A method for predicting the prestress loss of an anchoring structure

Abstract

The present invention provides a method for predicting the prestress loss of an anchoring structure, which includes: establishing a calculation model for the prestress of the cable in the anchoring structure, and establishing the theoretical solutions for the stress distributions of the cable, the mortar body and the rock mass; solving the axial displacement of the cable, the interfacial shear stress between the cable and the mortar body, the interfacial shear stress between the mortar body and the rock mass, and the axial stress distribution of the cable; analyzing the prestress loss of the anchoring structure, and establishing a prestress coupling model and a prestress decoupling model; calculating the prestress loss value and the final stable value of the cable. Based on the shear lag model, the present invention studies the mechanical properties of the three key elements of the prestressed cable anchoring structure and the load transfer mechanism, obtains the calculation formulas for the interfacial shear stress and the axial stress distribution of the cable in the anchoring structure, and further proposes a prestress coupling model and a prestress decoupling model respectively according to whether the interfacial shear stress between the cable and the mortar body exceeds the bonding strength of the contact interface between the two, and calculates the prestress loss value and the final stable value of the cable.

Description

Technical Field

[0001] The present invention relates to the technical field of anchoring engineering, and particularly relates to a method for predicting prestress loss of an anchoring structure. Background Art

[0002] Prestressed anchor cables can effectively improve the stability of structures such as slope rock masses and underground cavities, and have significant economic and social benefits. They have been widely used in high-slope support and landslide control, and are a hot research topic in the current geotechnical engineering field.

[0003] The applicable situations of existing prestress loss prediction models are limited to the coupling of anchor-rock deformation and the soft rock with strong creep properties of the anchored rock mass. However, the situations where the creep of the rock mass is inconsistent with the retraction deformation of the anchor cable or the anchored rock mass is hard rock are not applicable to the current prediction models, resulting in large prediction errors. Moreover, previous methods rarely involve the prestress loss caused by the decoupling of the anchoring system due to the debonding of the anchoring structure interface. Summary of the Invention

[0004] The present invention provides a method for predicting prestress loss of an anchoring structure to solve the technical problems in the prior art that the applicable situations of prestress loss prediction models are limited to the coupling of anchor-rock deformation and the soft rock with strong creep properties of the anchored rock mass; the situations where the creep of the rock mass is inconsistent with the retraction deformation of the anchor cable or the anchored rock mass is hard rock are not applicable to the current prediction models, resulting in large prediction errors; and previous studies rarely involve the prestress loss caused by the decoupling of the anchoring system due to the debonding of the anchoring structure interface.

[0005] To solve the above problems, the present invention provides a method for predicting prestress loss of an anchoring structure, and the prediction method includes:

[0006] S 1 : According to the shear lag model and the stress characteristics of the anchoring structure, establish a calculation model for the prestress of the anchor cable in the anchoring structure, and establish the theoretical solutions for the stress distributions of the anchor cable, the mortar body, and the surrounding rock mass;

[0007] S 2 : Solve the axial displacement u s of the anchor cable and the interfacial shear stress τ 1 between the anchor cable and the mortar body, the interfacial shear stress τ 2 between the mortar body and the surrounding rock mass, and the axial stress σ s of the anchor cable;

[0008] S 3 : Analyze the prestress loss of the anchoring structure, and establish a prestress loss coupling model and an anchor cable prestress decoupling model;

[0009] S 4 : Calculate the prestress loss value and the final stable value of the anchor cable.

[0010] Furthermore, in step S 1 , the specific steps for establishing the theoretical solution of the stress distribution of the anchor cable are as follows:

[0011] Step 1: Based on elastic theory analysis and calculation, establish a stress distribution model for the anchor cable micro-element;

[0012]

[0013] In the formula: σ s is the axial stress of the anchor cable, with the unit of Pa, τ 1 is the interfacial shear stress between the anchor cable and the mortar, with the unit of Pa, r 1 is the radius of the anchor cable, with the unit of m;

[0014] Step 2: After the anchor cable micro-element is loaded, the relationship between its axial stress and axial displacement is:

[0015]

[0016] In the formula: u s is the axial displacement of the anchor cable, with the unit of m, E s is the elastic modulus of the anchor cable, with the unit of Pa;

[0017] Step 3: Combine Equation (1) and Equation (2) to obtain:

[0018]

[0019] Furthermore, in step S 1 , the specific steps for establishing the theoretical solution of the stress distribution of the mortar are as follows:

[0020] Solve the displacement relationship between the inside and outside of the mortar;

[0021] From the axial equilibrium condition, we get:

[0022] 2πr 1 τ 1 dz - 2πr 2 τ 2 dz = 0 (4)

