and an early warning terminal 11. The computing terminal 10 and the early warning terminal 11 are connected via network communication.

[0111] The execution subject of the method of the embodiment of the present application is the early warning end 11, and the computing end 10 communicates with the early warning end 11. The computing end 10 is used to calculate the shear contribution of the anchor rod and send it to the early warning end 11. The early warning end 11 is used to give early warning of failure of the anchored rock mass, obtain the real-time working status of the anchored rock mass, and feed back the real-time working status to the computing end 10. The computing end 10 has a graphic user interface, and the results of the early warning of failure of the anchored rock mass can be displayed on the graphic interface. The computing end 10 can be provided with an alarm unit. For example, when the real-time working status of the anchored rock mass shows that the current anchor rod has a risk of failure, a reminder is given through the alarm unit.

[0112] For example, the computing terminal 10 is used to calculate the anchor shear contribution and feed the calculated anchor shear contribution to the warning terminal 11. The warning terminal 11 is used to construct an anchor contribution curve at different anchoring angles based on the anchor shear contribution; based on the anchor contribution curve, set a safety warning for the anchored rock system; and implement a failure warning based on all warning settings. The anchor contribution curve constructed by the warning terminal 11 can be fed to the computing terminal 10 and displayed on the computing terminal 10. The anchor contribution curve can show the working status of the anchor. At the same time, the warning terminal 11 can determine whether the current anchor is about to fail based on the final processing result. If it is in a state of about to fail, an alarm can be issued at the warning terminal 11, and the warning signal can be fed to the computing terminal 10 at the same time, and an alarm can be issued at the computing terminal 10 at the same time.

[0113] It is understandable that the anchor rock failure warning system can be set up Figure 1 In the early warning terminal 11, but the example shown in this embodiment Figure 1 The implementation environment shown is only exemplary. In other embodiments, the anchor rock failure warning method can also be applied to other implementation environments, and the anchor rock failure warning system can also be set in other structures in other implementation environments. No specific restrictions are made here.

[0114] In this embodiment, the computing end 10 is an electronic device on the user side, which can be a wired terminal with a visual structure or a wireless terminal. In other embodiments, the terminal can be an electronic device with a visual structure such as a mobile phone, computer, tablet, and vehicle-mounted equipment.

[0115] The early warning end 11 can be an edge environment and a cloud environment, such as a physical server, a server cluster, and a cloud server, etc., and there is no specific limitation here.

[0116] It is understandable that the anchor rock failure warning device can be set at Figure 1 In the early warning terminal 11, but the example shown in this embodiment Figure 1 The implementation environment shown is only exemplary. In other embodiments, the anchor rock failure warning method can also be applied to other implementation environments, and the anchor rock failure warning device can also be set in other structures in other implementation environments. No specific restrictions are made here.

[0117] Figure 2 This is a flowchart of an exemplary embodiment showing a method for early warning of anchor rock failure, which is applied to Figure 1 Implementation scenarios in Figure 2 As shown, the method includes steps S210 to S240, which are described in detail as follows:

[0118] S210. Calculate the shear contribution of the anchor rod.

[0119] Figure 3 This is a flowchart showing the calculation of anchor shear contribution in a method for early warning of anchor rock failure, as shown in an exemplary embodiment. Figure 3 As shown, in some embodiments, the anchor shear contribution is calculated through the following steps S211 to S214:

[0120] S211. Randomly select a first target point and a second target point in the anchor rod, establish a rectangular coordinate system on the right side of the first target point, with the origin of the rectangular coordinate system being the second target point, and determine the yield criterion of the anchor rod section based on the rectangular coordinate system.

[0121] In some embodiments, the yield criterion of the anchor section is expressed as:

[0122]

[0123] Among them, M A is the bending moment at the first target point, 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 of the second target point 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.

[0124] S212. Determine the axial deformation mechanism of the anchor rod based on the relationship between the displacement of the second target point and the axial force.

