Stress calculation method and system for elastic stage of pull-out load of non-full-length bonded anchor cable

Abstract

The present disclosure provides a method and system for calculating the stress of a non-full-length bonded anchor cable under a pull-out load in the elastic stage, which relates to the technical field of anchor cable support. The method includes establishing a mechanical equilibrium differential equation for the anchoring section and the free section by considering the influence of the free section grouting on the elastic stage load transfer of the anchor cable system; determining the stress boundary conditions and elastic deformation continuity conditions of the anchor rod end according to the actual stress state of the anchor rod, and determining the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and the elastic deformation continuity conditions; calculating the average stress of the anchoring section grouting and the steel strand, the axial stress of the free section grouting, and the displacement of the free section and the anchoring section grouting according to the undetermined coefficients of the mechanical equilibrium differential equation; establishing a stress equilibrium equation for the steel strand and the grouting in the anchoring section based on the calculated average axial stress of the anchor body of the anchor cable and the displacement of the grouting, and solving the stress equilibrium equation to determine the axial stress of the steel strand and the axial stress of the grouting in the anchoring section for subsequent anchor cable optimization design.

Description

Technical Field

[0001] The present disclosure 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 in the 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 international projects. The study of their anchoring mechanism plays an important role in accurately determining 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 tension is mainly caused by the relative movement of steel strands, grouting, and soil with different mechanical properties. However, most studies have only studied full-length bonded anchors. There is relatively little research on non-full-length bonded anchors, and only the load transfer mechanism of the anchoring section has been discussed, ignoring the influence of the free section. The grouting in the free section has a significant impact on the overall load transfer of the anchor cable during the anchor cable pulling process. If the free section grouting is not taken into account, the axial force and shear stress distribution patterns obtained from the anchor cable calculation formula are seriously inconsistent with the actual situation.

[0004] In existing methods, the stress distribution between the strands and the grouting in the theoretical model of the elastic phase of non-full-length bonded anchors is not fully considered, and the stress distribution of the grouting and strands in the anchoring section is not calculated. In practical applications, due to the difference in elastic modulus between the strands and the grouting, the stress distribution between the two is actually nonlinear. Especially under large tensile forces, the stress of the grouting is usually lower than that of the strands. In addition, the explanations of loads in related solutions are mostly empirical formulas. For example, the patent "Calculation Method for the Anchoring Force of Long Anchor Cables Crossing Fully Filled Caves" (Grant No. CN 110306548 B) uses the stress-strain relationship between the contact surface of the anchor and the rock mass under ideal conditions when analyzing the anchor body. It does not consider the stress distribution of the anchor cable system of the strands and grouting materials in the anchor body when it is tensile, nor the influence of the grouting in the free section on the pull-out bearing capacity of the anchor cable. 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 anchor cable pull-out load, the influence of the free section grouting on the load transfer of the anchor cable system is considered. 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 of 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 expression of the axial stress of the grouting body and the steel strand in the anchoring section is solved.

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

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

[0008] 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;

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

[0010] 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 undetermined coefficients of the mechanical equilibrium differential equation.

[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 cable 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 pull-out load of non-full-length bonded anchor cables includes:

[0014] Mathematical model building module, used to consider the influence of the grouting of 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] The boundary condition determination module is used to determine the boundary conditions and elastic deformation continuity conditions of the anchor rod end according to the actual stress state of the anchor rod, and determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and elastic deformation continuity conditions;

[0016] The stress calculation module is used to calculate the average stress of the grouting body and 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 based on 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 includes 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 under pull-out load.

[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, 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 to enable the electronic device to implement the elastic stage stress calculation method for the pull-out load of a non-full-length bonded anchor cable.

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

[0024] The disclosed stress calculation method for the elastic stage of the pull-out load of a non-full-length bonded anchor cable proposes a load transfer law analytical calculation method for the elastic stage of the pull-out load of a non-full-length bonded anchor cable based on the consideration of the stress distribution difference between the two and the influence of the anchor section and free section grouting on the load transfer of the anchor cable system. By considering the influence of the free section grouting on the pull-out bearing capacity of the anchor cable 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 cable system in the elastic stage is truly reflected. This provides theoretical support and engineering guidance for the design and construction of non-full-length bonded anchor cables, and is helpful to promote the standardization of the application of this technology in deep foundation pit support, rock and soil anchoring, slope protection and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0026] Figure 1 This 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 calculation 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 anchor cable mechanical model;

[0029] Figure 3 Schematic diagram of the distribution of axial stress and interface shear stress in the elastic stage of the anchor cable 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 will be further described below with reference to the accompanying drawings and embodiments.

