Non-full-length bonding type anchor cable drawing load elastic stage stress calculation method and system

Abstract

The invention provides a non-full-length bonding type anchor cable drawing load elastic stage stress calculation method and system, and relates to the technical field of anchor cable supporting, and the method comprises the steps: considering the influence of a free section grouting body on the elastic stage load transmission of an anchor cable system, and building an anchoring section and free section mechanical equilibrium differential equation; according to the actual stress state of the anchor rod, the stress boundary condition and the elastic deformation continuous condition of the end of the anchor rod are determined, and according to the boundary condition and the elastic deformation continuous condition, the undetermined coefficient of a mechanical equilibrium differential equation is determined; calculating the average stress of the anchoring section grouting body and the steel strand, the axial stress of the free section grouting body and the displacement of the free section grouting body and the anchoring section grouting body according to the undetermined coefficient of the mechanical equilibrium differential equation; based on the calculated average axial stress of the anchor body of the anchor cable and the displacement of the grouting body, establishing a stress balance equation of the steel strand in the anchoring section and the grouting body, and solving the stress balance equation to determine the axial stress of the steel strand and the axial stress of the grouting body of the anchoring section for subsequent optimization design of the anchor cable.

Description

Technical Field

[0001] The present invention relates to the technical field of anchor cable support, and in particular to a method and system for calculating the stress of a non-full-length bonded anchor cable under an elastic stage of a pull-out load. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] Prestressed anchor cables are widely used in geotechnical engineering reinforcement in domestic and foreign projects. The study of their anchoring mechanism plays an important role in accurately judging the stress stage of the anchor cable system and reasonably predicting the ultimate bearing capacity of the anchor cable. The load transfer mechanism of prestressed anchor cables under pulling action is mainly caused by the relative movement of steel strands, grouting bodies and soil bodies with different mechanical properties. However, most studies only study full-length bonded anchor rods, and there are relatively few studies on non-full-length bonded anchor rods. In addition, only the load transfer mechanism of the anchoring section is discussed, ignoring the influence of the free section. The free section grouting body has a significant influence on the overall load transfer of the anchor cable during the pulling process of the anchor cable. If the free section grouting body is not considered, the axial force and shear stress distribution law obtained by the anchor cable calculation formula is seriously inconsistent with the actual situation.

[0004] In the existing methods, the stress distribution of the steel strand and the grouting body in the theoretical model of the elastic stage of the non-full-length bonded anchor is not fully considered, and the stress distribution of the grouting body and the steel strand in the anchoring section is not calculated. In practical applications, due to the difference in elastic modulus between the steel strand and the grouting body, the stress distribution between the two is actually nonlinear, especially under large tensile forces, the stress of the grouting body is usually lower than the stress of the steel strand. In addition, the explanations of the load in the relevant schemes are mostly empirical formulas. For example, in the patent - Calculation method of anchoring force of long anchor cables through fully filled caves (authorization number CN 110306548 B), the stress-strain relationship between the contact surface of the anchor and the rock mass under ideal conditions is used when analyzing the anchor body, and the stress distribution of the anchor cable system of the steel strand and the grouting body material in the anchor body when being pulled, and the influence of the free section grouting body on the pull-out bearing capacity of the anchor cable are not considered. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a stress calculation method and system for the elastic stage of the pull-out load of a non-full-length bonded anchor cable. In the elastic stage of the pull-out load of the anchor cable, the influence of the free section grouting on the load transfer of the anchor cable system is considered, and based on the axial deformation characteristics, the mechanical equilibrium differential equations of the free section and the anchoring section are established. By solving the differential equations at different positions, the force boundary conditions at the anchor rod end and the continuity conditions of the grouting deformation are described, the unknown coefficients of the differential equations are determined, the average axial stress of the anchor body and the displacement of the grouting body are solved, and finally the expressions of the axial stresses of the grouting body and the steel strand in the anchoring section are solved.

