Anchoring rod bearing performance prediction method based on data driving and physical constraint and related device

Abstract

The present application belongs to the technical field of geotechnical and structural engineering, and discloses a kind of based on data driving and physical constraint's anchor rod bearing performance prediction method and related device, comprising: obtaining the short anchor test curve of to-be-tested anchor rod;Based on the short anchor test curve of to-be-tested anchor rod, and in combination with pre-constructed bond-slip model parameter identification model, obtain the multi-stage parameter of bond-slip model;Pre-constructed bond-slip model parameter identification model is the decision tree model with preset mathematical physical constraint introduced;The multi-stage parameter of bond-slip model is substituted into four-line bond-slip control equation, and the load-slip curve of to-be-tested anchor rod is generated;According to the load-slip curve of to-be-tested anchor rod, obtain the preset bearing performance index of to-be-tested anchor rod, as the bearing performance prediction result of to-be-tested anchor rod;The present application greatly reduces the test cost and improves the prediction effect, can maintain higher universality, provides reliable basis for the design and optimization of anchor rod.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical and structural engineering technology, and specifically relates to a method and related device for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints. Background Technology Anchoring systems, a key technology widely used in geotechnical and structural engineering, primarily rely on anchor bolts, anchor cables, and other components to tightly connect structures to the soil and rock mass. This leverages the shear strength of the soil and rock mass or the prestress transfer mechanism to enhance the stability and load-bearing capacity of the structure. The load-bearing performance of the anchor system is determined by the bond-slip relationship between the anchor body and the matrix. Numerous studies have shown that the bond-slip model mainly depends on the material properties (such as elastic modulus and strength) and the surface roughness of the interface, and is independent of the geometric dimensions of the anchor body, such as length and radius. This means that if the parameters of the bond-slip model can be accurately identified, the overall load-bearing performance of the anchoring system can be extrapolated and predicted under different length and radius conditions.

[0002] Currently, when faced with the task of predicting the load-bearing capacity of anchor bolts, researchers typically rely on long anchor pull-out tests to obtain load-slip curves, fit empirical or segmented bond-slip models, and then infer the load-bearing capacity of the anchor bolts. However, long anchor tests are expensive, especially in cultural relic protection or special geological conditions, and are often difficult to implement. In recent years, there have also been methods to deduce bond-slip model parameters from a small amount of short anchor data and then use them for load-bearing capacity prediction, which significantly reduces the test cost. However, there are still shortcomings in parameter identification accuracy, curve prediction ability, and interpretability.

[0003] Specifically, existing methods rely on manual point selection or simple fitting, making it difficult to accurately identify the multi-stage parameters of the bond-slip model from short anchor test curves. Secondly, existing methods lack mathematical and physical constraints, which can easily lead to the predicted load-slip curves deviating from actual physical laws, resulting in poor interpretability. Furthermore, most existing bond-slip models are bilinear or trilinear, making it difficult to uniformly describe complex multi-stage mechanical behavior, thus limiting the applicability of the models and their predictive capabilities. Summary of the Invention

[0004] To address the technical problems existing in the prior art, this invention provides a data-driven and physical constraint-based method and related apparatus for predicting the bearing capacity of anchor bolts, thereby solving the technical problems of insufficient parameter identification accuracy, curve prediction capability, and interpretability in existing anchor bolt bearing capacity prediction methods.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention provides a data-driven and physical constraint-based method for predicting the bearing capacity of anchor bolts, comprising: Obtain the short anchor test curve of the anchor rod to be tested; Based on the short anchor test curve of the anchor rod to be tested, and combined with the pre-constructed bond-slip model parameter identification model, the multi-stage parameters of the bond-slip model are obtained; among them, the pre-constructed bond-slip model parameter identification model is a decision tree model with preset mathematical and physical constraints. Substitute the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation to generate the load-slip curve of the anchor rod under test; Based on the load-slip curve of the anchor rod under test, the preset bearing capacity index of the anchor rod under test is obtained, which serves as the prediction result of the bearing capacity of the anchor rod under test.

[0006] Furthermore, based on the short anchor test curves of the anchor bolt under test, and combined with the pre-constructed bond-slip model parameter identification model, the process of obtaining the multi-stage parameters of the bond-slip model is as follows: The short anchor test curve of the anchor rod to be tested is preprocessed to obtain the preprocessed short anchor test curve; Feature extraction was performed on the preprocessed short anchor test curves to obtain key features of the short anchor test; among which, the key features of the short anchor test include the starting point of the elastic segment, the peak point of the elastic segment, and the residual segment of the load-displacement curve; The key features of the short anchor test are used as input to the pre-constructed bond-slip model parameter identification model, and the multi-stage parameters of the bond-slip model are obtained as output.