[0032] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as 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 intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate 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 boundary conditions and elastic deformation continuity conditions of the anchor rod end according to the actual stress state of the anchor rod, 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 based on 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. 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 cable optimization design.

[0040] As an embodiment, the present invention discloses a stress calculation method for the elastic phase of pull-out loads on non-full-length bonded anchor cables. This method considers the influence of the grouting in the anchoring and free segments on the load transfer of the anchor cable system. First, based on the axial deformation characteristics, a mechanical equilibrium differential equation for the free and anchoring segments is established. Subsequently, the differential equations are solved at different locations. Based on the boundary conditions of the anchor rod end and the continuity conditions of the grouting deformation, the coefficients of the differential equations are determined. The average axial stress of the anchor body and the displacement of the grouting are solved. Finally, the expression for the axial stress of the grouting in the anchoring segment and the strand is 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 and the displacement of the anchor section. 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 is the elastic modulus of the steel strand, MPa; A s is the cross-sectional area of ​​the steel strand, mm 2 .

[0048] Since the bonding strength between the rod and grout in the anchoring section is often higher than that between the grout and soil, the steel strands in the anchoring section are considered together with the grouting body. Figure 2As shown in (b) in the figure. The coordinate system is centered at O, and the AC direction is the positive x-axis. Considering that the mortar-sand-stone body often does not undergo overall destruction during the slip shear process, it is included in the calculated radius of the anchor body, and the radius from the outer edge of the mortar-sand-stone body to the anchor body axis is the calculated radius. As can be seen from the figure, based on the mechanical equilibrium relationship of the anchor segment micro-segment, we can obtain:

[0049]

[0050] Where, 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 is the elastic modulus of the steel strand, MPa; A 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. According to the mechanical equilibrium relationship, it can be obtained:

[0052]

[0053] Where u fg (x) is the displacement of the grouting body in the free section, 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 boundary conditions and elastic deformation continuity conditions at the anchor end based on the actual stress state of the anchor, and determine the undetermined coefficients of the mechanical equilibrium differential equation based on the boundary conditions and elastic deformation continuity conditions; calculate the average stress of the grouting body and the steel strand in the anchor 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 anchor section based on 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 elastic-plastic 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 has not yet reached shear strength and 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 can be obtained.

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

[0064]

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

[0066]

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

[0068]

[0069] In the formula, α, β are simplified coefficients, C1, C2, C3, and C4 are the unknown coefficients of the differential equation.

[0070] according to Figure 2 The boundary conditions of the anchor rod end and the continuous deformation conditions 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] Where, σ a is the average axial stress of the grouting body and 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 the boundary conditions, the unknown coefficients can be determined:

[0077]

[0078] Among them,

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

[0080]

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

[0082] The shear stress expression of the slurry-soil interface τ is given by formula (6): gs =k gsi u gs Combining equation (11) with equations (5) and (6) yields the shear stress and axial stress distribution laws 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, equations (11) and (12) reveal the average displacement and axial stress of the anchor cable. Due to the significant strength difference between the steel strands and the grouting in the anchor, the stress distribution between the two becomes even more important. Considering that the rod-grout interface often has a high shear strength, and based on the mechanical properties test results of the rod-grout interface, the shear stress and displacement at the rod-grout interface are considered to be a linear elastic function.

[0085] According to the stress balance relationship of the steel strand in the anchoring section, it can be obtained:

[0086]

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

[0088] Where, 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] Where, 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 steel strand in the anchoring section can be obtained according to the physical equation:

[0093]

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

[0095]

[0096] Similarly, by 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] Where C1, C2, C3, and C4 are the unknown coefficients of the differential equation.

[0101] Substituting formula (20) into formulas (16) and (17), the axial stress expressions of the grouting body and the steel strand in the anchoring 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] C4=0

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

[0114] Determine the parameters C1~C4 and substitute them into formula (21) to obtain the axial stress expression of the grouting body and steel strand in the anchoring section. The axial stress distribution diagram of the grouting body and steel strand along the entire length of the anchor cable in the elastic stage is as follows: Figure 4 shown.

[0115] Due to the complex overall stress 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 whole 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. This disclosure improves the calculation model, incorporates 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; combines the coupling analysis of the free section and the anchoring section to improve the scientificity and accuracy of the design of non-full-length bonded anchor cables.