[0006] According to some embodiments, the present disclosure adopts the following technical solutions:

[0007] The stress calculation method of the elastic stage of the pull-out load of the non-full-length bonded anchor cable includes:

[0008] Considering the influence of the grouting of the anchor section and the free section on the load transfer of the anchor cable system in the elastic stage, the mechanical equilibrium differential equations of the anchor section and the free section are established;

[0009] Determine the stress boundary conditions and elastic deformation continuity conditions of the anchor end according to the actual stress state of the anchor, and determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and elastic deformation continuity conditions;

[0010] According to the undetermined coefficients of the mechanical equilibrium differential equation, the average stress of the grouting body and the steel strand in the anchoring section, the axial stress of the grouting body in the free section, and the displacement of the grouting body in the free section and the anchoring section are calculated;

[0011] Based on the calculated average axial stress of the anchor body and the displacement of the grouting body, the stress balance equation of the steel strand and the grouting body in the anchoring section is established. The stress balance equation is solved to determine the axial stress of the steel strand and the axial stress of the grouting body in the anchoring section for subsequent anchor optimization design.

[0012] According to some embodiments, the present disclosure adopts the following technical solutions:

[0013] The stress calculation system for the elastic stage of the pull-out load of non-full-length bonded anchor cable includes:

[0014] Mathematical model building module, used to consider the influence of grouting in the anchor section and free section on the load transfer in the elastic stage of the anchor cable system, and to establish the mechanical equilibrium differential equations of the anchor section and free section;

[0015] A boundary condition determination module is used to determine the stress boundary conditions and elastic deformation continuity conditions of the anchor end according to the actual stress state of the anchor, and to determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and the elastic deformation continuity conditions;

[0016] The stress calculation module is used to calculate the average stress of the grouting body and the steel strand in the anchoring section, the axial stress of the grouting body in the free section, and the displacement of the grouting body in the free section and the anchoring section according to the unknown coefficients of the mechanical equilibrium differential equation; based on the calculated average axial stress of the anchor body of the anchor cable and the displacement of the grouting body, the stress balance equation of the steel strand and the grouting body in the anchoring section is established, and the stress balance equation is solved to determine the axial stress of the steel strand and the axial stress of the grouting body in the anchoring section for subsequent anchor cable optimization design.

[0017] According to some embodiments, the present disclosure adopts the following technical solutions:

[0018] A computer program product comprises a computer program, wherein when the computer program is executed by a processor, the method for calculating the stress of a non-full-length bonded anchor cable under a tension load in the elastic stage is implemented.

[0019] According to some embodiments, the present disclosure adopts the following technical solutions:

[0020] A non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the method for calculating the elastic stage stress of a non-full-length bonded anchor cable pull-out load is implemented.

[0021] According to some embodiments, the present disclosure adopts the following technical solutions:

[0022] An electronic device comprises: a processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device implements the elastic stage stress calculation method of the non-full-length bonded anchor cable pull-out load.

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The stress calculation method for the elastic stage of the pull-out load of a non-full-length bonded anchor disclosed in the present invention proposes an analytical calculation method for the load transfer law of the non-full-length bonded anchor in the elastic stress stage of the pull-out load on the basis of considering the difference in stress distribution between the two and the influence of the anchor section and the free section grouting on the load transfer of the anchor system. By considering the influence of the free section grouting on the pull-out bearing capacity of the anchor and finely analyzing the stress distribution law between the steel strand and the grouting, the non-uniform stress transfer characteristics caused by the difference in elastic modulus between the two are clarified, and the stress distribution of the anchor system in the elastic stage is truly reflected. The theoretical support and engineering guidance are provided for the design and construction of non-full-length bonded anchors, which is helpful to promote the application standardization of this technology in the fields of deep foundation pit support, rock and soil anchoring, slope protection, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The illustrative embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation on the present disclosure.