[0023] In the formula: τ 2 is the interfacial shear stress between the mortar and the rock mass, with the unit of Pa, r 3 is the influence radius of the interfacial shear stress in the rock mass, with the unit of m;

[0024] From elastic theory, inside the mortar, along the radial direction, there is:

[0025]

[0026] In the formula: Gm is the shear modulus of the mortar, in Pa, γ m is the radial shear strain of the mortar, u m is the displacement of a certain point inside the mortar body, in m;

[0027] By combining equations (4) and (5) and substituting the inner and outer boundary conditions of the mortar body, the inner and outer displacement relationship of the mortar body is obtained:

[0028]

[0029] Where: G m is the shear modulus of the mortar, in Pa, u 1 is the inner displacement of the mortar body, unit: m,u 2 is the outer displacement of the mortar body, unit: m.

[0030] Furthermore, in step S 1 The specific method for establishing the theoretical solution of stress distribution of the surrounding rock mass includes:

[0031] Step 1: Calculate the influence radius r of the interface shear stress in the surrounding rock mass 3 ;

[0032] The influence radius r of the interface shear stress in the surrounding rock mass 3 Calculated by the following formula:

[0033] r 3 =2.5(1-ν r )l (7)

[0034] Where: r 3 is the influence radius of the interface shear stress in the surrounding rock mass, unit: m; ν r is the Poisson's ratio of the rock mass; l is the length of the anchor cable, unit: m.

[0035] Step 2: Determine the boundary conditions of surrounding rock deformation and calculate the radial shear stress τ inside the surrounding rock mass r ;

[0036] The boundary condition of surrounding rock deformation affected by shear stress is:

[0037]

[0038] Where: u r is the displacement of surrounding rock under shear stress, unit: m.

[0039] Assume that the shear stress in the surrounding rock is r The distribution is as follows:

[0040] τ r =τ 2 r2 / r(r 2 ≤ r ≤ r 3 ) (9)

[0041] And according to the theory of elasticity, inside the surrounding rock mass, the shear stress τ r along the radial direction is:

[0042]

[0043] where: G r is the shear modulus of the rock mass, unit: Pa; γ r is the radial shear strain of the rock mass.

[0044] Step 3: Calculate the displacement u of the surrounding rock under the action of shear stress r ;

[0045] Combining Equation (8), Equation (9) and Equation (10), when r = r 2 , the relationship of the displacement u of the surrounding rock under the action of shear stress r is:

[0046]

[0047] 2 In step S

[0048] Specific steps for solving the stress of the anchoring structure include:

[0049]

[0050] where:

[0051]

[0052] Solving Equation (12) gives the general solution,

[0053] u s = Ae αz + Be -αz (14)

[0054] where: A and B are both constant coefficients.

[0055] According to the boundary conditions,

[0056]

[0057] Combining Equation (12), Equation (14) and Equation (15) gives:

[0058]

[0059]

[0060] The axial displacement u of the anchor cable s has the following expression:

[0061]

[0062] Furthermore, in step S 2 the shear stress τ 1 between the anchor cable and the mortar interface, the shear stress τ 2 between the mortar and the rock mass interface, and the axial stress σ s of the anchor cable have the following calculation expressions respectively:

[0063]

[0064]

[0065]

[0066] Furthermore, in step S 3 the specific method for establishing the prestress loss coupling model is as follows:

[0067] Step 1: Use the generalized Kelvin model to simulate the creep properties of the rock mass and establish the constitutive equation, and the constitutive equation is:

[0068]

[0069] where: σ r is the stress of the rock mass, unit: Pa; σ r ' is the stress change rate, ε r , ε r ' are the strain and strain change rate of the rock mass, E r is the elastic modulus of the rock mass, unit Pa; E k , η k are the elastic modulus and viscosity coefficient of the K body when simulating the creep of the rock mass;

[0070] Step 2: Use a spring to simulate the anchor cable to obtain the prestress loss coupling model;

[0071] Step 3: Solve the equivalent elastic modulus of the anchor cable, and the equivalent elastic modulus of the anchor cable can be solved by the following expression:

[0072] E s ' = E S A s / A r (23)

[0073] where, E s ' is the equivalent elastic modulus of the anchor cable, unit: Pa, Es is the elastic modulus of the cable bolt, unit: Pa, A s is the cross-sectional area of the cable bolt body, unit: m 2 , A r is the area of the rock mass within the effective anchorage range of the cable bolt, unit: m 2 ;

[0074] Step 4: Solve for the stress σ of the rock mass around the anchorage structure according to the constitutive equations and mutual relationships of the components in the prestress loss coupling model r ;

[0075] The stress σ of the rock mass around the anchorage structure r varies with time t as follows:

[0076]

[0077] where C is calculated by regression through the following formula 1 , C 2 and C 3 ,

[0078]

[0079] In the formula: ε 0 is the initial strain of the rock mass after the cable bolt is tensioned and locked, E r is the elastic modulus of the rock mass, unit: Pa, E s ' is the equivalent elastic modulus of the cable bolt, unit: Pa, E k is the elastic modulus of the K body when simulating the creep of the rock mass, unit: Pa, η k is the viscosity coefficient of the K body when simulating the creep of the rock mass;

[0080] Step 5: Obtain the formula for the change of the cable bolt prestress P(t) with time P = σ r A r :

[0081]

[0082] When t → ∞, the value of the cable bolt prestress loss when it tends to be stable can be calculated.

