Anchoring structure internal force calculation method of internal anchoring type anchor rod

Abstract

The invention belongs to the technical field of engineering protection and treatment, and discloses an anchoring structure internal force calculation method for an internal anchoring type anchor rod, and the method comprises the steps: building a first shear stress coupling relation between axial displacement and an anchor rod mortar interface according to the stress balance condition, axial stress and axial displacement of the anchor rod; presetting a load transfer mode from an anchor rod to a mortar body to a surrounding rock body in the anchoring structure based on the shear hysteresis model, and constructing a second shear stress coupling relationship between the axial displacement and the shear stress of the anchor rod mortar interface and the shear stress of the mortar surrounding rock interface according to the load transfer mode; based on the first shear stress coupling relation, the second shear stress coupling relation and stress boundary conditions of the anchoring structure, an anchor rod axial force analytical equation and an internal shear stress analytical equation set of the anchoring structure are constructed; and calculating the axial force and the internal shear stress of the anchor rod of the anchoring structure according to the physical parameters and the construction parameters of the anchoring structure. According to the invention, the transmission analysis of the drawing load in the anchoring structure is realized, and the displacement axial force and interface shear stress distribution of the internal anchoring type anchor rod can be calculated.

Description

Technical Field

[0001] The invention discloses a method for calculating the internal force of an anchoring structure of an internal anchorage type anchor rod, belonging to the technical field of engineering protection and treatment. Background Art

[0002] With the rapid development of large-scale water conservancy and hydropower project construction in China, the geotechnical anchoring technology has been increasingly widely applied in permanent projects such as high-steep slopes, underground caverns and concrete dams. As the core component to ensure the safety of the project, the accurate analysis of the internal force distribution of the anchoring structure is directly related to the stability and durability of the anchoring system. However, there are significant limitations in the traditional analysis methods in terms of theoretical models and practical applications.

[0003] Currently, the research on the internal force of the anchoring structure is mainly based on classical mechanical models such as Mindlin, Kelvin and Boussinesq. Such methods simplify the surrounding rock mass and the mortar body into a homogeneous continuum, and deduce the distribution law of the shear stress at the anchor rod-mortar interface through the overall force analysis. Although these models can provide preliminary calculation methods, their defect is that they do not fully consider the independent mechanical properties and interaction mechanisms of the three elements of the anchoring structure (anchor rod, mortar body and surrounding rock mass). For example, the traditional model can only simply describe the shear stress distribution at the interface between the anchor rod and the mortar, but lacks a refined characterization of key issues such as the stress transfer between the mortar body and the surrounding rock mass interface and the variation of the anchor rod axial force along the way. This limitation makes it difficult for traditional methods to comprehensively evaluate the true response of the anchoring structure under complex loads, especially there are deviations in the safety prediction under high stress or long-term service conditions.

[0004] In recent years, as an interface stress analysis tool, the shear lag model has attracted attention due to its successful application in the field of composite materials (such as fiber-reinforced matrix). By corresponding the fiber, the cementing body and the matrix to the anchor rod, the mortar body and the surrounding rock mass respectively, this model reveals the similarity between the anchoring structure and the composite material in the unidirectional axial load transfer from the force mechanism. However, there are still obvious deficiencies in the adaptability of the existing research on the shear lag model in the field of geotechnical anchoring: First, the analysis of the double shear stress coupling effect at the interface between the anchor rod-mortar body and the mortar body-rock mass interface is relatively rough, and the cooperative load transfer relationship between the two interfaces has not been established; Second, there is a lack of systematic theoretical derivation for the distribution of the anchor rod axial force, the radial deformation of the mortar body and the evolution of the stress field of the surrounding rock mass; Third, the existing methods do not form a complete internal force calculation system for the anchoring structure, and cannot quantitatively describe the displacement and internal force distribution laws at any position inside the structure. These problems seriously restrict the practical application value of the shear lag model in the anchoring project. Summary of the Invention

[0005] The object of the present invention is to solve the technical problem that the existing technology is difficult to meet the requirements of refined design and safety assessment of anchoring structures for large-scale projects and there are limitations in homogenization assumptions. To achieve the above object, the present invention proposes a method for calculating the internal force of the anchoring structure of an internal anchorage type anchor rod, and the specific scheme is as follows:

[0006] A method for calculating the internal force of the anchoring structure of an internal anchorage type anchor rod, comprising the following steps:

[0007] Step 1: Construct a first shear stress coupling relationship between the axial displacement and the interface of the anchor rod and mortar according to the force balance condition, axial stress and axial displacement of the anchor rod;