[0116] Example 2

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

[0118] Mathematical model building module, used to consider the influence of the grouting of 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] The boundary condition determination module is used to determine the boundary conditions and elastic deformation continuity conditions of the anchor rod end according to the actual stress state of the anchor rod, and determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and elastic deformation continuity conditions;

[0120] The stress calculation module is used to calculate the average stress of the grouting body and 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 based on 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] One 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 under pull-out load.

[0123] Example 4

[0124] An embodiment of the present disclosure discloses a non-transitory computer-readable storage medium for storing 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, comprising: 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 for the pull-out load of a 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 produce 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 operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device 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. Those skilled in the art 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 stress calculation method for 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 system in the elastic stage, the mechanical equilibrium differential equations of the anchor section and the free section are established; The bond strength between the rod and grout in the anchoring section is higher than that between the grout and soil. 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 anchoring section microelement, it can be obtained: Where, E a is the equivalent elastic modulus of the anchoring section, is the displacement of the grouting body in the anchoring section; A a Calculate the cross-sectional area for the anchorage segment; E g is the elastic modulus of the grouting body; A g is the cross-sectional area of ​​the grouting body; E mix is the elastic modulus of the mortar-sand stone body; E s is the elastic modulus of the steel strand; A mix is the cross-sectional area of ​​the slurry-sand stone body; A s is the cross-sectional area of ​​the steel strand; D c Calculate the diameter for the grout body, ; 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; When the tensile load on the anchor cable is small, the slurry-soil interface has not reached 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: ; Where, is the displacement of the free section grouting body, E fg is the elastic modulus of the free segment anchor, is the reference initial shear stiffness of the slurry-soil interface, α , β To simplify the coefficients, ; C1, C2, C3, C4 are the unknown coefficients of the differential equation; Determine the boundary conditions and elastic deformation continuity conditions of the anchor rod end according to the actual stress state of the anchor rod, and determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and elastic deformation continuity conditions; 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 undetermined coefficients of the mechanical equilibrium differential equation. 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 cable 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. The tensile deformation of the free section steel strand and the displacement of the anchoring section 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, wherein: The boundary conditions for the anchor end stress and the continuous conditions for the grouting body deformation are as follows: The axial stress in the grouting body can be obtained according to the physical equation: Where, is the average axial stress of the grouting body and steel strand in the anchoring section; is the axial stress of the grouting body in the free section; F is the anchor cable tension; the unknown coefficient can be determined by combining the boundary conditions: Among them, .

4. 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, wherein: 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 high shear strength, based on 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 steel strand in the anchor section is: in: is the axial stress of the steel strand; is the axial stress of the grouting body in the anchoring section.

5. The stress calculation system for the elastic stage of the pull-out load of non-full-length bonded anchor cable is characterized by: include: Mathematical model building module, used to consider the influence of the grouting of 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; The bond strength between the rod and grout in the anchoring section is higher than that between the grout and soil. 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 anchoring section microelement, it can be obtained: Where, E a is the equivalent elastic modulus of the anchoring section, is the displacement of the grouting body in the anchoring section; A a Calculate the cross-sectional area for the anchorage segment; E g is the elastic modulus of the grouting body; A g is the cross-sectional area of ​​the grouting body; E mix is the elastic modulus of the mortar-sand stone body; E s is the elastic modulus of the steel strand; A mix is the cross-sectional area of ​​the slurry-sand stone body; A s is the cross-sectional area of ​​the steel strand; D c Calculate the diameter for the grout body, ; 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; When the tensile load on the anchor cable is small, the slurry-soil interface has not reached 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: ; Where, is the displacement of the free section grouting body, E fg is the elastic modulus of the free segment anchor, is the reference initial shear stiffness of the slurry-soil interface, α , β To simplify the coefficients, ; C1, C2, C3, C4 are the unknown coefficients of the differential equation; The boundary condition determination module is used to determine the boundary conditions and elastic deformation continuity conditions of the anchor rod end according to the actual stress state of the anchor rod, and determine the undetermined coefficients of the mechanical equilibrium differential equation according to the boundary conditions and elastic deformation continuity conditions; The stress calculation module is used to calculate the average stress of the grouting body and 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 based on 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.

6. 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 stress of a non-full-length bonded anchor cable under a pull-out load in the elastic stage as described in any one of claims 1 to 4 is implemented.

7. 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 4 is implemented.

8. An electronic device, characterized in that: include: 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 to enable the electronic device to implement 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 4.

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