Anchoring rock mass failure early warning method

Abstract

The invention provides an anchoring rock mass failure early warning method, and belongs to the technical field of failure early warning. The method comprises the following steps: calculating the shearing resistance contribution of the anchor rod; constructing an anchor rod contribution curve under different anchoring angles based on the shear resistance contribution of the anchor rod; based on the anchor rod contribution curve, safety early warning setting is conducted on the anchored rock mass system; failure early warning is realized based on safety early warning setting. According to the method, the problems of low calculation efficiency and high operation cost are solved, so that the working state of the anchored rock mass is accurately pointed out, and failure early warning is performed.

Description

Technical Field

[0001] The present application relates to the technical field of failure warning, and in particular to a failure warning method for anchored rock mass. 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 force characteristics of anchor rods (cables) in rock and soil media, including the axial force of the anchor rod (cable) body, the shear stress distribution characteristics at the interface between the rod body and the rock and soil body, etc. This is also a hot topic for many scholars to study.

[0003] Traditionally, in the existing anchor (cable) anchoring design specifications, when performing anchor bearing capacity design verification, it is generally assumed that the shear stress between the anchor (cable) anchor body and the rock and soil is evenly distributed. However, a large number of experimental studies have shown that the force on the anchor in the rock and soil medium should be non-uniform, and the shear stress is not evenly distributed. For this reason, the existing technology has also made many assumptions about the stress distribution characteristics of the anchor system interface, and proposed a theoretical model of the corresponding interface stress distribution form.

[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." is based on the basic theory of elastic mechanics. The shear stress and axial force distribution models of the anchoring section interface of full-length bonding, tension concentration, tension dispersion, pressure concentration and pressure dispersion anchors (cables) are derived respectively. Systematic experiments and field test research are 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 body 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, the existing technology is difficult to accurately give the key points of normal operation and failure warning of the anchored rock mass when realizing the failure warning of the anchored rock mass. Therefore, how to accurately realize the failure warning of the anchored rock mass 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 of normal operation and failure early warning of the anchored rock mass.

[0010] The present 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 for 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] Further, 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 a state of imminent instability.

[0020] Further, 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] Further, the calculation of anchor shear contribution includes:

[0023] A first target point and a second target point are randomly selected in the anchor rod, a rectangular coordinate system is established on the right side of the first target point, the origin of the rectangular coordinate system is the second target point, and a criterion for yielding the anchor rod section is determined 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 lateral deformation mechanism of the anchor rod and the axial deformation mechanism of the anchor rod;

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

[0027] Furthermore, the criterion for the yield 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 bolt diameter, N0 is the axial force at the second target point in the bolt, 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, according to the relationship between the displacement of the second target point in the anchor and the axial force, the axial deformation mechanism of the anchor is determined, which specifically includes:

[0031] 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;

[0032] For the effective joint 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, and L p Indicates the length of the softening section;

[0038] For the grouting 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 at points x0, L1 and the second target point on the anchor 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 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 is expressed as formula (13):

[0056]

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

[0058]

[0059] u0=ΣΔu i (15)

[0060] Among them, △u i represents the lateral displacement increment of the anchor rod, △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, the axial force and shear force at the time of failure are determined based on the lateral deformation mechanism and the axial deformation mechanism of the anchor rod, specifically including:

[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 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 anchor deflection angle increment 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 The axial stress corresponding to the ultimate failure is u As shown in formula (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 of 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 force of axial force and shear force is calculated by the following formula:

[0085]

[0086] In the formula, 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 by the following formula:

[0088]

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

[0090] The axial force and shear force parallel to the shear plane 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] In the formula, R ot and R on are the axial force and shear force parallel to the shear plane and perpendicular to the shear plane, respectively,

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

[0095]

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

[0097] The anchor rock failure warning method provided in this application can not only comprehensively consider the constitutive model of the stress distribution of the anchor interface, but also consider the influence of the large elastic-plastic deformation of the local area of ​​the anchor. This makes it possible to make a more accurate and comprehensive assessment of the shear contribution and failure risk of the anchor rock mass, which helps 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 The present invention is a flow chart of an anchor rock failure early warning method shown in an exemplary embodiment;

[0101] Figure 3 The present invention is a flowchart of calculating the contribution of anchor rods in a method for early warning of failure of anchored rock mass, shown as an exemplary embodiment.

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

[0103] 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

[0104] 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.

[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 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.

[0107] The anchor rock failure warning method provided in the present application can be implemented in 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 separately on an electronic device in any environment (for example: deployed separately 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 make any restrictive division on 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 possession 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 end 10 and a warning end 11. The computing end 10 and the warning end 11 are connected via network communication.

[0111] The executor of the method of the embodiment of the present application is the early warning terminal 11, and the computing terminal 10 communicates with the early warning terminal 11. The computing terminal 10 is used to calculate the shear contribution of the anchor rod and send it to the early warning terminal 11. The early warning terminal 11 is used for early warning of failure of the anchored rock mass, and obtains the real-time working status of the anchored rock mass. The real-time working status can be fed back to the computing terminal 10. The computing terminal 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 terminal 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] Exemplarily, the calculation end 10 is used to calculate the anchor shear contribution, and feed the calculated anchor shear contribution to the early warning end 11. The early warning end 11 is used to construct the anchor contribution curve under different anchoring angles based on the anchor shear contribution; based on the anchor contribution curve, set a safety early warning for the anchored rock system; and implement failure early warning based on all early warning settings. Among them, the anchor contribution curve constructed by the early warning end 11 can be fed to the calculation end 10 and displayed in the calculation end 10. The anchor contribution curve can show the working status of the anchor. At the same time, the early warning end 11 can judge whether the current anchor is in a state of imminent failure based on the final processing result. If it is in a state of imminent failure, an alarm can be issued at the early warning end 11, and the early warning signal can be fed to the calculation end 10 at the same time, and an alarm can be issued at the calculation end 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, without specific limitations 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 visualization structure or a wireless terminal. In other embodiments, the terminal can be an electronic device with a visualization structure such as a mobile phone, a computer, a tablet, and a vehicle-mounted device.