[0008] Step 2: Preset the load transfer mode from the anchor rod to the mortar body to the surrounding rock mass in the anchoring structure based on the shear lag model, and construct a second shear stress coupling relationship between the axial displacement, the shear stress at the interface of the anchor rod and mortar, and the shear stress at the interface of the mortar and surrounding rock according to the load transfer mode;

[0009] Step 3: Based on the first shear stress coupling relationship, the second shear stress coupling relationship and the force boundary conditions of the anchoring structure, construct an analytical equation for the axial force of the anchor rod and a system of analytical equations for the internal shear stress of the anchoring structure;

[0010] Step 4: According to the physical parameters and construction parameters of the anchoring structure, calculate the axial force of the anchor rod and the internal shear stress of the anchoring structure by using the analytical equation for the axial force of the anchor rod and the system of analytical equations for the internal shear stress respectively.

[0011] Preferably, step 1 specifically includes:

[0012] Based on the force balance condition of the anchor rod, construct a force balance equation between the pulling force applied to the anchor rod and the interface of the anchor rod and mortar;

[0013] Determine the linear relationship between the axial stress and axial displacement of the anchor rod according to the elastic theory;

[0014] Construct the first shear stress coupling relationship between the axial displacement and the interface of the anchor rod and mortar according to the force balance equation and the linear relationship.

[0015] Preferably, in step 2, constructing the second shear stress coupling relationship between the axial displacement, the interface of the anchor rod and mortar, and the interface of the mortar and surrounding rock according to the load transfer mode specifically includes:

[0016] Determine the shear stress and deformation displacement of the mortar body at a preset position, and construct a mortar coupling relationship between the shear stress of the mortar body and its deformation displacement according to the elastic theory;

[0017] Determine the shear stress and deformation displacement of the surrounding rock mass at a preset position, and construct a surrounding rock coupling relationship between the shear stress of the surrounding rock mass and its deformation displacement according to the elastic theory;

[0018] Construct a second shear stress coupling relationship between the axial displacement, the shear stress at the bolt-mortar interface, and the shear stress at the mortar-surrounding rock interface according to the load transfer method, the mortar coupling relationship, and the surrounding rock coupling relationship.

[0019] Preferably, step 3 specifically includes:

[0020] Step 3.1: Construct an analytical equation for the bolt axial force at a preset position in the anchoring structure according to the first shear stress coupling relationship, the second shear stress coupling relationship, and the force boundary conditions of the bolt.

[0021] Step 3.2: Construct an analytical system of equations for the internal shear stress of the anchoring structure according to the second shear stress coupling relationship and the analytical equation for the bolt axial force.

[0022] Preferably, step 3.1 further includes:

[0023] Construct an analytical equation for the displacement of the bolt at a preset position according to the first shear stress coupling relationship, the second shear stress coupling relationship, and the force boundary conditions of the bolt.

[0024] Preferably, constructing an analytical system of equations for the internal shear stress of the anchoring structure according to the second shear stress coupling relationship and the analytical equation for the bolt axial force is specifically as follows:

[0025] Construct a first shear stress equation for the bolt-mortar interface according to the second shear stress coupling relationship, the load transfer method, and the analytical equation for the displacement.

[0026] Construct a second shear stress equation for the mortar-surrounding rock interface according to the first shear stress equation and the load transfer method.

[0027] The first shear stress equation and the second shear stress equation represent the analytical system of equations for the internal shear stress.

[0028] Preferably, constructing an analytical system of equations for the internal shear stress of the anchoring structure according to the second shear stress coupling relationship and the analytical equation for the bolt axial force is specifically as follows:

[0029] Construct a third shear stress equation according to the first transfer method at the bolt-mortar interface in the load transfer method, the first shear stress equation, and the second shear stress equation.

[0030] Construct a fourth shear stress equation according to the second transfer method at the mortar-surrounding rock interface in the load transfer method, the first shear stress equation, and the second shear stress equation.

[0031] The first shear stress equation, the second shear stress equation, the third shear stress equation, and the fourth shear stress equation represent the analytical system of equations for the internal shear stress.

[0032] Preferably, after the step 3, the following steps are further included:

[0033] According to the linear relationship and the internal shear stress analysis equations of the anchoring structure, a first displacement equation at a preset position in the mortar body and a second displacement equation at a preset position in the surrounding rock body are constructed.

[0034] Preferably, after the step 4, the following steps are further included:

[0035] According to the solution of the Kelvin problem, an axial force distribution function of the bolt in the anchoring structure and a shear stress distribution function of the bolt-mortar interface are constructed;

[0036] According to the axial force distribution function and the axial force analysis equation of the bolt, the demarcation point of the bolt is determined;

[0037] According to the demarcation point, the axial force of the bolt and the shear stress of the bolt-mortar interface are calculated.