[0083] Furthermore, in step S 3 the specific method for establishing the cable bolt prestress decoupling model is as follows:

[0084] Step 1: When the anchorage structure is coupled, solve for the total displacement S of the cable bolt 1 as:

[0085]

[0086] Solving the above formula, we get

[0087]

[0088] Step 2: Solve for the axial displacement u of the decoupled anchor cable in the anchorage section s , the interfacial shear stress τ between the anchor cable and the mortar body 1 and the axial stress σ of the anchor cable s distribution;

[0089] Substitute P in equations (18), (19) and (21) 0 with P', and l 1 with l 1 ', then the axial displacement u of the decoupled anchor cable in the anchorage section can be obtained s , the interfacial shear stress τ between the anchor cable and the mortar body 1 and the axial stress σ of the anchor cable s distribution:

[0090]

[0091]

[0092]

[0093] Step 3: Solve for the axial displacement u of the decoupled anchor cable in the anchorage section s , the shear stress τ between the anchor cable and the mortar body interface 1 and the axial stress σ of the anchor cable s distribution;

[0094] When the anchorage structure is decoupled, the total displacement S of the anchor cable 2 is:

[0095]

[0096] Solving the above equation gives

[0097]

[0098] Step 4: According to the fact that the displacement of the bottom of the anchorage section relative to the hole mouth O remains unchanged before and after decoupling, from S 1 = S 2 , the tension P' acting on the anchorage section b-c after decoupling can be obtained;

[0099]

[0100] In the formula,

[0101]

[0102]

[0103] where when z = l 1 ', τ 1 = τ u , then

[0104]

[0105] Furthermore, in step S 4 , the specific method for calculating the prestress loss value and the final stable value of the anchor cable is as follows:

[0106] Step 1: According to the total displacement S 2 of the anchor cable and the tension P' of the anchorage section b-c, obtain the function formula of the free section length l 1 ';

[0107] By combining equations (33) and (34), we get:

[0108]

[0109] Step 2: Solve equation (36) by the bisection method to obtain the decoupled free section length l 1 ';

[0110] Step 3: Obtain the prestress stable value P' caused by the decoupling of the anchorage system through equation (34).

[0111] Compared with the prior art, the present invention has significant advantages and beneficial effects, which are specifically reflected in the following aspects:

[0112] 1. Utilize the shear lag theory to construct a mechanical model of the prestressed anchorage structure, and solve to obtain the shear stress, axial stress, and interface displacement distribution of the anchorage section of the prestressed anchorage structure;

[0113] 2. The present invention uses the generalized Kelvin model (H+K body) to simulate the creep properties of the rock mass, and obtains the decoupling length of the anchorage section under any prestress loading and the loss amount of the prestress as the decoupling occurs;

[0114] 3. The present invention respectively considers the coupling and decoupling situations, and can accurately predict the stable value of the prestress loss of the anchorage structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Figure 1 is the step flow chart of the method for predicting the prestress loss of the anchorage structure in the embodiment of the present invention;

[0116] Figure 2 is the schematic diagram of the shear lag model in the embodiment of the present invention;

[0117] Figure 3 is the schematic diagram of the calculation model of the prestressed anchor cable anchorage structure in the embodiment of the present invention;

[0118] Figure 4 Schematic diagram of the stress distribution of the cable element in the embodiment of the present invention;

[0119] Figure 5 Schematic diagram of the prestress loss coupling model in the embodiment of the present invention;

[0120] Figure 6 Schematic diagram of the prestress decoupling model in the embodiment of the present invention. Detailed implementation manners

[0121] To make the above objects, features and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention is provided in conjunction with the accompanying drawings.

[0122] The embodiment of the present invention provides a method for predicting the prestress loss of an anchoring structure, and the prestress loss prediction method includes:

[0123] S 1 : According to the shear lag model and the stress characteristics of the anchoring structure, establish a cable prestress calculation model in the anchoring structure, and establish the theoretical solutions of the stress distributions of the cable, the mortar body and the surrounding rock mass.