[0007] Furthermore, the pre-defined mathematical and physical constraints include parameter monotonicity constraints, compatibility constraints, energy consistency constraints, and physical boundary condition constraints. The constraints include: parametric monotonicity constraints, specifically the order relationship between the stage displacement and shear stress of the anchor bolt; compatibility constraints, specifically the compatibility conditions of the piecewise solution of the anchor bolt; energy consistency constraints, specifically the consistency relationship between the integral area of ​​the constraint prediction curve of the anchor bolt from the origin to the peak value and the energy of the experimental data; and physical boundary condition constraints, as follows:

[0008]

[0009] at

[0010]

[0011] in, Along the length of the anchor rod to be measured The slip function at the point; These are parameters related to the properties of the anchor bolt material being tested; Along the length of the anchor rod to be measured The shear stress function at the location; The elastic modulus of the anchor rod to be tested; Let be the radius of the anchor rod to be measured; The bearing capacity of the anchor rod to be tested; The length of the anchor rod to be measured is given.

[0012] Furthermore, the multi-stage parameters of the bond-slip model include displacement parameters and stress parameters; among which, the displacement parameters include the slip at the elastic limit, the slip at the end of the first softening stage and the beginning of the second softening stage, and the slip at the end of the second softening stage and the beginning of the friction stage; the stress parameters include the shear stress at the elastic limit, the shear stress at the end of the first softening stage and the beginning of the second softening stage, and the shear stress at the end of the second softening stage and the beginning of the friction stage. The four-line bond-slip control equations are as follows:

[0013] in, This represents the shear stress at different locations along the length of the anchor rod to be measured. This is the bonding stiffness coefficient at the elastic limit; This represents the slippage at different locations along the length of the anchor rod being measured. The bonding stiffness coefficient is located at the end of the first softening stage and the beginning of the second softening stage. This represents the slip at the elastic limit. This represents the shear stress at the elastic limit. This is the bonding stiffness coefficient at the end of the second softening stage and the beginning of the friction stage; This refers to the amount of slippage between the end of the first softening stage and the beginning of the second softening stage. The shear stress at the end of the first softening stage and the beginning of the second softening stage; This refers to the shear stress at the end of the second softening stage and the beginning of the friction stage.

[0014] Furthermore, the process of substituting the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation to generate the load-slip curve of the anchor rod under test is as follows: Substituting the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation, and combining the length and radius of the anchor rod under test, the analytical solutions of the anchor rod under test in the elastic segment, the first softening segment, the second softening segment and the friction segment are calculated in sequence, and then spliced ​​into a complete curve to obtain the load-slip curve of the anchor rod under test.

[0015] Furthermore, the preset bearing capacity indicators of the anchor bolt to be tested include the peak bearing capacity, peak slippage, and energy dissipation index of the anchor bolt to be tested.

[0016] This invention provides a data-driven and physical constraint-based anchor bolt bearing capacity prediction system, comprising: The data acquisition module is used to acquire the short anchor test curve of the anchor rod under test; The parameter identification module is used to obtain the multi-stage parameters of the bond-slip model based on the short anchor test curve of the anchor rod under test and in combination with the pre-constructed bond-slip model parameter identification model; wherein, the pre-constructed bond-slip model parameter identification model is a decision tree model with preset mathematical and physical constraints. The curve generation module is used to substitute the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation to generate the load-slip curve of the anchor rod to be tested. The index recognition module is used to obtain the preset bearing capacity index of the anchor rod under test based on the load-slip curve of the anchor rod under test, and use it as the bearing capacity prediction result of the anchor rod under test.

[0017] The present invention also provides an electronic device, comprising: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, performs the aforementioned method for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints.

[0018] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints.

[0019] The present invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the aforementioned method for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention provides a data-driven and physically constrained method for predicting the load-bearing capacity of anchor bolts. By introducing a decision tree model with preset mathematical and physical constraints as the parameter identification model for the bond-slip model, it can accurately identify multi-stage parameters of the bond-slip model from short anchor test curves, significantly improving parameter identification accuracy and effectively overcoming the problem of insufficient parameter identification accuracy caused by existing methods relying on manual point selection or simple fitting. At the same time, the introduction of mathematical and physical constraints into the bond-slip model parameter identification model ensures that the predicted load-slip curve conforms to actual physical laws, enhancing interpretability. In addition, the use of a four-line bond-slip control equation can uniformly describe complex multi-stage mechanical behavior, improving model applicability and predictive ability. Overall, the present invention significantly reduces test costs and improves prediction results, maintaining universality under various material and interface conditions, and providing a reliable basis for anchor bolt design and optimization.

