Non-linear fluctuation analysis method for working stress of prestressed anchorage device in isotropic structure

Abstract

The invention relates to the technical field of building anchorage devices, in particular to a nonlinear fluctuation analysis method for working stress of a prestressed anchorage device in an isotropic structure, which comprises the following steps of: 1, establishing an anchorage device model: establishing the prestressed anchorage device model of an isotropic material, and assuming that the anchorage device is subjected to unidirectional tensile stress in an isotropic medium; step 2, acoustic elasticity theory analysis: analyzing the relationship between stress and elastic wave velocity in the prestressed anchorage device based on a nonlinear fluctuation theory; supposing that the medium is a continuum, the small disturbance of the sound wave is superposed on the static large deformation of the medium; the one-dimensional acoustic-elastic relation in a one-way stress medium is deduced according to the nonlinear wave equation, the working stress of the pre-stressed anchor cable can be accurately monitored through a nonlinear wave analysis method, the too high or too low stress condition can be found and processed in time, structural faults are prevented, and the reliability of the pre-stressed anchor cable is improved. And the safety and reliability of the project are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of construction anchors, and specifically to a method for analyzing the non-linear fluctuation of the working stress of prestressed anchors in an isotropic structure. Background Art

[0002] Prestressed anchors are widely used in isotropic structures, mainly in projects such as slope reinforcement, building foundation pit support, and hydraulic structure reinforcement. In the 1960s, China began to use prestressed anchor cables and achieved success in projects such as the foundation reinforcement of Meishan Reservoir Dam in Anhui. The main function of prestressed anchor cables is to transfer the tensile force to the rock and soil mass or other structures to be anchored through the anchors, improving the stability of the structure. Prestressed anchor cables are divided into an inner anchorage section, a free section, and an exposed section. The inner anchorage section transfers the load through the bond of the grouting body. The axial stress is the same everywhere in the free section. The exposed section is fixed to the surface of the rock and soil mass through the anchor.

[0003] The working stress of prestressed anchor cables is an important factor affecting the safety of prestressed structures. Excessive working stress of the anchor cable may cause the anchor cable to break, and conversely, the reinforcement effect of the prestressed anchor cable cannot be exerted. Therefore, it is very important to monitor the working stress of prestressed anchor cables in real time. Prestress loss is an important factor leading to changes in working stress. In addition, changes in hydrogeological conditions, uncertainties during construction, and changes in slope conditions will also affect the working stress of prestressed anchor cables, thereby affecting the stability of the structure. Therefore, a method for analyzing the non-linear fluctuation of the working stress of prestressed anchors in an isotropic structure is proposed to solve the above problems. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for analyzing the non-linear fluctuation of the working stress of prestressed anchors in an isotropic structure to solve the problems raised in the above background art.

[0005] To achieve the above purpose, the present invention provides the following technical solutions:

[0006] A method for analyzing the non-linear fluctuation of the working stress of prestressed anchors in an isotropic structure, comprising the following steps:

[0007] Step 1: Establish an anchor model: Establish a prestressed anchor model of an isotropic material, assuming that the anchor is subjected to a unidirectional tensile stress in an isotropic medium;

[0008] Step 2: Acoustoelastic theory analysis: Based on the non-linear wave theory, analyze the relationship between stress and elastic wave velocity in the prestressed anchor; assume that the medium is a continuum, and the small perturbation of the sound wave is superimposed on the static large deformation of the medium;

[0009] Step 3: Derivation of the non-linear wave equation: Based on the non-linear wave equation, derive the one-dimensional acoustoelastic relationship in a unidirectional stress medium. Assume that the medium is unidirectionally tensioned, derive its dynamic equilibrium equation, and obtain the relationship between stress and wave speed:

[0010]

[0011] where σ is the stress, v is the wave speed, ρ is the medium density, and C is the sound speed constant;

[0012] Step 4: Analysis of the dispersion phenomenon: Consider the dispersion phenomenon when the wave propagates in the anchor, analyze the influence of dispersion on the wave speed measurement, and propose methods to reduce the dispersion effect, such as selecting an appropriate excitation frequency;

[0013] Step 5: Experimental verification: Through laboratory tests, use existing engineering equipment to detect the working stress of the anchor, verify the theoretical analysis results, and discuss the errors and accuracy in the detection.