[0124] As Figure 1 shown is the mechanical calculation model of the prestressed anchoring structure obtained by combining the shear lag model and the actual stress characteristics analysis. At this time, the cable, the mortar body and the surrounding rock are all in the stage of coordinated deformation. Among them, the z-axis is the axial direction of the cable, the r-axis is the radial direction of the cable cross-section, P 0 is the prestress tension locking value of the cable (unit: N), l is the length of the cable (unit: m), l 1 is the length of the free section of the cable (unit: m), γ 1 is the radius of the cable (m), γ 2 is the outer radius of the mortar body (m), γ 3 is the influence radius of the interfacial shear stress in the rock mass (m).

[0125] Next, the load transfer process of the anchoring structure will be analyzed from three parts: the cable, the mortar body and the surrounding rock to obtain the theoretical solution of the stress distribution of the anchoring structure.

[0126] The first step: Establish the theoretical solution of the stress distribution of the cable.

[0127] Step 1: According to the elastic theory analysis and calculation, establish the stress distribution model of the cable element;

[0128]

[0129] In the formula: σ s is the axial stress of the cable (Pa), τ 1is the interfacial shear stress (Pa) between the anchor cable and the mortar body, γ 1 is the radius (m) of the anchor cable.

[0130] Step 2: After the anchor cable microelement is loaded, the relationship between its axial stress and axial displacement is:

[0131]

[0132] In the formula: u s is the axial displacement (m) of the anchor cable, E s is the elastic modulus (Pa) of the anchor cable.

[0133] Step 3: Combining Equation (2) and Equation (3), we can obtain:

[0134]

[0135] Second step: Establish the theoretical solution of the stress distribution of the mortar body.

[0136] Solve the displacement relationship between the inner and outer sides of the mortar body;

[0137] According to the shear lag model, the inner side displacement u of the mortar body 1 , that is, when r = r 1 , u 1 = u s , which is consistent with the deformation coordination of the anchor cable; the outer side displacement u of the mortar body 2 , that is, when r = r 2 , it is consistent with the deformation coordination of the surrounding rock.

[0138] From the axial equilibrium condition:

[0139] 2πr 1 τ 1 dz - 2πr 2 τ 2 dz = 0 (4)

[0140] In the formula: τ 2 is the interfacial shear stress between the mortar body and the rock mass (unit: Pa).

[0141] According to the elastic theory, inside the mortar body, along the radial direction, there is

[0142]

[0143] In the formula: G m is the shear modulus of the mortar body (unit: Pa), γ m is the radial shear strain of the mortar body, u m is the displacement of a certain point inside the mortar body (unit: m).

[0144] Considering the shear lag model and respectively assuming the inner side displacement u of the mortar body1 Coordinated with the deformation of the cable anchor, the outer displacement u of the mortar body 2 Coordinated with the deformation of the surrounding rock, by combining Eqs. (4) and (5) and substituting the boundary conditions of the inner and outer sides of the mortar body, the relationship between the inner and outer displacements of the mortar body is obtained:

[0145]

[0146] where: G m is the shear modulus of the mortar body (Pa).

[0147] Step 3: Establish the theoretical solution of the stress distribution of the surrounding rock mass.

[0148] Step 1: Calculate the influence radius r of the interface shear stress in the surrounding rock mass 3 .

[0149] The tensile stress of the prestressed cable anchor is transmitted to the surrounding rock of the anchorage section through the shear deformation of the mortar body, and its action range is r 3 , and the influence radius r of the interface shear stress in the surrounding rock mass 3 can be calculated by the following formula:

[0150] r 3 = 2.5(1 - ν r )l (7)

[0151] where: ν r is the Poisson's ratio of the rock mass.

[0152] Step 2: Determine the boundary conditions of the surrounding rock deformation and calculate the shear stress τ along the radial direction inside the surrounding rock mass r .

[0153] The boundary conditions of the surrounding rock deformation affected by the shear stress are:

[0154]

[0155] where: u r is the displacement of the surrounding rock under the action of the shear stress (unit: m).

[0156] Considering the non-linear decreasing characteristic of the shear stress in the surrounding rock, it is assumed that the shear stress τ in the surrounding rock r is distributed as follows:

[0157] τ r = τ 2 r 2 / r (r 2 ≤ r ≤ r 3 ) (9)

[0158] And according to the elastic theory, inside the surrounding rock mass, the shear stress τ r along the radial direction has:

[0159]

[0160] Where: G r is the shear modulus of the rock mass (unit: Pa); γ r is the radial shear strain of the rock mass.

[0161] Step 3: Calculate the displacement u of the surrounding rock under the action of shear stress r .

[0162] By combining Equation (8), Equation (9) and Equation (10), when r = r 2 , the relationship of the displacement u of the surrounding rock under the action of shear stress r is:

[0163]

[0164] Fourth step: Solve the stress of the anchoring structure.