[0026] Figure 1 It is a flow chart of a method for calculating stress in the elastic stage of a pull-out load of a full-length bonded anchor cable according to an embodiment of the present disclosure;

[0027] Figure 2 A simplified diagram of a computing model of an embodiment of the present disclosure;

[0028] in, Figure 2 (a) is a schematic diagram of the stress on the non-full-length bonded anchor cable; Figure 2 (b) is the mechanical model of the anchor cable;

[0029] Figure 3 It is a schematic diagram of the distribution of axial stress and interface shear stress of the anchor cable in the elastic stage according to an embodiment of the present disclosure;

[0030] Figure 4 The axial stress distribution of the grouting body and the steel strand along the entire length of the anchor cable in the elastic stage of the embodiment of the present disclosure. DETAILED DESCRIPTION

[0031] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0032] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0033] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0034] Example 1

[0035] In one embodiment of the present disclosure, a method for calculating the stress of a non-full-length bonded anchor cable under a pull-out load in the elastic stage is provided, comprising the following steps:

[0036] Step 1: Considering the influence of the grouting of the anchor section and the free section on the load transfer of the anchor system in the elastic stage, the mechanical equilibrium differential equations of the anchor section and the free section are established;

[0037] Step 2: Determine the stress boundary conditions and elastic deformation continuity conditions of the anchor end according to the actual stress state of the anchor, and determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and elastic deformation continuity conditions;

[0038] Step 3: Calculate the average stress of the grouting body and the steel strand in the anchoring section, the axial stress of the grouting body in the free section, and the displacement of the grouting body in the free section and the anchoring section according to the undetermined coefficients of the mechanical equilibrium differential equation;

[0039] Step 4: Based on the calculated average axial stress of the anchor body and the displacement of the grouting body, establish the stress balance equation of the steel strand and the grouting body in the anchoring section, and solve the stress balance equation to determine the axial stress of the steel strand and the axial stress of the grouting body in the anchoring section for subsequent anchor optimization design.

[0040] As an embodiment, the present invention discloses a method for calculating the stress of the elastic stage of the pull-out load of a non-full-length bonded anchor cable. Considering the influence of the anchoring section and the free section grouting on the load transfer of the anchor cable system, the mechanical equilibrium differential equation of the free section and the anchoring section micro-element is first established based on the axial deformation characteristics. Then, the differential equations at different positions are solved, and the coefficients of the differential equations are determined through the force boundary conditions at the end of the anchor rod and the continuous conditions of the grouting deformation. The average axial stress of the anchor body and the displacement of the grouting body are solved, and finally the expressions of the axial stress of the anchoring section grouting body and the steel strand are solved. The specific implementation process is as follows:

[0041] Step 1: Considering the influence of the grouting of the anchor section and the free section on the load transfer of the anchor system in the elastic stage, the mechanical equilibrium differential equations of the anchor section and the free section are established;

[0042] Specifically, the total displacement u of the anchor end is composed of the tensile deformation of the free section steel strand, the displacement of the anchor section, the straightening of the steel strand, the gap between the anchor and the pad, and the locking of the anchor clip. In the early stage of anchor cable tensioning, the influence of straightening and gap can be basically eliminated. This disclosure mainly considers two parts of deformation: the tensile deformation u of the free section steel strand f and the displacement u of the anchoring segment a .

[0043] The total displacement of the anchor head can be expressed as:

[0044] u=u f +u a

[0045] The tensile deformation of the free section steel strand is:

[0046]

[0047] Where, F is the anchor cable tension, N; L f is the free segment length, m; E s A is the elastic modulus of the steel strand, MPa; s is the cross-sectional area of ​​the steel strand, mm 2 .

[0048] Since the bond strength between the rod and the grout in the anchor section is often higher than that between the grout and the soil, the steel strands in the anchor section are considered together with the grouting body. Figure 2As shown in (b) in the figure. The coordinate system takes O as the origin and AC as the positive direction of the x-axis. Considering that the mortar-sand-stone body often does not produce overall damage during the sliding shear process, it is included in the calculation radius of the anchor body, and the calculation radius is from the outer edge of the mortar-sand-stone body to the axis of the anchor body. As can be seen from the figure, according to the mechanical equilibrium relationship of the micro-element segment of the anchoring section, it can be obtained:

[0049]