[0014] Preferably, the prestressed anchor is a steel anchor, and the isotropic medium is concrete or rock; the wave speed measurement uses longitudinal waves, and it is recommended to select an excitation wave with a frequency not exceeding 200 kHz to reduce the influence of the dispersion effect; the derivation process of the non-linear wave equation considers the physical non-linearity of the medium and uses the Murnaghan potential function for parametric description.

[0015] Preferably, the acoustoelastic relationship obtains the stress magnitude in the prestressed anchor through wave speed measurement, and its formula is as follows:

[0016] σ = f(v)

[0017] where σ is the stress, v is the wave speed, and f is the functional relationship derived according to the non-linear wave theory.

[0018] Preferably, the experimental verification step includes the following sub-steps:

[0019] a. Preparation of test equipment: Select test equipment that can accurately measure the wave propagation time to ensure that the measurement accuracy of the equipment meets the requirements;

[0020] b. Application of prestress: Apply a known prestress to the anchor and record the prestress value;

[0021] c. Wave speed measurement: Under the action of prestress, measure the propagation speed of elastic waves in the anchor;

[0022] d. Data analysis: According to the measured wave speed data, use the acoustoelastic relationship formula to calculate the stress in the anchor and compare and analyze it with the known prestress value.

[0023] Preferably, the relationship between wave speed and stress is further refined to:

[0024]

[0025] Among them, A is a constant, and v0 is the wave velocity in the stress-free state.

[0026] Preferably, the method for reducing the dispersion effect includes selecting appropriate exciting wave frequencies and wavelengths to make the wave propagation speed uniform and reducing the wave velocity measurement error caused by the dispersion effect; the acoustoelastic relation formula is obtained through experimental calibration, and the experimental steps include measuring the wave velocity under known stress conditions and fitting the functional relationship between stress and wave velocity; the nonlinear wave analysis is combined with the finite element method for simulation calculation to verify the accuracy and applicability of the theoretical derivation.

[0027] Preferably, the finite element simulation calculation steps include the following sub-steps:

[0028] a. Finite element model establishment: Establish a finite element model of the prestressed anchor, and define the material properties and boundary conditions;

[0029] b. Mesh generation: Generate a mesh for the model to ensure the accuracy and calculation efficiency of the mesh;

[0030] c. Application of prestress: Apply prestress to the model and perform a static analysis to obtain the initial stress distribution of the anchor;

[0031] d. Dynamic analysis: Apply a wave excitation and perform a dynamic analysis to calculate the propagation process of the wave and the stress change in the anchor;

[0032] e. Result verification: Compare the finite element calculation results with the experimental data to verify the accuracy of the model.

[0033] Preferably, the analysis of the dispersion phenomenon considers the influence of different exciting frequencies and wavelengths on the wave velocity, and the formula is as follows:

[0034]

[0035] Among them, v is the wave velocity, v0 is the fundamental wave velocity, k is the wave number, and w is the angular frequency.

[0036] Preferably, the experimental verification steps further include measuring the wave velocity under different prestress conditions multiple times to ensure the repeatability and reliability of the data, and the formula is as follows:

[0037]

[0038] Among them, σ i is the stress of the i-th measurement, n is the number of measurements, and α ij is the

[0039] j data.

[0040] Preferably, the nonlinear wave analysis process also considers the influence of material isotropy and anisotropy on wave propagation. The formula is as follows:

[0041] σ = B·v 2 ·(1 + αcos(θ))

[0042] Where B is a constant, α is the material anisotropy coefficient, and θ is the angle between the wave propagation direction and the main direction of the material.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0044] 1. In the present invention, through the nonlinear wave analysis method, the working stress of the prestressed anchor cable can be accurately monitored, high or low stress conditions can be detected and processed in time, structural failures can be prevented, and the safety and reliability of the project can be improved;

[0045] 2. In the present invention, this method realizes the precise monitoring of the stress of the prestressed anchor cable through a high-precision algorithm and complex formula, and can maintain high precision and stability even in a complex engineering environment; by using real-time data acquisition and analysis technology, the working stress of the prestressed anchor cable can be monitored and dynamically adjusted in real time to ensure the stability and safety of the structure under different working conditions;

[0046] 3. In the present invention, compared with the traditional detection method, the method of the present invention does not require a large number of physical sensors to be arranged, and precise monitoring can be achieved through algorithms and models, reducing the engineering cost; through the real-time monitoring and adjustment of the working stress of the prestressed anchor cable, the fracture or failure of the anchor cable caused by overstress or stress loss can be effectively prevented, and the service life of the anchor cable can be extended;