[0165] By combining Equation (3), (6) and (11), we can get:

[0166]

[0167] Where:

[0168]

[0169] Solve Equation (12) to obtain the general solution,

[0170] u s = Ae αz + Be -αz (14)

[0171] Where: A and B are both constant coefficients.

[0172] According to the boundary conditions,

[0173]

[0174] By combining Equation (12), Equation (14) and Equation (15), we can get:

[0175]

[0176]

[0177] S 2 : Solve the axial displacement u s of the anchor cable and the interfacial shear stress τ 1 between the anchor cable and the mortar, the interfacial shear stress τ 2 between the mortar and the surrounding rock mass, and the axial stress σ s of the anchor cable.

[0178] S 21 : Solve for the axial displacement u of the cable bolt s ;

[0179] The axial displacement u of the cable bolt s is as follows:

[0180]

[0181] S 22 : Solve for the shear stress τ at the interface between the cable bolt and the mortar, 1 the shear stress τ at the interface between the mortar and the rock mass, 2 and the axial stress σ of the cable bolt s ;

[0182] The shear stress τ at the interface between the cable bolt and the mortar 1 、the shear stress τ at the interface between the mortar and the rock mass 2 and the axial stress σ of the cable bolt s are expressed as follows:

[0183]

[0184]

[0185]

[0186] Thus, the present invention utilizes the shear lag theory to construct a mechanical model of the prestressed anchorage structure and obtains the distributions of the shear stress, axial stress, and interface displacement in the anchorage section of the prestressed anchorage structure by solving.

[0187] S 3 : Analyze the prestress loss of the anchorage structure and establish a prestress loss coupling model and a cable bolt prestress decoupling model.

[0188] Generally, the creep of the anchored rock mass and the relaxation of the cable bolt are in a coupled state. During the creep process of the rock mass, the prestress of the cable bolt is constantly changing. Therefore, during the construction of engineering cable bolts, multi-stage tensioning or over-tensioning of the cable bolts is mostly adopted to fully adjust the forces of the steel strands of each bundle of the cable bolt, significantly reducing the prestress loss of the cable bolt.

[0189] However, when the cable bolt is subjected to excessive loads during multi-stage tensioning or over-tensioning, it will directly damage the contact interface between the cable bolt, the mortar, and the surrounding rock, resulting in the relaxation of the cable bolt and further leading to prestress loss. In addition, rock excavation and blasting are also the reasons for interface damage. Therefore, a conventional prestress coupling model is used to study the anchor-rock coupling situation.

[0190] S 31 : Establish a prestress coupling model.

[0191] After the prestressed anchor cable is tensioned and locked, if the interfacial shear stress τ 1 between the anchor cable and the mortar body does not exceed its bond strength τ u , then the interface is intact, the anchoring system is coupled, the strains of the anchor cable, the mortar body and the rock mass are coordinated, and the prestress loss of the anchor cable is coupled with the creep of the rock mass.

[0192] S 311 : The creep properties of the rock mass are simulated by using the generalized Kelvin model, and the constitutive equation is established.

[0193] To describe the coupling process of the prestress loss of the anchor cable and the creep of the rock mass, here, the generalized Kelvin model (H + K body) is used to simulate the creep properties of the rock mass. Its constitutive equation is:

[0194]

[0195] In the formula: σ r , σ r ' are the stress (Pa) and stress change rate of the rock mass, ε r , ε r ' are the strain and strain change rate of the rock mass, E r is the elastic modulus (Pa) of the rock mass, E k , η k are the elastic modulus (Pa) and viscosity coefficient of the K body when simulating the creep of the rock mass.

[0196] Thus, the present invention uses the generalized Kelvin model (H + K body) to simulate the creep properties of the rock mass, and obtains the decoupling length of the anchorage section under any prestress loading and the loss amount of the prestress as the decoupling occurs.

[0197] S 312 : The anchor cable is simulated by using a spring to obtain a prestress loss coupling model.

[0198] Please refer to Figure 5 shown. In the embodiment of the present invention, when considering the coupling effect of the creep of the rock mass surrounding the rock and the relaxation of the prestressed anchor cable, the anchor cable is simulated by using a spring, and the simulated anchor cable is connected in parallel with the simulated surrounding rock mass to obtain a prestress loss coupling model.

[0199] S 313 : Solve the equivalent elastic modulus of the anchor cable.

[0200] The equivalent elastic modulus of the anchor cable can be solved from the following expression:

[0201] E s ' = E S A s / A r (23)

[0202] Among them, E s ' is the equivalent elastic modulus of the anchor cable (unit: Pa), and E s is the elastic modulus of the anchor cable (unit: Pa), and A s is the cross-sectional area of the anchor cable body (unit: m 2 ), and A r is the area of the rock mass within the effective anchorage range of the anchor cable (unit: m 2 ).