[0125] In some embodiments, the axial deformation mechanism of the anchor rod is determined based on the relationship between the displacement of the second target point in the anchor rod and the axial force, specifically including:

[0126] Establishing a shear stress distribution diagram of the anchor section that takes into account the effect of lateral displacement on the effective bonding length, wherein the shear stress distribution diagram of the anchor section includes a grouting crushing section, a softening section, and an effective bonding section;

[0127] For the effective bonding section, the shear stress is expressed as:

[0128]

[0129] Where: s p is the shear stress at the proximal end, s′ p is the shear stress at the far end, c is the interface failure coefficient, L e is the effective binding segment length;

[0130] For the softening stage, the shear stress distribution is expressed as:

[0131]

[0132] Where Δ=s p -μp u ;μp u represents the static friction force of the grouting crushing section, μ represents the friction coefficient, L p Indicates the length of the softening section;

[0133] For the grouting and crushing section, the shear stress distribution is expressed as:

[0134] τ1(x)=μp u (4)

[0135] Based on the shear stress distribution of each segment, the axial stress of the anchor point x0, L1 and the second target point is obtained by integrating Equations (5)-(7), and L is obtained by Equations (8)-(10). e 、L p And the axial deformation of L1:

[0136]

[0137]

[0138] 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 the second target point, 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;

[0139] The axial displacement of the first target point on the anchor is expressed as:

[0140] u0=u e +u p +u1 (11)

[0141] Substituting formulas (5)-(10) into formula (11) and rearranging them, we obtain:

[0142]

[0143] Where: ξ=4L e c+L p c+L p represents the anchoring effect coefficient;

[0144] represents the interface damage effect coefficient;

[0145] represents the friction effect coefficient;

[0146] Before the plastic hinge appears, the relationship between the axial force and axial displacement of the second target point on the anchor rod is expressed as formula (13):

[0147]

[0148] According to the geometric relationship between lateral deformation and axial deformation, the relationship between the anchor bolt lateral displacement increment and axial deformation increment in each iteration is shown in Equation (14). The total axial deformation of the second target point is obtained by Equation (15):

[0149]

[0150] Among them, △u i represents the anchor rod lateral displacement increment, △v0 represents the axial deformation increment, ω 0(i) It represents the deflection angle of the anchor rod at the second target point calculated in the i-th iteration, and u0 represents the axial displacement of the anchor rod at the second target point.

[0151] S213. Determine the axial force and shear force at failure based on the lateral deformation mechanism and axial deformation mechanism of the anchor rod.

[0152] In some embodiments, determining the axial force and shear force at failure based on the lateral deformation mechanism and the axial deformation mechanism of the anchor rod specifically includes:

[0153] After the plastic hinge of the anchor rod is formed, the bending moment of the first target point reaches the maximum allowable limit, and a partial anchor rod is formed from the first target point to the second target point. The length of the partial anchor rod begins to rotate around the first target point and continuously lengthens. The length of the partial anchor rod rotates around the first target point and is accompanied by continuous elongation. After each iteration, the length of the partial anchor rod, the increment of the deflection angle, the deflection angle, and the total shear displacement are expressed by the following formula:

[0154]

[0155] U0=U oe +iΔU (19)

[0156] Among them, w oe The shear displacement of the second target point of the anchor bolt after the rotation angle and plastic hinge 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 the anchor deflection angle at the second target point during the i-1th iteration calculation, w op is the anchor rod deflection angle at the second target point, U0 is the anchor rod shear displacement at the second target point, i is the i-th iteration calculation, U oe is the ultimate shear displacement of the anchor in the elastic stage;

[0157] After yielding, the analysis of the axial force of the anchor bolt is approximated by the metal strain hardening model, as shown in Equation (20). At the beginning of the plastic hinge, the corresponding axial stress is equivalent to the yield stress, expressed as σ e , the axial strain at yield is expressed as Axial stress σ corresponding to ultimate failure u As shown in Equation (21), the axial strain at failure is expressed as ε u , the fitting process of strength coefficient and strain hardening exponent in metal strain hardening model is shown in Equations (22) and (23):