[0047] 4. In the present invention, the present invention uses a complex nonlinear wave algorithm, which can more accurately reflect the stress changes of the prestressed anchor cable under different loads and environmental conditions, improving the reliability and accuracy of the detection results; through the collection and analysis of a large amount of data, a detailed stress change model of the prestressed anchor cable can be established, providing reliable data support for subsequent engineering design and optimization; Detailed implementation mode

[0048] The present invention provides a technical solution:

[0049] A method for nonlinear wave analysis of the working stress of prestressed anchors in an isotropic structure, comprising the following steps:

[0050] Step 1: Establish an anchor model: Establish a prestressed anchor model of an isotropic material, assuming that the anchor is under unidirectional tensile stress in an isotropic medium;

[0051] Step 2: Acoustoelastic theory analysis: Based on the nonlinear wave theory, analyze the relationship between stress and elastic wave velocity in prestressed anchorages; assume that the medium is a continuum, and small perturbations of sound waves are superimposed on the static large deformation of the medium.

[0052] Step 3: Derivation of the nonlinear wave equation: According to the nonlinear wave equation, derive the one-dimensional acoustoelastic relationship in a unidirectional stress medium. Assume that the medium is unidirectionally tensioned, derive its dynamic equilibrium equation, and obtain the relationship between stress and wave velocity:

[0053]

[0054] where σ is the stress, v is the wave velocity, ρ is the density of the medium, and C is the sound velocity constant.

[0055] Step 4: Dispersion phenomenon analysis: Consider the dispersion phenomenon when the wave propagates in the anchorage, analyze the influence of dispersion on wave velocity measurement, and propose methods to reduce the dispersion effect, such as selecting an appropriate excitation frequency.

[0056] Step 5: Experimental verification: Through laboratory tests, use existing engineering equipment to detect the working stress of the anchorage, verify the results of theoretical analysis, and discuss the errors and accuracy in the detection.

[0057] This method ensures the accurate monitoring of prestressed anchorages in isotropic structures through comprehensive analysis steps, improving the safety and reliability of the project.

[0058] The prestressed anchorage among them is a steel anchorage, and the isotropic medium is concrete or rock; this setting can be applied to a variety of common engineering materials, making the method have wide applicability and being able to be applied in different actual engineering environments, improving the generality of the method; the wave velocity measurement among them uses longitudinal waves, and it is recommended to select an excitation wave with a frequency not exceeding 200 kHz to reduce the influence of the dispersion effect. By selecting the appropriate measurement wave type and frequency, the dispersion effect is effectively reduced, and the accuracy of wave velocity measurement is improved; the derivation process of the nonlinear wave equation among them considers the physical nonlinearity of the medium and uses the Murnaghan potential function for parametric description, considering the physical nonlinear characteristics of the medium, making the wave analysis more in line with the actual situation and improving the accuracy and reliability of the analysis.

[0059] The acoustoelastic relationship among them obtains the stress magnitude in the prestressed anchorage through wave velocity measurement, and its formula is as follows:

[0060] σ = f(v)

[0061] where σ is the stress, v is the wave velocity, and f is the functional relationship derived according to the nonlinear wave theory. Through the specific functional relationship, the stress magnitude in the prestressed anchorage can be directly calculated, improving the accuracy and real-time performance of stress monitoring.

[0062] The experimental verification steps include the following sub-steps:

[0063] a. Preparation of test equipment: Select test equipment that can accurately measure the wave propagation time to ensure that the measurement accuracy of the equipment meets the requirements;

[0064] b. Application of prestress: Apply a known prestress to the anchor and record the prestress value;

[0065] c. Measurement of wave velocity: Under the action of prestress, measure the propagation velocity of elastic waves in the anchor;

[0066] d. Data analysis: According to the measured wave velocity data, use the acoustoelastic relationship formula to calculate the stress in the anchor and compare and analyze it with the known prestress value.

[0067] The experimental verification steps are detailed and highly operable, ensuring the reliability and accuracy of the theoretical analysis results in practical applications.

[0068] The relationship between wave velocity and stress is further refined as:

[0069]

[0070] where A is a constant and v0 is the wave velocity in the stress-free state.

[0071] Through the more refined formula, the accuracy of stress calculation is further improved, providing a more accurate stress monitoring method for practical engineering applications.