[0038] Preferably, calculating the axial force of the bolt and the shear stress of the bolt-mortar interface according to the demarcation point specifically includes:

[0039] Calculating the axial force of the bolt on the side of the demarcation point close to the anchoring section port according to the axial force distribution function;

[0040] Calculating the axial force of the bolt on the side of the demarcation point far from the anchoring section port according to the axial force analysis equation of the bolt;

[0041] Calculating the shear stress of the bolt-mortar interface on the side of the demarcation point close to the anchoring section port according to the shear stress distribution function of the bolt-mortar;

[0042] Calculating the shear stress of the bolt-mortar interface on the side of the demarcation point far from the anchoring section port according to the first shear stress equation.

[0043] Beneficial effects: The method of the present invention is based on the shear lag model for formula derivation, with clear physical and mechanical concepts and high formula refinement degree, and is mainly applicable to internal anchoring type bolts.

[0044] The present invention realizes the transfer analysis of the pull-out load among the three elements of the anchoring structure (bolt, mortar body and surrounding rock mass), and can calculate the displacement, axial force distribution of the internal anchoring type bolt, the shear stress distribution of the bolt-mortar interface and the shear stress distribution of the mortar body and the surrounding rock mass.

[0045] The method of the present invention can further calculate the displacement and internal force distribution at any position in the internal anchoring type bolt anchoring structure.

[0046] The present invention combines the shear lag model and the solution of the Kelvin problem to construct a segmented composite calculation method for the axial force of the bolt. This method calculates the internal force of the bolt in segments, improving the accuracy and refinement degree of the internal force of the bolt. Description of the Drawings

[0047] Figure 1 Schematic diagram of the calculation model of the anchoring structure in the embodiment of the present invention;

[0048] Figure 2 Schematic diagram of the force analysis of the bolt in the embodiment of the present invention.

[0049] In the figure: 1, bolt; 2, mortar body; 3, surrounding rock mass. Specific embodiments

[0050] In order to make the purpose, technical solutions and advantages of the present invention clearer, the following further details the present invention in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the protection scope of the present invention.

[0051] Through the calculation method of the present invention, engineers can design projects such as high-steep slopes and tunnel supports more accurately, significantly improving the safety and economy of the anchoring structure.

[0052] A method for calculating the internal force of the anchoring structure of an internal anchoring type bolt disclosed by the present invention specifically includes the following steps:

[0053] Step 1: Construct a coupling relationship between the axial displacement and the first shear stress at the bolt-mortar interface according to the force balance condition, axial stress and axial displacement of the bolt;

[0054] Further, step 1 specifically includes: based on the force balance condition of the bolt, construct a force balance equation between the pulling force applied to the bolt and the force at the bolt-mortar interface;

[0055] As Figure 1 shown in the schematic diagram of the calculation model of the anchoring structure, 1 represents the bolt, 2 represents the mortar body, and 3 represents the surrounding rock mass. Based on the force balance condition of the bolt in the anchoring structure, it can be known that the free section of the bolt only bears the tensile force, and the load applied to the internal anchoring type bolt is transmitted to the mortar body through the bonding and frictional effects at the anchoring section of the bolt and the bolt-mortar interface, and then transmitted to the surrounding rock mass through the interaction between the mortar body and the surrounding rock mass; from the above, it can be seen that the pulling force received by the bolt is equal to the frictional resistance Figure 2 of the mortar body to the anchoring section of the bolt. As shown in the figure, and

[0056] are the lengths of the free section and the anchoring section of the bolt respectively.

[0057] (1)

[0058] After sorting out, it can be obtained:

[0059] (2)

[0060] Wherein:

[0061] is the pulling force on the anchor rod;

[0062] is the radius of the anchor rod (m);

[0063] is the axial stress (Pa) of any cross-section of the anchor rod;

[0064] is the interfacial shear stress (Pa) of any cross-section of the anchor rod mortar.

[0065] Determine the linear relationship between the axial stress and axial displacement of the anchor rod according to the elastic theory;

[0066] Specifically, when the anchor rod is in the elastic deformation state, the linear relationship between the axial stress and axial displacement of any cross-section of the anchor rod is as shown in the following formula:

[0067] ;

[0068] Wherein;

[0069] is the axial stress (Pa) of any cross-section of the anchor rod;

[0070] is the elastic modulus of the anchor rod;

[0071] is the axial displacement of the anchor rod.

[0072] Construct the coupling relationship between the axial displacement of the anchor rod and the first shear stress at the anchor rod mortar interface according to the force balance equation and the linear relationship.