[0203] S 314 : According to the constitutive equations and mutual relationships of the components in the prestress loss coupling model, solve the stress σ r of the rock mass around the anchorage structure.

[0204] The formula for the stress σ r of the rock mass around the anchorage structure changing with time t is as follows:

[0205]

[0206] Among them, C 1 , C 2 and C 3 can be regression calculated based on the monitoring data through the following formula,

[0207]

[0208] In the formula: ε 0 is the initial strain of the rock mass after the anchor cable is tensioned and locked, and E r is the elastic modulus of the rock mass (Pa), and E s ' is the equivalent elastic modulus of the anchor cable (Pa), and E k is the elastic modulus of the K body when simulating the creep of the rock mass (Pa), and η k is the viscosity coefficient of the K body when simulating the creep of the rock mass.

[0209] S 315 : Obtain the formula for the change of the prestress P(t) of the anchor cable with time P = σ r A r :

[0210]

[0211] When t → ∞, the value when the prestress loss of the anchor cable tends to be stable can be calculated.

[0212] Thus, the present invention can quantitatively calculate the decoupling section length and prestress loss amount between the front-end anchor cable and the mortar of the anchorage section under any prestress loading of the anchorage structure, which can further improve the overall safety and avoid the damage of the anchorage system caused by excessive prestress loading.

[0213] S 32: Establish a decoupling model for the prestress of the cable bolt;

[0214] According to the existing technology, debonding decoupling at the interface between the cable bolt and the mortar body is the main form of the failure of the anchoring structure. Accordingly, it is assumed that the decoupling of the anchoring structure only occurs at the cable bolt-mortar body interface, and the bonding at the mortar body-surrounding rock interface is good. If the prestress P 0 is applied, and the shear stress at the cable bolt-mortar body interface exceeds its bonding strength τ u (Pa), this interface will gradually debond, the anchoring system will decouple, the anchoring effect of the decoupling section will fail, and it will become a "free section", which will further lead to the relaxation of the cable bolt, the re-adjustment of the strain, and the redistribution of the axial stress and the interface shear stress of the cable bolt.

[0215] Please refer to Figure 6 as shown, which is a schematic diagram of the decoupling model for the prestress loss of the cable bolt, where l 2 is the decoupling length (m), and l 1 ' is the length of the free section (m) after the decoupling of the anchoring structure.

[0216] S 321 : When the anchoring structure is coupled, solve the total displacement S of the cable bolt 1 as:

[0217]

[0218] Solving the above formula, we can get

[0219]

[0220] S 322 : Solve the axial displacement u s , the shear stress τ 1 at the cable bolt-mortar body interface, and the distribution of the axial stress σ s of the cable bolt;

[0221] Please refer to Figure 6 as shown. After the decoupling of the anchoring structure, the prestress of the cable bolt decays to P', the decoupling section length l2 loses the anchoring effect, and the length of the "free section" becomes l 1 ', and the actual "anchoring section" length is l - l 1 '. According to the theoretical formulas obtained from the force analysis of the cable bolt in the second section, substitute P 0 in formulas (18), (19), and (21) with P', and l 1 with l 1 ', and then the axial displacement u s , the shear stress τ 1 at the cable bolt-mortar body interface, and the distribution of the axial stress σ s of the cable bolt can be obtained:

[0222]

[0223]

[0224]

[0225] S 323 : Solve for the axial displacement u of the anchor cable in the decoupled anchorage section s , the shear stress τ at the anchor cable-mortar interface 1 and the axial stress σ of the anchor cable s distribution;

[0226] When the anchoring system is decoupled, the total displacement S of the anchor cable 2 is:

[0227]

[0228] Substitute equations (23 - 25) into equation (26) to solve the above equation, and we can get

[0229]

[0230] S 324 : According to the fact that the displacement of the bottom of the anchorage section relative to the hole mouth O before and after decoupling is unchanged, from S 1 = S 2 , the tensile force P' acting on the anchorage section b - c after decoupling can be obtained;

[0231]

[0232] In the formula,

[0233]

[0234]

[0235] where when z = l 1 ', τ 1 = τ u , then

[0236]

[0237] S 4 : Calculate the prestress loss value and the final stable value of the anchor cable.

[0238] In step S 4 The specific method for calculating the prestress loss value and the final stable value of the anchor cable is:

[0239] S 41 : According to the total displacement S of the anchor cable 2 and the tensile force P' of the anchorage section b - c, obtain the free section length l 1Function formula of ''

[0240] Combining equations (33) and (34), we get:

[0241]

[0242] S 42 : By solving equation (36) using the bisection method, the decoupled free segment length l 1 ''

[0243] S 43 : The stable value P' of the prestress caused by the decoupling of the anchoring system is obtained through equation (34).