[0072] The methods for reducing the dispersion effect include selecting appropriate excitation wave frequencies and wavelengths to make the wave propagation velocity uniform and reducing the wave velocity measurement error caused by the dispersion effect, effectively reducing the influence of the dispersion effect on wave velocity measurement and improving the accuracy of wave velocity measurement to ensure the reliability of stress monitoring; the acoustoelastic relationship formula is obtained through experimental calibration. The experimental steps include measuring the wave velocity under known stress conditions and fitting the functional relationship between stress and wave velocity. The acoustoelastic relationship formula obtained through experimental calibration ensures the practicality and reliability of the stress monitoring method, making the stress monitoring results more valuable for reference; the nonlinear wave analysis is combined with the finite element method for simulation calculation to verify the accuracy and applicability of the theoretical derivation. The accuracy of the theoretical analysis is verified through finite element simulation, improving the credibility and engineering applicability of the method.

[0073] The finite element simulation calculation steps include the following sub-steps:

[0074] a. Establishment of finite element model: Establish a finite element model of the prestressed anchor and define the material properties and boundary conditions;

[0075] b. Mesh generation: Generate a mesh for the model to ensure the accuracy of the mesh and the computational efficiency;

[0076] c. Prestress application: Apply prestress to the model and perform a static analysis to obtain the initial stress distribution of the anchor;

[0077] d. Dynamic analysis: Apply a fluctuating excitation and perform a dynamic analysis to calculate the propagation process of the fluctuations and the stress changes in the anchor;

[0078] e. Result verification: Compare the finite element calculation results with the experimental data to verify the accuracy of the model.

[0079] The detailed finite element simulation calculation steps ensure a high degree of consistency between the theoretical analysis and the actual situation, improving the reliability and engineering practicability of the stress monitoring method.

[0080] The analysis of the dispersion phenomenon therein considers the influence of different excitation frequencies and wavelengths on the wave velocity, and the formula is as follows:

[0081]

[0082] Where, v is the wave velocity, v0 is the fundamental wave velocity, k is the wave number, and w is the angular frequency.

[0083] By considering the influence of different excitation frequencies and wavelengths on the wave velocity, the accuracy of the wave velocity measurement is improved, ensuring the reliability of the stress monitoring results.

[0084] The experimental verification steps therein further include measuring the wave velocity under different prestress conditions multiple times to ensure the repeatability and reliability of the data, and the formula is as follows:

[0085]

[0086] Where, σ i is the stress of the i-th measurement, n is the number of measurements, and σ ij is the

[0087] j-th data in the i-th measurement.

[0088] By measuring multiple times, the repeatability and reliability of the data are ensured, improving the credibility and accuracy of the stress monitoring results.

[0089] 10. The method for analyzing the nonlinear fluctuation of the working stress of the prestressed anchor in the isotropic structure according to claim 1, characterized in that: the nonlinear fluctuation analysis process therein also considers the influence of the isotropy and anisotropy of the material on the wave propagation, and the formula is as follows:

[0090] σ = B·v 2 ·(1 + αcoss(θ))

[0091] Wherein, B is a constant, α is the material anisotropy coefficient, and θ is the angle between the wave propagation direction and the main direction of the material.

[0092] By considering the isotropy and anisotropy of the material, the accuracy of stress monitoring is improved, ensuring the wide applicability of the method in different materials.

[0093] In this article, specific examples are used to elaborate on the principles and implementation methods of the present invention. The descriptions of the above examples are only used to help understand the method of the present invention and its core idea. The above are only the preferred implementation methods of the present invention. It should be noted that due to the limitations of literal expression and objectively infinite specific structures, for those of ordinary skill in the art, without departing from the principles of the present invention, several improvements, refinements or changes can be made, or the above technical features can be combined in an appropriate manner; these improvements, refinements, changes or combinations, or directly applying the concept and technical solution of the invention to other occasions without improvement, should all be regarded as the protection scope of the present invention.