[0073] Specifically, substituting the linear relationship formula into the force balance equation obtained by sorting, that is, formula (2), the coupling relationship between the axial displacement and the first shear stress at the anchor rod mortar interface can be obtained after the anchor rod is stressed.

[0074] The first shear stress coupling relationship is specifically the relationship formula between the axial displacement of the anchor rod and the shear stress at the anchor rod mortar interface:

[0075] (3)

[0076] Wherein:

[0077] is the axial displacement of the anchor rod;

[0078] is the shear stress at the bolt-mortar interface (Pa).

[0079] Step 2: Based on the shear lag model, preset the load transfer mode from the bolt to the mortar and then to the surrounding rock mass in the anchoring structure. According to the load transfer mode, construct the second shear stress coupling relationship between the axial displacement and the shear stress at the bolt-mortar interface and the shear stress at the mortar-surrounding rock interface;

[0080] Specifically, the shear lag model was first used for the stress analysis of composite material interfaces. The fibers, cementitious materials, and matrix it contains are similar to the mechanical properties of the cable bolt / bolt: the fibers in the shear lag model can be regarded as bolts, the cementitious materials simulate the mortar, and the matrix corresponds to the surrounding rock mass; from the analysis of the stress state, both the bolt and the fiber bear unidirectional axial loads, so their mechanical characteristics are the same. Therefore, preset the load transfer mechanism of the anchoring structure based on the shear lag model.

[0081] Furthermore, in Step 2, according to the load transfer mode, construct the second shear stress coupling relationship between the axial displacement and the shear stress at the bolt-mortar interface and the shear stress at the mortar-surrounding rock interface, which specifically includes:

[0082] Determine the shear stress and deformation displacement of the mortar at the preset position, and construct the mortar coupling relationship between the shear stress of the mortar and its deformation displacement according to the elastic theory;

[0083] Determine the shear stress and deformation displacement of the surrounding rock mass at the preset position, and construct the surrounding rock coupling relationship between the shear stress of the surrounding rock mass and its deformation displacement according to the elastic theory;

[0084] According to the load transfer mode, the mortar coupling relationship, and the surrounding rock coupling relationship, construct the second shear stress coupling relationship between the axial displacement and the shear stress at the bolt-mortar interface and the shear stress at the mortar-surrounding rock interface.

[0085] Specifically, according to the load transfer mode of the shear lag model: the load is transferred in the form of shear load in the mortar and the surrounding rock mass, and it can be obtained that in the load transfer mode, the shear stress decays along the radial direction of the anchoring structure with the following attenuation relationship shown in the formula:

[0086] (4)

[0087] In the formula:

[0088] ;

[0089] is the shear stress at the bolt-mortar interface (Pa);

[0090] is the shear stress at the mortar-surrounding rock interface (Pa);

[0091] is the shear stress at the boundary of the surrounding rock mass;

[0092] is the shear stress of any cross-section inside the mortar body and the surrounding rock mass;

[0093] is the action radius at any position inside the mortar body and the surrounding rock mass;

[0094] is the outer radius of the mortar body;

[0095] is the action range of the pulling force on the surrounding rock mass;

[0096] is the Poisson's ratio of the rock mass.

[0097] According to the elastic theory, there is the following relationship between the shear stress of any point inside the mortar body and the deformation displacement of this point, the shear stress of any point inside the surrounding rock mass and the deformation displacement of this point:

[0098] (5)

[0099] In the formula:

[0100] is the shear stress of any point inside the mortar body;

[0101] is the shear stress of any point inside the surrounding rock mass;

[0102] is the axial displacement of any point inside the mortar body;

[0103] is the axial displacement of any point inside the surrounding rock mass;

[0104] is the shear modulus of the mortar body (Pa);

[0105] is the shear modulus of the surrounding rock mass (Pa).

[0106] The above formula represents the coupling relationship between the shear stress and displacement of the mortar body and the surrounding rock mass respectively. By organizing formulas (4) and (5), we can get:

[0107] (6)

[0108] In the formula:

[0109] 、 are arbitrary constants.

[0110] Subsequently, according to the boundary condition: the displacements at the interface of the bolt-mortar body-rock mass are equal. The relationship between the axial displacement of the bolt and the shear stress at the interface of the bolt-mortar body-rock mass can be obtained, that is, the second shear stress coupling relationship, as shown in the following formula:

[0111] (7)

[0112] Step 3: Based on the first shear stress coupling relationship, the second shear stress coupling relationship, and the force boundary conditions of the anchoring structure, construct the analytical equation of the bolt axial force and the analytical equation set of the internal shear stress of the anchoring structure;

[0113] Furthermore, Step 3 specifically includes:

[0114] Step 3.1: According to the first shear stress coupling relationship, the second shear stress coupling relationship, and the force boundary conditions of the bolt, construct the analytical equation of the bolt axial force at a preset position in the anchoring structure.