[0050] In the formula, E a is the equivalent elastic modulus of the anchoring section, GPa; u a (x) is the displacement of the grouting body in the anchoring section, m; A a Calculate the cross-sectional area of ​​the anchoring section, mm 2 ; E g is the elastic modulus of the grouting body, GPa; A g is the cross-sectional area of ​​the grouting body, mm 2 ; E mix is the elastic modulus of the mortar-sand stone body, GPa; E s A is the elastic modulus of the steel strand, MPa; mix is the cross-sectional area of ​​the slurry-sand stone body, mm 2 ; A s is the cross-sectional area of ​​the steel strand, mm 2 ;D c Calculate the diameter of the grouting body, m, D c =D+2t mix ;t mix is the thickness of the slurry-sand stone body, m; τ gs (x) is the shear stress at the slurry-soil interface, kPa; L a is the length of the anchoring section, m.

[0051] Considering the influence of the free section grouting on the load transfer mode of the anchor cable system, the free section grouting is taken as a microelement segment, and according to the mechanical equilibrium relationship, it can be obtained:

[0052]

[0053] In the formula, u fg (x) is the displacement of the free section grouting body, m; E fg is the elastic modulus of the free segment anchor, GPa; A fg is the cross-sectional area of ​​the free segment anchor, mm 2 , A fg =A g +A mix .

[0054] The displacement of the grouting body can be expressed as:

[0055]

[0056] Where ua(x) is the displacement of the grouting body in the anchoring section, m; u fg (x) is the displacement of the free section grouting body, m; u gs (x) is the shear deformation of the slurry-soil interface, m; u soil (x) is the shear deformation of the soil, m.

[0057] u gs It plays a controlling role in the displacement of the grouting body. To simplify the calculation, the shear deformation of the soil is ignored. soil .

[0058] Step 2: Determine the stress boundary conditions and elastic deformation continuity conditions of the anchor end according to the actual stress state of the anchor, and determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and elastic deformation continuity conditions; calculate the average stress of the anchor section grouting body and the steel strand, the axial stress of the free section grouting body, and the displacement of the free section and the anchor section grouting body according to the undetermined coefficients of the mechanical equilibrium differential equation;

[0059] Specifically, the shear mechanics relationship of the slurry-soil interface is assumed to be an ideal line elastoplastic model, and its expression can be expressed as:

[0060] τ gs =k gsi u gs (6)

[0061] τ gs is the shear stress at the slurry-soil interface, kPa; k gsi is the reference initial shear stiffness of the slurry-soil interface, kPa / m.

[0062] When the tensile load on the anchor cable is small, the slurry-soil interface does not reach the shear strength and the interface is in an elastic state. Based on the deformation and force analysis of the anchor cable system, the load transfer law of the anchor cable in the elastic state can be obtained.

[0063] Substituting equation (5) and equation (6) into equation (1), we can get the differential equation:

[0064]

[0065] Similarly, substituting equation (5) and equation (6) into equation (3), we can get the differential equation:

[0066]

[0067] Solving equation (7) and equation (8) yields:

[0068]

[0069] In the formula, α, β are simplified coefficients, C 1 ,C 2 ,C3 ,C 4 are the unknown coefficients of the differential equation.

[0070] according to Figure 2 The force boundary condition at the end of the middle anchor and the continuous deformation condition of the grouting body can be obtained as follows:

[0071] σ a (x) x＝0 =0

[0072]

[0073] The axial stress in the grouting body (or anchor body) can be obtained according to the physical equation:

[0074]

[0075] In the formula, σ a is the average axial stress of the grouting body and the steel strand in the anchoring section, kPa; σ fg is the axial stress of the free section grouting body, kPa; F is the anchor cable tension, N.

[0076] Combining equations (9) and (10) and combining boundary conditions, the unknown coefficients can be determined:

[0077]

[0078] Among them,

[0079] Based on the derivation of the displacement function of the grouting body by formula (9), the average axial stress of the anchor body and the displacement of the grouting body in the elastic stage can be obtained:

[0080]

[0081] Among them, α, β are simplified coefficients,

[0082] According to formula (6), the shear stress expression of the slurry-soil interface is τ gs =k gsi u gs , combining equation (11) with equation (5) and (6) to obtain the shear stress and axial stress distribution law of the non-full-length bonded anchor mortar-soil interface, as follows: Figure 3 shown.