[0158] σ=Kε m (20)

[0159]

[0160] Where: σ is the stress on the material, Q e is the shear force at the second target point of the anchor bolt after the plastic hinge is formed, σ0 is the yield stress, K is the strength coefficient, ε For strain, m is the strain hardening exponent;

[0161] The axial force is approximated by accumulating the product of each local incremental strain and the tangent modulus; the iterative steps are shown in formulas (25)-(28). If the axial force N0 exceeds the yield tensile force N y , then the calculation of the anchor axial force increment is transferred from formula (27) to formula (29):

[0162]

[0163]

[0164] N 0(i+1) =N 0(i) +ΔN 0(i) (28)

[0165] ΔN 0(i) =E′Δε (29)

[0166] The shear force at the second target point is expressed as

[0167] Q0=p u L 1(i+1) (30)

[0168] The interaction point between the anchor 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:

[0169]

[0170] 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.

[0171] S214. Calculate the shear contribution of the anchor rod based on the axial force and shear force at failure.

[0172] In some embodiments, the shear contribution of the anchor bolt is calculated based on the axial force and shear force at failure, specifically including:

[0173] The resultant of the axial force and the shear force is calculated using the following formula:

[0174]

[0175] Where R0 is the resultant force of axial force and shear force;

[0176] The loading angle between the shear force and the axial force is calculated using the following formula:

[0177]

[0178] Where γ0 is the loading angle between the shear force and the axial force;

[0179] The axial force and shear force parallel to and perpendicular to the shear plane are calculated using the following formulas:

[0180] R ot =R0cos(θ-γ0-w0) (34)

[0181] R on =R0sin(θ-γ0-w0) (35)

[0182] Where R ot and R on are the axial force and shear force parallel to and perpendicular to the shear plane, respectively,

[0183] The total shear contribution of the anchor is calculated using the following formula:

[0184]

[0185] Where T is the total contribution of anchor rod to shear resistance, is the joint friction angle.

[0186] S220. Based on the shear contribution of the anchor rod, the anchor rod contribution curves at different anchoring angles are constructed.

[0187] For example, the anchor contribution curves at different anchoring angles are as follows: Figure 4 As shown in Figure 2, under different anchoring angles, the anchor contribution curve generally shows two inflection points and three regional characteristics. Figure 4 The figure shows three regions: one region is the normal elastic working region of the anchor bolt at the joint, another region is the elastic-plastic development region, and the last region is the plastic failure region. The intersection of the normal elastic working region and the elastic-plastic development region is the elastic critical point, and the intersection of the elastic-plastic development region and the plastic failure region is the elastic-plastic critical point. Based on these two critical points, safety warnings can be set for the anchored rock system. When the shear displacement is less than the elastic critical point, the anchored rock mass can be considered to be in a safe and normal working state. When the shear displacement is greater than the elastic-plastic critical point, the anchored rock mass can be considered to be in a state of imminent instability.

[0188] S230. Based on the anchor contribution curve, set safety warning for the anchor rock system.

[0189] In some embodiments, based on the anchor contribution curve, a safety warning setting is performed on the anchor rock system, including:

[0190] The anchor contribution curve shows three areas, namely the elastic normal working area, the elastic-plastic development area and the plastic failure area. The intersection of the elastic normal working area and the elastic-plastic development area is the elastic critical point, and the intersection of the elastic-plastic development area and the plastic failure area is the elastic-plastic critical point. Based on the elastic critical point and the elastic-plastic critical point, a safety warning is set for the anchor rock system.

[0191] In some embodiments, based on the first elastic critical point and the second elastoplastic critical point, a safety warning setting is performed on the anchor rock system, specifically including:

[0192] When the shear displacement is less than the elastic critical point, it is determined that the anchored rock mass is in a safe and normal working state;

[0193] When the shear displacement is greater than the elastoplastic critical point, it is determined that the anchored rock mass is in an unstable state.