[0115] Furthermore, Step 3.1 also includes constructing the displacement analytical equation of the bolt at a preset position according to the first shear stress coupling relationship, the second shear stress coupling relationship, and the force boundary conditions of the bolt.

[0116] Specifically, substitute the above second shear stress coupling relationship, i.e., formula (7), into the first shear stress coupling relationship, i.e., formula (3), and couple the force boundary conditions of the internal anchorage type bolt to obtain the displacement analytical equation and the bolt axial force analytical equation at the preset position of the bolt.

[0117] The boundary conditions specifically include:

[0118] When time, , is the initial tensile force (N) of the bolt;

[0119] When time, .

[0120] The displacement analytical equation at any position of the bolt is:

[0121] (8)

[0122] In the formula: ;

[0123] The axial force analytical equation at any position of the bolt is:

[0124] (9)

[0125] Step 3.2: According to the second shear stress coupling relationship and the bolt axial force analytical equation, construct the analytical equation set of the internal shear stress of the anchoring structure.

[0126] Furthermore, according to the second shear stress coupling relationship and the bolt axial force analytical equation, an analytical equation set of internal shear stress of the anchoring structure is constructed, specifically as follows:

[0127] Construct the first shear stress equation of the bolt mortar interface according to the second shear stress coupling relationship, the load transfer mode and the displacement analytical equation;

[0128] Construct the second shear stress equation of the mortar surrounding rock interface according to the first shear stress equation and the said load transfer mode;

[0129] The first shear stress equation and the second shear stress equation are characterized as the analytical equation set of internal shear stress.

[0130] Specifically, by coupling the second shear stress coupling relationship, the load transfer mode and the displacement analytical equation, the first shear stress equation of the bolt mortar interface is obtained as shown in the following formula:

[0131] (10)

[0132] According to the first shear stress equation and the said load transfer mode, the second shear stress equation of the mortar surrounding rock interface is obtained as shown in the following formula:

[0133] (11)

[0134] Furthermore, according to the second shear stress coupling relationship and the bolt axial force analytical equation, an analytical equation set of internal shear stress of the anchoring structure is constructed, specifically as follows:

[0135] Construct the third shear stress equation according to the first transfer mode of the bolt mortar interface in the load transfer mode, the first shear stress equation and the second shear stress equation;

[0136] Construct the fourth shear stress equation according to the second transfer mode of the mortar surrounding rock interface in the load transfer mode, the first shear stress equation and the second shear stress equation;

[0137] The first shear stress equation, the second shear stress equation, the third shear stress equation and the fourth shear stress equation are characterized as the analytical equation set of internal shear stress.

[0138] Specifically, by coupling the first shear stress equation, the second shear stress equation and the first transfer mode representing the bolt mortar interface in the load transfer mode, the third shear stress equation at any position in the mortar body is:

[0139] (12)

[0140] By coupling the first shear stress equation, the second shear stress equation and the second transfer mode representing the mortar surrounding rock interface in the load transfer mode, the fourth shear stress equation at any position in the surrounding rock body is:

[0141] (13)

[0142] Further, after step 3, it further includes:

[0143] Construct the first displacement equation at a preset position in the mortar body and the second displacement equation at a preset position in the surrounding rock mass according to the linear relationship and the internal shear stress analysis equations of the anchoring structure.

[0144] Specifically, by coupling the linear relationship, the first shear stress equation, and the third shear stress equation, the first displacement equation at any position in the mortar body is obtained as follows:

[0145] (14)

[0146] By coupling the linear relationship, the second shear stress equation, and the fourth shear stress equation, the second displacement equation at any position in the surrounding rock mass is obtained as follows:

[0147] (15)

[0148] Further, before step 4, it includes: obtaining the physical parameters and construction parameters of the anchoring structure;

[0149] The physical parameters include the elastic modulus of the bolt in the anchoring structure, the shear modulus of the mortar body, the shear modulus of the surrounding rock mass, and the Poisson's ratio;

[0150] The construction parameters include the initial tensile force of the bolt in the anchoring structure, the free length of the bolt, and the anchorage length.

[0151] Step 4: According to the physical parameters and construction parameters of the anchoring structure, use the bolt axial force analysis equation and the internal shear stress analysis equations to calculate the bolt axial force and internal shear stress of the anchoring structure respectively.