Claims

1. The nonlinear fluctuation analysis method of working stress of prestressed anchor in isotropic structure is characterized by: The following steps are involved: Step 1: Establish anchor model: Establish a prestressed anchor model of isotropic material, assuming that the anchor is subjected to unidirectional tensile stress in an isotropic medium; Step 2: Acoustoelastic theory analysis: Based on nonlinear wave theory, the relationship between stress and elastic wave velocity in the prestressed anchor is analyzed; assuming that the medium is a continuum, the small disturbance of the acoustic wave is superimposed on the static large deformation of the medium; Step 3: Derivation of nonlinear wave equation: Based on the nonlinear wave equation, the one-dimensional acoustic-elastic relationship in the unidirectional stress medium is derived. Assuming that the medium is unidirectionally tensile, its dynamic equilibrium equation is derived, and the relationship between stress and wave velocity is obtained: Among them, σ is stress, v is wave velocity, ρ is medium density, and C is the sound velocity constant; Step 4: Dispersion phenomenon analysis: Consider the dispersion phenomenon of waves propagating in the anchor, analyze the influence of dispersion on wave velocity measurement, and propose methods to reduce the dispersion effect, such as selecting an appropriate excitation frequency; Step 5: Experimental verification: Through laboratory tests, use existing engineering equipment to test the working stress of the anchor, verify the theoretical analysis results, and discuss the errors and accuracy in the test.

2. The method for analyzing nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The prestressed anchor is a steel anchor, and the isotropic medium is concrete or rock; the wave velocity measurement adopts longitudinal wave, and the exciting wave with a frequency not exceeding 200kHz is selected to reduce the influence of dispersion effect; the derivation process of nonlinear wave equation takes into account the physical nonlinearity of the medium, and uses Murnaghan potential function for parameterized description.

3. The method for analyzing the nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The acoustic-elastic relationship is used to measure the wave velocity to obtain the stress in the prestressed anchor, and the formula is as follows: σ=f(v) Among them, σ is stress, v is wave velocity, and f is the functional relationship derived from nonlinear wave theory.

4. The method for analyzing nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The experimental verification step includes the following sub-steps: a. Test equipment preparation: Select test equipment that can accurately measure wave propagation time to ensure that the equipment's measurement accuracy meets the requirements; b. Prestress application: Apply known prestress on the anchor and record the prestress value; c. Wave velocity measurement: Under the action of prestress, measure the propagation velocity of elastic waves in the anchor; d. Data analysis: Based on the measured wave velocity data, the stress in the anchor is calculated using the acoustic-elastic relationship and compared with the known prestress value.

5. The method for analyzing nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The relationship between wave velocity and stress is further refined as follows: Among them, A is a constant and v0 is the wave velocity in the stress-free state.

6. The method for analyzing nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The method for reducing the dispersion effect includes selecting appropriate excitation wave frequency and wavelength to make the wave propagation speed uniform and reduce the wave velocity measurement error caused by the dispersion effect; the acoustic-elastic relationship is obtained through experimental calibration, and the experimental steps include measuring the wave velocity under known stress conditions and fitting the functional relationship between stress and wave velocity; the nonlinear wave analysis is combined with the finite element method for simulation calculation to verify the accuracy and applicability of the theoretical derivation.

7. The method for analyzing nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The finite element simulation calculation step includes the following sub-steps: a. Establishment of finite element model: Establish the finite element model of the prestressed anchor and define the material properties and boundary conditions; b. Meshing: Meshing the model to ensure mesh accuracy and computational efficiency; c. Apply prestress: Apply prestress in the model and perform static analysis to obtain the initial stress distribution of the anchor; d. Dynamic analysis: Apply wave excitation, conduct dynamic analysis, and calculate the wave propagation process and stress changes in the anchor; e. Result verification: Compare the finite element calculation results with the experimental data to verify the accuracy of the model.

8. The method for analyzing nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The dispersion phenomenon analysis takes into account the influence of different excitation frequencies and wavelengths on the wave velocity. The formula is as follows: Among them, v is the wave velocity, v0 is the fundamental wave velocity, k is the wave number, and w is the angular frequency.

9. The method for analyzing nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The experimental verification step further includes multiple measurements of wave velocity under different prestress conditions to ensure the repeatability and reliability of the data. The formula is as follows: Among them, σ i is the stress measured for the i-th time, n is the number of measurements, σ ij is the first j data.

10. The method for analyzing nonlinear fluctuation of working stress of prestressed anchor in isotropic structure according to claim 1, characterized in that: The nonlinear wave analysis process also takes into account the influence of the isotropy and anisotropy of the material on the wave propagation. The formula is as follows: σ=B·v 2 ·(1+αcos(θ)) Among them, B is a constant, α is the anisotropy coefficient of the material, and θ is the angle between the wave propagation direction and the main direction of the material.

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