[0083] Step 3: Based on the calculated average axial stress of the anchor cable and the displacement of the grouting body, establish the stress balance equation of the steel strand and the grouting body in the anchoring section. Solve the stress balance equation to determine the axial stress of the steel strand and the axial stress of the grouting body in the anchoring section for subsequent support design.

[0084] Specifically, the average displacement and axial stress of the anchor body of the anchor cable can be obtained through equations (11) and (12). Due to the large difference in strength between the steel strand and the grouting body in the anchor body, the stress distribution between the two is more important. Considering that the rod-slurry interface often has a high shear strength, according to the test results of the mechanical properties of the rod-slurry interface, the shear stress and displacement of the rod-slurry interface are regarded as a linear elastic function relationship.

[0085] According to the stress balance relationship of the steel strand in the anchor section:

[0086]

[0087] τ gt (x) = k gti [u s (x)-u ag (x)]0≤x≤L a (14)

[0088] In the formula, σ s (x) is the axial stress of the steel strand, kPa; D s is the diameter of the steel strand, m; A S is the cross-sectional area of ​​the steel strand, mm 2 ; τ gt (x) is the shear stress at the rod-slurry interface, kPa; kgti is the reference initial shear stiffness at the rod-slurry interface, kPa / m; u s (x) is the displacement of the steel strand in the anchoring section, m; u ag (x) is the displacement of the grouting body in the anchoring section, m.

[0089] The stress balance relationship of the grouting body in the anchoring section can be obtained:

[0090]

[0091] In the formula, σ ag (x) is the axial stress of the grouting body in the anchoring section, kPa.

[0092] The axial stress of the grouting body and the steel strand in the anchoring section can be obtained according to the physical equation:

[0093]

[0094] Substituting equation (14) and equation (17) into equation (13), we can get the differential equation:

[0095]

[0096] Similarly, substituting equations (6), (14) and (16) into equation (15), we can obtain the differential equation:

[0097]

[0098] Combining equations (18) and (19), we can get s (x) and u ag (x) is a non-homogeneous linear differential equation system, let M = E s A s E fg A fg / (πD s k gti ), N=E a A a , The system of differential equations can be solved:

[0099]

[0100] In the formula, C 1 ,C 2 ,C 3 ,C 4 are the unknown coefficients of the differential equation.

[0101] Substituting formula (20) into formula (16) and (17), the axial stress expression of the grouting body and the steel strand in the anchor section can be obtained:

[0102]

[0103] Among them, σ s (x) is the axial stress of the steel strand, kPa; σ ag (x) is the axial stress of the grouting body in the anchoring section, kPa.

[0104] According to the stress and deformation conditions of the anchor bolt anchoring section, the following boundary conditions are obtained:

[0105]

[0106] u′ s (x)E s | x＝0 =0

[0107] u′ ag (x)E fg | x＝0 =0

[0108]

[0109] Where, F is the anchor cable tension, N; E s is the elastic modulus of the steel strand, MPa.

[0110] The unknown coefficients can be determined by combining equation (20) with the boundary conditions:

[0111]

[0112] C 4 =0

[0113] In the formula, α, β—simplification coefficients,

[0114] Determine the parameter C 1 ~C 4 Substituting into formula (21), the axial stress expression of the grouting body and the steel strand in the anchoring section can be obtained. The axial stress distribution diagram of the grouting body and the steel strand along the entire length of the anchor cable in the elastic stage is shown as follows: Figure 4 shown.

[0115] Due to the complex overall force of the anchor rod, a more accurate calculation method is needed to guide engineering applications. Calculating the stress distribution of the anchor cable plays an important role in optimizing design, improving safety, controlling deformation, predicting long-term performance and guiding construction. By fully understanding the stress distribution law of the anchor cable in the elastic stage, the full life cycle optimization of the anchor cable design, construction and operation can be achieved, providing a reliable theoretical basis and practical guidance for anchor cable projects under complex geological conditions. The present invention improves the calculation model, integrates the role of the free section grouting body into the analysis of the elastic stage, improves the accuracy of the bearing capacity assessment based on the solution results, and optimizes the anchor cable design; combined with the coupling analysis of the free section and the anchoring section, the scientificity and accuracy of the design of non-full-length bonded anchor cables are improved.