[0152] Specifically, substituting the obtained initial tensile force of the bolt, the free length of the bolt, and the anchorage length, the elastic modulus of the bolt in the anchoring structure, the shear modulus of the mortar body, the shear modulus of the surrounding rock mass, and the Poisson's ratio into formulas (8) to (15), the displacement and axial force distribution of the internal anchorage type bolt, the shear stress distribution at the bolt-mortar interface, the shear stress distribution in the mortar body and the surrounding rock mass, and the displacement and internal force distribution at any position in the internal anchorage type bolt anchoring structure can be obtained.

[0153] Further, after step 4, it further includes:

[0154] Optimizing the physical parameters and / or construction parameters of the anchoring structure.

[0155] Based on the above-obtained calculation results, compare the axial force distribution curves of different bolt types (including different steel materials and diameter changes), different mortar ratios, different bolt pull-out loads, and different anchorage lengths. Through the axial force distribution of internal anchorage bolts, the effective anchorage length can be determined to further optimize the design and adjust the construction process.

[0156] Compare the shear stress distribution curves at the interfaces of bolt-mortar body-rock mass for different bolt types (including different steel materials and diameter changes), different mortar ratios, different bolt pull-out loads, and different anchorage lengths. By comparing the bond strengths between the selected bolts and the mortar body, the mortar body and the rock mass with the shear stress distribution at the bolt-mortar body-rock mass interfaces, the possible debonding failures can be determined to further optimize the design and adjust the construction process.

[0157] Compare the axial displacements of bolts, and the distribution laws of displacements of mortar bodies and rock masses for different bolt types (including different steel materials and diameter changes), different mortar ratios, different bolt pull-out loads, and different anchorage lengths. Judge whether the displacements within the anchorage structure are within the displacement control range, and then optimize the design and adjust the construction process.

[0158] The method of the present invention is based on the shear lag model for formula derivation, with clear physical and mechanical concepts and a high degree of formula refinement, and is mainly applicable to internal anchorage bolts.

[0159] The present invention realizes the transfer analysis of the pull-out load among the three elements of the anchorage structure (bolt, mortar body, and rock mass), and can calculate the displacements and axial force distributions of internal anchorage bolts, the shear stress distributions at the bolt-mortar interfaces, and the shear stress distributions between the mortar body and the rock mass.

[0160] The method of the present invention can further calculate the displacements and internal force distributions at any position within the anchorage structure of internal anchorage bolts.

[0161] Aiming at the characteristics of rock masses at the construction site, the present invention can compare the influence laws of different bolt types (including different steel materials and diameter changes) and different mortar ratios on the distribution characteristics of internal forces of the anchorage structure, and then optimize the selection of anchorage materials that coordinate safety and economy; it can also study the internal force distribution laws of the anchorage structure under different bolt pull-out loads and different anchorage lengths to guide the optimization design of the construction methods for internal anchorage bolts. This method provides a theoretical reference for the stability evaluation and safety control of geotechnical anchorage projects.

[0162] In a further embodiment, to further improve the accuracy and refinement degree of bolt internal force analysis, it further includes constructing the axial force distribution function of the bolt and the shear stress distribution function at the bolt-mortar interface in the anchorage structure according to the solution of the Kelvin problem.

[0163] Specifically, the solution of the Kelvin problem refers to a point in an infinite space body without considering body forces. under the action of a concentrated force . The solution of this problem for the axial displacement in the shaft direction is expressed as:

[0164] (16)

[0165] where:

[0166] ;

[0167] , are the shear modulus and Poisson's ratio of the semi-infinite space body, respectively;

[0168] , , respectively represent the action ranges of the semi-infinite space body on the axes in the , , directions;

[0169] represents the distance from any point in the semi-infinite space body to the point.

[0170] If it is assumed that during the tensioning process of the anchor bolt, the anchor bolt, the mortar body, and the surrounding rock mass are in an elastic state and no relative cracks are generated; and it is assumed that the properties of the rock mass and the mortar body are similar, or the mortar body is relatively thin, then the solution of the Kelvin problem can be used to analyze the stress of the anchorage section of the anchor bolt.

[0171] At the origin , , then (16) can be simplified to:

[0172] (17)

[0173] where: is the combined elastic modulus (Pa) of the surrounding rock mass and the mortar body.

[0174] According to the load-displacement reciprocity theorem, the elongation of the anchor bolt is equal to the displacement of the surrounding anchor body, and the equilibrium equation is established as:

[0175] (18)

[0176] Calculating the above formula, we can obtain:

[0177] (19)

[0178] where:

[0179] is an arbitrary constant;

[0180] ;

[0181] is the radius of the anchor rod (m);

[0182] is the Poisson's ratio of the rock mass;

[0183] is the combined elastic modulus of the surrounding rock mass and the mortar (Pa), and can be calculated by the following formula:

[0184] ;

[0185] In this formula: is the elastic modulus of the mortar (Pa); is the elastic modulus of the surrounding rock mass (Pa), is the elastic modulus of the anchor rod (Pa).