[0244] Thus, the present invention can accurately predict the stable value after the prestress loss of the anchoring structure by separately considering the coupled and decoupled cases.

[0245] Although the present disclosure is disclosed as above, the scope of protection of the present disclosure is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present disclosure, and these changes and modifications will all fall within the protection scope of the present invention.

Claims

1. A method for predicting the prestress loss of an anchoring structure, characterized in that, it includes: S 1 : According to the shear lag model and the mechanical characteristics of the anchorage structure, a calculation model for the prestress of the cable in the anchorage structure is established, and the theoretical solutions for the stress distributions of the cable, the mortar body and the surrounding rock mass are established. S 2 : Solve the axial displacement u of the cable bolt s and the interfacial shear stress τ between the cable bolt and the mortar 1 , the interfacial shear stress τ between the mortar and the surrounding rock mass 2 and the axial stress σ of the cable bolt s ; S 3 : Analysis of the prestress loss of the anchoring structure, and establishment of a prestress loss coupling model and a cable prestress decoupling model; Among them, the specific method for establishing the prestress loss coupling model is: Step 1: Use the generalized Kelvin model to simulate the creep properties of the rock mass and establish a constitutive equation, and the constitutive equation is: Where: σ r is the stress of the rock mass, unit: Pa; σ r ' is the stress change rate, ε r , ε r ' are the strain and strain change rate of the rock mass, E r is the elastic modulus of the rock mass, unit: Pa; E k , η k are the elastic modulus and viscosity coefficient of the K body when simulating the creep of the rock mass; Step 2: Use a spring to simulate the anchor cable to obtain a prestress loss coupling model; Step 3: Solve the equivalent elastic modulus of the anchor cable, and the equivalent elastic modulus of the anchor cable can be obtained by solving the following expression: E s ' = E S A s / A r (23) Among them, E s ' is the equivalent elastic modulus of the anchor cable, unit: Pa, E s is the elastic modulus of the anchor cable, unit: Pa, A s is the cross-sectional area of the anchor cable body, unit: m 2 , A r is the area of the rock mass within the effective anchorage range of the anchor cable, unit: m 2 ; Step 4: Solve for the stress σ of the rock mass around the anchoring structure according to the constitutive equations and mutual relationships of the components in the prestress loss coupling model r ; The stress σ of the rock mass around the anchoring structure r changes with time t according to the following formula: Among them, C is calculated by regression using the following formula 1 , C 2 and C 3 , Where: ε 0 is the initial strain of the rock mass after the anchor cable is tensioned and locked, E r is the elastic modulus of the rock mass (Pa), E s ' is the equivalent elastic modulus of the anchor cable (Pa), E k is the elastic modulus of the K body when simulating the creep of the rock mass (Pa), η k is the viscosity coefficient of the K body when simulating the creep of the rock mass; Step 5: Obtain the formula for the change of the prestress P(t) of the cable with r A r time: When t→∞, the value when the prestress loss of the anchor cable tends to be stable can be calculated; The specific method for establishing the prestress decoupling model of the anchor cable is: Step 1: When the anchoring structure is coupled, solve for the total displacement S of the cable 1 It is: Solving the above formula, we can get, Step 2: Solve the axial displacement u of the decoupled anchor cable in the anchorage section s , the interfacial shear stress τ between the anchor cable and the mortar 1 and the distribution of the axial stress σ of the anchor cable s ; Substitute P in Equation (18), Equation (19) and Equation (21) 0 with P', and l 1 with l 1 ', then the axial displacement u s of the decoupled anchor cable in the anchorage section, the interfacial shear stress τ 1 between the anchor cable and the mortar, and the axial stress σ s distribution can be obtained: Step 3: Solve the axial displacement u of the decoupled anchor cable in the anchorage section s , the shear stress τ between the anchor cable and the mortar interface 1 and the distribution of the axial stress σ of the anchor cable s ; When the anchoring structure is decoupled, the total displacement S of the cable 2 is: Solving the above formula, we can get, Step 4: According to the fact that the displacement of the bottom of the anchorage section relative to the hole mouth O remains unchanged before and after decoupling, from S 1 = S 2 , the tension P' acting on the anchorage section b-c after decoupling can be obtained; In the formula, where when z = l 1 ', τ 1 = τ u , then S 4 : Calculate the prestress loss value and the final stable value of the cable anchor.