[0194] S240: Implement failure warning based on safety warning settings.

[0195] In some embodiments, implementing failure warning based on security warning settings includes:

[0196] When the anchored rock mass is about to become unstable, a failure warning is issued.

[0197] The present application provides a computer-readable storage medium having computer-executable instructions stored thereon; when the computer-executable instructions are executed by a processor, they are used to implement the anchor rock failure warning method as described in any of the above embodiments.

[0198] 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 anchor rock failure early warning method is implemented.

[0199] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of the present application and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, and the true scope and spirit of the present application are indicated by the following claims.

[0200] It should be understood that the present application is not limited to the exact structure 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 early warning of anchor rock failure, characterized in that: include: Calculate the shear contribution of anchor bolts; Based on the anchor rod shear contribution, construct anchor rod contribution curves at different anchoring angles; Based on the anchor contribution curve, a safety warning setting is performed on the anchor rock system; Implementing failure warning based on the safety warning setting; Based on the anchor contribution curve, safety warning settings are performed on the anchor rock system, including: The anchor contribution curve shows three regions, namely, the elastic normal working region, the elastic-plastic development region, and the plastic failure region. The intersection of the elastic normal working region and the elastic-plastic development region is the elastic critical point, and the intersection of the elastic-plastic development region and the plastic failure region is the elastic-plastic critical point. Based on the elastic critical point and the elastic-plastic critical point, a safety warning setting is performed for the anchor rock system. The calculation of anchor shear contribution includes: Randomly selecting a first target point and a second target point in the anchor rod, establishing a rectangular coordinate system to the right of the first target point, with the origin of the rectangular coordinate system being the second target point, and determining a yield criterion for the anchor rod cross section based on the rectangular coordinate system; determining the axial deformation mechanism of the anchor bolt according to the relationship between the displacement of the second target point and the axial force; Determining the axial force and shear force at failure based on the anchor rod lateral deformation mechanism and the anchor rod axial deformation mechanism; Calculate the anchor shear contribution based on the axial and shear forces at failure; According to the relationship between the displacement of the second target point in the anchor bolt and the axial force, the axial deformation mechanism of the anchor bolt is determined, which specifically includes: Establishing a shear stress distribution diagram of the anchor section that takes into account the effect of lateral displacement on the effective bonding length, wherein the shear stress distribution diagram of the anchor section includes a grouting crushing section, a softening section, and an effective bonding section; For the effective joint section, the shear stress distribution is expressed as: Where: s p is the shear stress at the proximal end, s′ p is the shear stress at the far end, c is the interface failure coefficient, L e is the effective binding segment length; For the softening stage, the shear stress distribution is expressed as: Where Δ=s p -μp u ;μp u represents the static friction force of the grouting crushing section, μ represents the friction coefficient, L p Indicates the length of the softening section; For the grouting and crushing section, the shear stress distribution is expressed as: τ1(x)=μp u (4) Based on the shear stress distribution of each segment, the axial stress of the anchor point x0, L1 and the second target point is obtained by integrating Equations (5)-(7), and L is obtained by Equations (8)-(10). 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 the second target point, 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, D b is the anchor diameter; The axial displacement of the first target point on the anchor is expressed as: u0=u e +in p +u1 (11) Substituting formulas (5)-(10) into formula (11) and rearranging them, we obtain: Where: ξ=4L e c+L p c+L p represents the anchoring effect coefficient; represents the interface damage effect coefficient; represents the friction effect coefficient; Before the plastic hinge appears, the relationship between the axial force and axial displacement of the second target point on the anchor rod is expressed as formula (13): According to the geometric relationship between lateral deformation and axial deformation, the relationship between the anchor bolt lateral displacement increment and axial deformation increment in each iteration is shown in Equation (14). The total axial deformation of the second target point is obtained by Equation (15): u0=∑Δu i (15) Among them, △u i represents the anchor rod lateral displacement increment, △v0 represents the axial deformation increment, ω 0(i) It represents the deflection angle of the anchor rod at the second target point calculated in the i-th iteration, and u0 represents the axial displacement of the anchor rod at the second target point.