[0186] Substitute the boundary conditions: the port of the anchorage section (the junction of the anchorage section and the free section of the anchor rod), the bottom of the anchorage section ; .

[0187] The distribution function of the shear stress at the interface between the anchor rod and the mortar along the axis of the anchorage section of the anchor rod can be obtained and the distribution function of the axial force , that is, the distribution function of the shear stress at the interface between the anchor rod and the mortar and the distribution function of the axial force of the anchor rod in the anchoring structure:

[0188] (20)

[0189] (21)

[0190] Subsequently, determine the demarcation point of the anchor rod according to the axial force distribution function and the analytical equation of the axial force of the anchor rod;

[0191] Specifically, set formula (21) equal to formula (9), and it can be analytically obtained that at a certain position in the anchorage section of the anchor rod, the axial forces are equal, and this position is marked as the demarcation point of the anchor rod.

[0192] Determine the calculation method of the axial force of the anchor rod according to the demarcation point.

[0193] Furthermore, calculate the axial force of the anchor rod on the side of the demarcation point close to the port of the anchorage section according to the axial force distribution function; calculate the axial force of the anchor rod on the side of the demarcation point far from the port of the anchorage section according to the analytical equation of the axial force of the anchor rod.

[0194] Specifically, through verification, it is known that the axial force distribution function of the bolt constructed according to the solution of the Kelvin problem can better reflect the change trend of the axial force of the bolt on the side of the boundary point close to the anchorage section port; while the analytical equation of the axial force of the bolt constructed based on the shear lag model can better reflect the change trend of the axial force of the bolt on the side of the boundary point far from the anchorage section port.

[0195] Based on this, the calculation formula for the axial force of the bolt determined according to the boundary point is as follows:

[0196] (22)

[0197] Furthermore, the embodiment of the present invention also includes calculating the shear stress of the bolt mortar interface on the side of the boundary point close to the anchorage section port according to the shear stress distribution function of the bolt mortar; calculating the shear stress of the bolt mortar interface on the side of the boundary point far from the anchorage section port according to the first shear stress equation.

[0198] Based on this, the calculation formula for the shear stress of the bolt mortar interface determined according to the boundary point is as follows:

[0199] (23)

[0200] The present invention uses the above-mentioned segmented composite calculation method to construct the calculation formula of the bolt axial force. Specifically, taking the intersection point of the two calculation models as the boundary, the Kelvin problem solution is used to describe the interface bond-slip behavior on the side of the boundary point close to the anchorage section port, and the shear lag model is used to characterize the shear stress diffusion characteristics on the side of the boundary point far from the anchorage section port. The prediction accuracy of this segmented composite method is more in line with the physical essence of the mechanical response of the anchorage interface than a single method.

[0201] The above are only several embodiments of the present invention, and do not impose any form of limitation on the present invention. Although the present invention is disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art, without departing from the scope of the technical solution of the present invention, making some changes or modifications using the disclosed technical content is equivalent to an equivalent embodiment, and all belong to the scope of the technical solution.

Claims

1. A method for calculating the internal force of the anchoring structure of an internal anchoring type bolt, characterized in that, It includes the following steps: Step 1: Construct the first shear stress coupling relationship between the axial displacement and the bolt-mortar interface based on the force balance condition, axial stress, and axial displacement of the bolt; Step 2: Preset the load transfer mode from the bolt to the mortar body to the surrounding rock mass in the anchoring structure based on the shear lag model, and construct the second shear stress coupling relationship between the axial displacement, the shear stress at the bolt-mortar interface, and the shear stress at the mortar-surrounding rock interface according to the load transfer mode; Step 3: Based on the first shear stress coupling relationship, the second shear stress coupling relationship, and the force boundary conditions of the anchoring structure, construct the bolt axial force analytical equation and the internal shear stress analytical equation set of the anchoring structure; Step 4: Calculate the bolt axial force and the internal shear stress of the anchoring structure respectively using the bolt axial force analytical equation and the internal shear stress analytical equation set according to the physical parameters and construction parameters of the anchoring structure.