[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 no specific limitation is made here.

[0116] It can be understood 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, without specific limitation here.

[0117] Figure 2 is a flowchart of an anchor rock failure early warning method shown in an exemplary embodiment, 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 FIG. 1 is a flowchart showing a calculation flow 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, the origin of the rectangular coordinate system is 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 criterion for the yield 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 bolt diameter, N0 is the axial force at the second target point in the bolt, 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 according to the relationship between the displacement of the second target point and the axial force.

[0125] In some embodiments, according to the relationship between the displacement of the second target point in the anchor rod and the axial force, the axial deformation mechanism of the anchor rod is determined, which specifically includes:

[0126] 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;

[0127] For the effective joint 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, and L p Indicates the length of the softening section;

[0133] For the grouting 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 at points x0, L1 and the second target point on the anchor 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 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 is expressed as formula (13):

[0147]

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

[0149]

[0150] Among them, △u i represents the lateral displacement increment of the anchor rod, △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, the axial force and shear force at failure are determined based on the lateral deformation mechanism of the anchor rod and the axial deformation mechanism of the anchor rod, specifically including:

[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 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 anchor deflection angle increment 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 The axial stress corresponding to the ultimate failure is u As shown in formula (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 of 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 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 the shear force at failure, specifically including:

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

[0174]

[0175] In the formula, 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 by the following formula:

[0177]

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

[0179] The axial force and shear force parallel to the shear plane 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] In the formula, R ot and R on are the axial force and shear force parallel to the shear plane and perpendicular to the shear plane, respectively,

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

[0184]

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

[0186] S220. Based on the shear contribution of the anchor rod, the anchor rod contribution curve under different anchoring angles is 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 presents two inflection points and three regional characteristics. Figure 4 Three areas are shown in the figure, one of which is the elastic normal working area of ​​the anchor at the joint, one is the elastic-plastic development area, and the last is 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 these two critical points, a safety warning can be set for the anchored rock system. When the shear displacement is less than the elastic critical point, the anchored rock 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 can be considered to be in an unstable state.

[0188] S230. Based on the anchor contribution curve, a safety warning is set 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 presents 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 anchoring 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 anchoring rock mass 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 a state of imminent instability.

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

[0195] In some embodiments, implementing failure warning based on safety 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, on which computer-executable instructions are stored; 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 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. 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.

[0200] 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 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 for the anchor rock system; Failure warning is implemented based on the safety warning setting.

2. The method according to claim 1, characterized in that Based on the anchor contribution curve, a safety warning setting is performed for the anchor rock system, including: 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.

3. The method according to claim 2, characterized in that 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: 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 a state of imminent instability.

4. The method according to any one of claim 3, 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.

5. The method according to any one of claims 1 to 4, characterized in that The calculation of anchor shear contribution includes: A first target point and a second target point are randomly selected in the anchor rod, a rectangular coordinate system is established on the right side of the first target point, the origin of the rectangular coordinate system is the second target point, and a criterion for yielding the anchor rod section is determined 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 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.

6. The method according to claim 5, characterized in that The criterion for the yield 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 rod, D b is the bolt diameter, N0 is the axial force at the second target point in the bolt, 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.

7. The method according to claim 6, characterized in that According to the relationship between the displacement of the second target point in the anchor and the axial force, the axial deformation mechanism of the anchor is determined, which specifically includes: 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; For the effective joint section, the shear stress 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, and L p Indicates the length of the softening section; For the grouting 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 at points x0, L1 and the second target point on the anchor 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 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; 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 is expressed as formula (13): According to the geometric relationship between lateral deformation and axial deformation, the relationship between the lateral displacement increment and the axial deformation increment of the anchor in each iteration is shown in formula (14). The total axial deformation of the second target point is obtained by formula (15): u0=∑Δu i (15) Among them, △u i represents the lateral displacement increment of the anchor rod, △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.

8. The method according to claim 7, 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: 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: U0=U oe +iΔU (19) Among them, w oe The shear displacement of the second target point of the anchor bolt 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 anchor deflection angle increment 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 The axial stress corresponding to the ultimate failure is u As shown in formula (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 of 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; 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.

9. The method according to claim 8, 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 calculated by the following formula: In the formula, R0 is the resultant force of axial force and shear force; The loading angle between the shear force and the axial force is calculated by the following formula: Where γ0 is the loading angle between shear force and axial force; The axial force and shear force parallel to the shear plane 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) In the formula, R ot and R on are the axial force and shear force parallel to the shear plane and perpendicular to the shear plane, respectively, The total shear contribution of the anchor is calculated by the following formula: Where T is the total contribution of anchor bolt to shear resistance, is the friction angle of the joint surface.

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