2. The method for predicting the prestress loss of an anchoring structure according to claim 1, characterized in that, In step S 1 , the specific steps for establishing the theoretical solution of the stress distribution of the anchor cable are as follows: Step 1: According to elastic theory analysis and calculation, establish a stress distribution model of the anchor cable microelement; Step 2: After the anchor cable microelement is loaded, the relationship between its axial stress and axial displacement is: Step 3: Combine formula (1) and formula (2) to obtain: In the formula: σ s is the axial stress of the cable bolt, with the unit of Pa; τ 1 is the interfacial shear stress between the cable bolt and the mortar, with the unit of Pa; r 1 is the radius of the cable bolt, with the unit of m; u s is the axial displacement of the cable bolt, with the unit of m, and E s is the elastic modulus of the cable bolt, with the unit of Pa.

3. The method for predicting the prestress loss of an anchoring structure according to claim 2, characterized in that, In step S 1 the establishment of the theoretical solution of the stress distribution of the mortar body specifically includes the following steps: Solve the displacement relationship between the inside and outside of the mortar body; From the axial equilibrium condition, we get: 2πr 1 τ 1 dz - 2πr 2 τ 2 dz = 0 (4) Where: τ 2 is the shear stress at the mortar-rock interface, with the unit of Pa; r 3 is the influence radius of the interface shear stress in the rock, with the unit of m; According to elastic theory, inside the mortar body, along the radial direction, there is: Where: G m is the shear modulus of the mortar, in Pa, γ m is the radial shear strain of the mortar, u m is the displacement of a certain point inside the mortar, in m; Combine formula (4) and formula (5), and substitute the boundary conditions of the inside and outside of the mortar body to obtain the displacement relationship between the inside and outside of the mortar body: where: G m is the shear modulus of the mortar body (Pa), u 1 is the inner displacement of the mortar body, in m, u 2 is the outer displacement of the mortar body, in m.

4. The method for predicting the prestress loss of an anchoring structure according to claim 3, characterized in that, In step S 1 The specific method for establishing the theoretical solution of the stress distribution of the surrounding rock mass includes: Step 1: Calculate the influence radius r of the interface shear stress within the surrounding rock mass 3 ; The influence radius r of the interface shear stress in the surrounding rock mass 3 is calculated by the following formula: r 3 = 2.5(1 - ν r )l(7) Step 2: Determine the boundary conditions of the surrounding rock deformation and calculate the radial shear stress τ inside the surrounding rock mass r ; The boundary condition of the surrounding rock deformation affected by the shear stress is: Assume that the shear stress τ in the surrounding rock r is distributed as follows: τ r = τ 2 r 2 / r(r 2 ≤ r ≤ r 3 ) (9) And inside the surrounding rock mass, the shear stress τ r Along the radial direction, there is: Step 3: Calculate the surrounding rock displacement u under the action of shear stress r ; Combined equations (8), (9) and (10), when r = r 2 The relationship of the surrounding rock displacement u r under the action of shear stress is: where: r 3 is the influence radius of the interface shear stress in the surrounding rock mass, with the unit of m; ν r is the Poisson's ratio of the rock mass; l is the length of the anchor cable, with the unit of m; u r is the displacement of the surrounding rock under the action of shear stress, with the unit of m; G r is the shear modulus of the rock mass, with the unit of Pa; γ r is the radial shear strain of the rock mass.

5. The method for predicting the prestress loss of an anchoring structure according to claim 4, characterized in that, In step S 2 the specific steps for solving the stress of the anchoring structure include: Combining formula (3), (6) and (11) can obtain: Among them: Solve formula (12) to obtain the general solution, u s = Ae αz + Be -αz (14) According to the boundary conditions, Combining formula (12), formula (14) and formula (15) can obtain: The axial displacement u of the anchor cable s has the following expression: In the formula: A and B are both constant coefficients.

6. The method for predicting the prestress loss of an anchoring structure according to claim 5, characterized in that, In step S 2 the calculation expressions for the shear stress τ 1 between the cable anchor and the mortar interface, the shear stress τ 2 between the mortar and the rock mass interface, and the axial stress σ s of the cable anchor are as follows: where: τ 1 represents the shear stress between the interface of the cable anchor and the mortar body, τ 2 represents the shear stress between the interface of the mortar body and the rock mass, σ s represents the axial stress of the cable anchor.

7. The method for predicting the prestress loss of an anchoring structure according to claim 1, characterized in that, In step S 4 The specific method for calculating the prestress loss value and the final stable value of the cable anchor is as follows: Step 1: Obtain the function formula of the free section length l 2 ' according to the total displacement S of the cable anchor 1 and the tensile force P' of the anchorage section b-c Combining formula (33) and (34), we get: Step 2: Solve Equation (36) by the bisection method to obtain the decoupled free segment length l 1 '; Step 3: Obtain the stable prestress value P' caused by the decoupling of the anchoring system through formula (34).

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