2. The method for calculating the internal force of the anchoring structure according to claim 1, characterized in that, The specific content of Step 1 includes: Based on the force balance condition of the bolt, construct the force balance equation between the pulling force applied to the bolt and the force at the bolt-mortar interface; Determine the linear relationship between the axial stress and the axial displacement of the bolt according to the elastic theory; Construct the first shear stress coupling relationship between the axial displacement and the bolt-mortar interface according to the force balance equation and the linear relationship.

3. The method for calculating the internal force of the anchoring structure according to claim 1, characterized in that, In Step 2, constructing the second shear stress coupling relationship between the axial displacement, the shear stress at the bolt-mortar interface, and the shear stress at the mortar-surrounding rock interface according to the load transfer mode specifically includes: Determine the shear stress and the deformation displacement of the mortar body at the preset position, and construct the mortar coupling relationship between the shear stress of the mortar body and its deformation displacement according to the elastic theory; Determine the shear stress and the deformation displacement of the surrounding rock mass at the preset position, and construct the surrounding rock coupling relationship between the shear stress of the surrounding rock mass and its deformation displacement according to the elastic theory; Construct the second shear stress coupling relationship between the axial displacement, the shear stress at the bolt-mortar interface, and the shear stress at the mortar-surrounding rock interface according to the load transfer mode, the mortar coupling relationship, and the surrounding rock coupling relationship.

4. The method for calculating the internal force of the anchoring structure according to claim 2, characterized in that, The specific content of Step 3 includes: Step 3.1: Construct the bolt axial force analytical equation of the bolt at the preset position in the anchoring structure according to the first shear stress coupling relationship, the second shear stress coupling relationship, and the force boundary condition of the bolt; Step 3.2: Construct the internal shear stress analytical equation set of the anchoring structure according to the second shear stress coupling relationship and the bolt axial force analytical equation.

5. The method for calculating the internal force of the anchoring structure according to claim 4, characterized in that, Step 3.1 further includes: Construct the displacement analytical equation of the bolt at the preset position according to the first shear stress coupling relationship, the second shear stress coupling relationship, and the force boundary condition of the bolt.

6. The method for calculating the internal force of the anchoring structure according to claim 5, characterized in that, Constructing the internal shear stress analytical equation set of the anchoring structure according to the second shear stress coupling relationship and the bolt axial force analytical equation specifically means: Construct the first shear stress equation of the bolt-mortar interface according to the second shear stress coupling relationship, the load transfer mode, and the displacement analytical equation; Construct the second shear stress equation of the mortar-surrounding rock interface according to the first shear stress equation and the load transfer mode; The first shear stress equation and the second shear stress equation are characterized as the internal shear stress analytical equation set.

7. The method for calculating the internal force of the anchoring structure according to claim 6, characterized in that, According to the second shear stress coupling relationship and the analytical equation of the bolt axial force, an analytical equation system of the internal shear stress of the anchoring structure is constructed, specifically as follows: A third shear stress equation is constructed according to the first transfer mode of the bolt-mortar interface in the load transfer mode, the first shear stress equation and the second shear stress equation; A fourth shear stress equation is constructed according to the second transfer mode of the mortar-surrounding rock interface in the load transfer mode, the first shear stress equation and the second shear stress equation; The first shear stress equation, the second shear stress equation, the third shear stress equation and the fourth shear stress equation are characterized as the analytical equation system of the internal shear stress; 8. The method for calculating the internal force of the anchoring structure according to claim 2, characterized in that, After the step 3, it further includes: According to the linear relationship and the analytical equation system of the internal shear stress of the anchoring structure, a first displacement equation at a preset position in the mortar body and a second displacement equation at a preset position in the surrounding rock body are constructed.

9. The method for calculating the internal force of the anchoring structure according to claim 6, characterized in that, After the step 4, it further includes: According to the solution of the Kelvin problem, an axial force distribution function of the bolt in the anchoring structure and a shear stress distribution function of the bolt-mortar interface are constructed; The demarcation point of the bolt is determined according to the axial force distribution function and the analytical equation of the bolt axial force; The bolt axial force and the shear stress of the bolt-mortar interface are calculated according to the demarcation point.

10. The internal force calculation method of the anchoring structure according to claim 9, characterized in that, Calculating the bolt axial force and the shear stress of the bolt-mortar interface according to the demarcation point specifically includes: Calculating the bolt axial force on the side of the demarcation point close to the anchoring section port according to the axial force distribution function; Calculating the bolt axial force on the side of the demarcation point far from the anchoring section port according to the analytical equation of the bolt axial force; Calculating the shear stress of the bolt-mortar interface on the side of the demarcation point close to the anchoring section port according to the shear stress distribution function of the bolt-mortar; Calculating the shear stress of the bolt-mortar interface on the side of the demarcation point far from the anchoring section port according to the first shear stress equation.

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