2. The method according to claim 1, characterized in that Based on the elastic critical point and the elastoplastic critical point, a safety warning setting is performed on the anchor rock system, specifically including: When the shear displacement is less than the elastic critical point, it is determined that the anchored rock mass is in a safe and normal working state; When the shear displacement is greater than the elastoplastic critical point, it is determined that the anchored rock mass is in an unstable state.

3. The method according to any one of claim 2, characterized in that Implementing failure warning based on the safety warning setting includes: When the anchored rock mass is about to become unstable, a failure warning is issued.

4. The method according to claim 1, wherein The yield criterion of the anchor section is expressed as: Among them, M A is the bending moment at the first target point, M p is the elastic limit bending moment, which is σ y is the yield strength of the anchor, N0 is the axial force of the second target point in the anchor, 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.

5. The method according to claim 1, wherein 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: After the plastic hinge of the anchor rod is formed, the bending moment of the first target point reaches the maximum allowable limit, and a partial anchor rod is formed from the first target point to the second target point. The length of the partial anchor rod begins to rotate around the first target point and continuously lengthens. The length of the partial anchor rod rotates around the first target point and is accompanied by continuous elongation. After each iteration, the length of the partial anchor rod, the increment of the deflection angle, the deflection angle, and the total shear displacement are expressed by the following formula: Among them, w oe The shear displacement of the second target point of the anchor bolt after the rotation angle and plastic hinge 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 the anchor deflection angle at the second target point during the i-1th iteration calculation, w op is the anchor rod deflection angle at the second target point, U0 is the anchor rod shear displacement at the second target point, 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 bolt is approximated by the metal strain hardening model, as shown in Equation (20). At the beginning of the plastic hinge, the corresponding axial stress is equivalent to the yield stress, expressed as σ e , the axial strain at yield is expressed as Axial stress σ corresponding to ultimate failure u As shown in Equation (21), the axial strain at failure is expressed as ε u , the fitting process of strength coefficient and strain hardening exponent in metal strain hardening model is shown in Equations (22) and (23): σ=Kε m (20) Where: σ is the stress on the material, Q e is the shear force at the second target point of the anchor bolt after the plastic hinge is formed, σ0 is the yield stress, K is the strength coefficient, ε is the strain, and m is the strain hardening exponent; The axial force is approximated by accumulating the product of each local incremental strain and the tangent modulus; the iterative steps are shown in formulas (25)-(28). If the axial force N0 exceeds the yield tensile force N y , then the calculation of the anchor axial force increment is transferred from formula (27) to formula (29): N 0(i+1) =N 0(i) +ΔN 0(i) (28) ΔN 0(i) =E′Dε (29) The shear force at the second target point is expressed as Q0=p u IT 1(i+1) (30) The interaction point between the anchor 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: 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.

6. The method according to claim 5, characterized in that The shear contribution of the anchor is calculated based on the axial force and shear force at failure, including: The resultant of the axial force and the shear force is calculated using the following formula: Where R0 is the resultant force of axial force and shear force; The loading angle between the shear force and the axial force is calculated using the following formula: Where γ0 is the loading angle between the shear force and the axial force; The axial force and shear force parallel to and perpendicular to the shear plane are calculated using the following formulas: R ot =R0cos(θ-γ0-w0) (34) R on =R0sin(θ-γ0-w0) (35) Where R ot and R on are the axial force and shear force parallel to and perpendicular to the shear plane, respectively, The total shear contribution of the anchor is calculated using the following formula: Where T is the total contribution of anchor rod to shear resistance, is the joint friction angle.

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