[0116] Example 2

[0117] An embodiment of the present disclosure discloses a stress calculation system for elastic stage of pull-out load of non-full-length bonded anchor cable, comprising:

[0118] Mathematical model building module, used to consider the influence of grouting in the anchor section and free section on the load transfer in the elastic stage of the anchor cable system, and to establish the mechanical equilibrium differential equations of the anchor section and free section;

[0119] A boundary condition determination module is used to determine the stress boundary conditions and elastic deformation continuity conditions of the anchor end according to the actual stress state of the anchor, and to determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and the elastic deformation continuity conditions;

[0120] The stress calculation module is used to calculate the average stress of the grouting body and the steel strand in the anchoring section, the axial stress of the grouting body in the free section, and the displacement of the grouting body in the free section and the anchoring section according to the unknown coefficients of the mechanical equilibrium differential equation; based on the calculated average axial stress of the anchor body of the anchor cable and the displacement of the grouting body, the stress balance equation of the steel strand and the grouting body in the anchoring section is established, and the stress balance equation is solved to determine the axial stress of the steel strand and the axial stress of the grouting body in the anchoring section for subsequent anchor cable optimization design.

[0121] Example 3

[0122] An embodiment of the present disclosure discloses a computer program product, including a computer program, which, when executed by a processor, implements the method for calculating the elastic stage stress of a non-full-length bonded anchor cable pull-out load.

[0123] Example 4

[0124] An embodiment of the present disclosure discloses a non-transitory computer-readable storage medium, which is used to store computer instructions. When the computer instructions are executed by a processor, the method for calculating the elastic stage stress of a non-full-length bonded anchor cable pull-out load is implemented.

[0125] Example 5

[0126] An embodiment of the present disclosure discloses an electronic device, including: a processor, a memory and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the elastic stage stress calculation method of the pull-out load of the non-full-length bonded anchor cable.

[0127] The present disclosure is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present disclosure. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0128] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0129] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. The method for calculating the stress of the elastic stage of the pull-out load of the non-full-length bonded anchor cable is characterized by: include: Considering the influence of the grouting of the anchor section and the free section on the load transfer of the anchor cable system in the elastic stage, the mechanical equilibrium differential equations of the anchor section and the free section are established; Determine the stress boundary conditions and elastic deformation continuity conditions of the anchor end according to the actual stress state of the anchor, and determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and elastic deformation continuity conditions; According to the undetermined coefficients of the mechanical equilibrium differential equation, the average stress of the grouting body and the steel strand in the anchoring section, the axial stress of the grouting body in the free section, and the displacement of the grouting body in the free section and the anchoring section are calculated; Based on the calculated average axial stress of the anchor body and the displacement of the grouting body, the stress balance equation of the steel strand and the grouting body in the anchoring section is established. The stress balance equation is solved to determine the axial stress of the steel strand and the axial stress of the grouting body in the anchoring section for subsequent anchor optimization design.

2. The method for calculating the stress of the non-full-length bonded anchor cable under the elastic stage of the pull-out load according to claim 1, characterized in that: In the elastic stage, two deformations are considered, namely, the tensile deformation of the free section steel strand and the displacement of the anchoring section, which constitute the total displacement of the anchor rod end.

3. The method for calculating the stress of the non-full-length bonded anchor cable under the elastic stage of the pull-out load according to claim 1, characterized in that: The bonding strength of the rod-grout interface in the anchoring section is higher than that of the grout-soil interface. The steel strands in the anchoring section are considered together with the grouting body. Considering that the grout-sand-stone body often does not produce overall damage during the sliding shear process, it is included in the calculation radius of the anchor body. The calculation radius is from the outer edge of the grout-sand-stone body to the axis of the anchor body. According to the mechanical equilibrium relationship of the micro-element of the anchoring section, it can be obtained: In the formula, E a is the equivalent elastic modulus of the anchoring section, u a (x) is the displacement of the grouting body in the anchoring section; A a Calculate the cross-sectional area for the anchor section; E g is the elastic modulus of the grouting body; A g is the cross-sectional area of ​​the grouting body; E mix E is the elastic modulus of the mortar-sand stone body; s A is the elastic modulus of the steel strand; mix A is the cross-sectional area of ​​the slurry-sand stone body; s is the cross-sectional area of ​​the steel strand; D c Calculate the diameter of the grouting body, D c =D+2t mix ;t mix is the thickness of the slurry-sand stone body; τ gs (x) is the shear stress at the slurry-soil interface; L a is the length of the anchoring section.

4. The method for calculating the stress of the elastic stage of the pull-out load of the non-full-length bonded anchor cable according to claim 1, characterized in that: When the tensile load on the anchor cable is small, the slurry-soil interface does not reach the shear strength and the interface is in an elastic state. Based on the deformation and stress analysis of the anchor cable system, the load transfer law of the anchor cable in the elastic state is obtained as follows: Solving the above two formulas, we get: In the formula, u fg (x) is the displacement of the grouting body in the free section, E fg is the elastic modulus of the free segment anchor, k gsi is the reference initial shear stiffness of the slurry-soil interface, α, β are simplified coefficients, C1, C2, C3, C4 are the unknown coefficients of the differential equation.

5. The method for calculating the stress of the non-full-length bonded anchor cable under the elastic stage of the pull-out load according to claim 1, characterized in that: The boundary conditions for the anchor end stress and the continuous deformation conditions of the grouting body are as follows: s a (x) x＝0 =0 The axial stress in the grouting body can be obtained according to the physical equation: In the formula, σ a is the average axial stress of the grouting body and the steel strand in the anchoring section; fg is the axial stress of the free section grouting body; F is the anchor cable tension; the unknown coefficient can be determined by combining the boundary conditions: Among them, 6. The method for calculating the stress of the non-full-length bonded anchor cable under the elastic stage of the pull-out load according to claim 1, characterized in that: The strength difference between the steel strand and the grouting body in the anchor body is large. Considering that the rod-grout interface often has a high shear strength, according to the test results of the mechanical properties of the rod-grout interface, the shear stress and displacement of the rod-grout interface are regarded as a linear elastic function. The axial stress expression of the grouting body and the steel strand in the anchor section is: Where: s (x) is the axial stress of the steel strand; σ ag (x) is the axial stress of the grouting body in the anchoring section.

7. The stress calculation system for the elastic stage of the pull-out load of the non-full-length bonded anchor cable is characterized by: include: Mathematical model building module, used to consider the influence of grouting in the anchor section and free section on the load transfer in the elastic stage of the anchor cable system, and to establish the mechanical equilibrium differential equations of the anchor section and free section; A boundary condition determination module is used to determine the stress boundary conditions and elastic deformation continuity conditions of the anchor end according to the actual stress state of the anchor, and to determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and the elastic deformation continuity conditions; The stress calculation module is used to calculate the average stress of the grouting body and the steel strand in the anchoring section, the axial stress of the grouting body in the free section, and the displacement of the grouting body in the free section and the anchoring section according to the unknown coefficients of the mechanical equilibrium differential equation; based on the calculated average axial stress of the anchor body of the anchor cable and the displacement of the grouting body, the stress balance equation of the steel strand and the grouting body in the anchoring section is established, and the stress balance equation is solved to determine the axial stress of the steel strand and the axial stress of the grouting body in the anchoring section for subsequent anchor cable optimization design.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method for calculating the elastic stage stress of a non-full-length bonded anchor cable pull-out load as described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the method for calculating the elastic stage stress of the pull-out load of a non-full-length bonded anchor cable as described in any one of claims 1 to 6 is implemented.

10. An electronic device, characterized in that: include: A processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes the method for calculating the elastic stage stress of the pull-out load of a non-full-length bonded anchor cable as described in any one of claims 1 to 6.

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