[0021] The anchor bolt bearing capacity prediction system, electronic device, computer-readable storage medium, and computer program product based on data-driven and physical constraints provided by this invention possess all the advantages of the aforementioned anchor bolt bearing capacity prediction method based on data-driven and physical constraints. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart of the anchor bolt bearing capacity prediction method based on data-driven and physical constraints provided in Example 1; Figure 2 This is a schematic diagram illustrating the principle of the anchor bolt bearing capacity prediction method based on data-driven and physical constraints provided in Example 1. Figure 3 The prediction accuracy curve of the pre-constructed bond-slip model parameter identification model in Example 1; Figure 4 This is a comparison chart of the analytical results and experimental data of the four-line bond-slip control equation in Example 1; Figure 5 This is a structural block diagram of the anchor bolt bearing capacity prediction system based on data-driven and physical constraints provided in Example 2; Figure 6 This is a structural block diagram of the electronic device provided in Example 3. Detailed Implementation

[0024] To make the technical problems, technical solutions, and beneficial effects solved by this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0025] This invention provides a method for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints, comprising the following steps: Step 100: Obtain the short anchor test curve of the anchor rod to be tested.

[0026] Step 200: Based on the short anchor test curve of the anchor rod to be tested, and combined with the pre-constructed bond-slip model parameter identification model, obtain the multi-stage parameters of the bond-slip model; wherein, the pre-constructed bond-slip model parameter identification model is a decision tree model with preset mathematical and physical constraints.

[0027] Step 300: Substitute the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation to generate the load-slip curve of the anchor to be tested.

[0028] Step 400: Based on the load-slip curve of the anchor rod to be tested, obtain the preset bearing capacity index of the anchor rod to be tested, which is used as the bearing capacity prediction result of the anchor rod to be tested.

[0029] In the above implementation method, compared with long anchor tests, obtaining the short anchor test curve of the anchor rod to be tested is easier to implement under various complex conditions such as cultural relic protection and special strata, and the cost is significantly reduced, greatly improving the applicability of the prediction method and enabling the prediction of the load-bearing performance of anchor rods in more scenarios. Secondly, based on the short anchor test curve of the anchor rod to be tested, and combined with a pre-constructed decision tree model with preset mathematical and physical constraints, the multi-stage parameters of the bond-slip model are obtained. The decision tree model has good data processing and analysis capabilities. By introducing preset mathematical and physical constraints, it can extract key information from the short anchor test curve more scientifically and accurately, avoiding the subjectivity of manual point selection and the limitations of simple fitting, thereby significantly improving the recognition accuracy of the multi-stage parameters of the bond-slip model. Among them, the pre-constructed bond-slip model parameter recognition model introduces preset mathematical and physical constraints, so that the actual physical laws are followed in the process of generating bond-slip model parameters and subsequent generating load-slip curves. The obtained multi-stage parameters are substituted into the four The load-slip curve of the anchor rod under test is generated in the linear bond-slip control equation. Due to the constraints of mathematical physics, the generated load-slip curve is more consistent with the actual situation, greatly enhancing the curve prediction ability and reflecting the actual mechanical behavior of the anchor rod more accurately. The use of a four-line bond-slip control equation, compared to bilinear or trilinear models, can more finely divide and describe the mechanical behavior of the anchor rod at different stages. It can uniformly and more accurately describe complex multi-stage mechanical processes, thereby improving the model's applicability and providing more reliable load-bearing performance predictions for anchor rods under different working conditions. This further enhances the prediction ability and makes the final prediction results more interpretable, facilitating understanding and application by engineering technicians. The method described in this invention has significant beneficial effects in reducing experimental costs, improving parameter identification accuracy, enhancing curve prediction ability, improving model applicability and prediction ability, and improving interpretability. It maintains universality under various material and interface conditions, providing a reliable basis for anchor rod design and optimization.

[0030] The following specific embodiments further explain the anchor bolt bearing capacity prediction method based on data-driven and physical constraints provided by the present invention: Example 1 As attached Figure 1 As shown in the figure, this embodiment 1 provides a method for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints, including the following steps: Step 1: Obtain the short anchor test curve of the anchor rod to be tested. Specifically, based on the structural characteristic data, elastic modulus, short anchor test strain data, and pull-out test results of the anchor rod to be tested, the short anchor test curve of the anchor rod is fitted. The structural characteristic data of the anchor rod to be tested includes its length and radius. Taking a bamboo anchor rod as an example, based on the pull-out test results of the bamboo anchor rod, and combined with its length, radius, elastic modulus, and short anchor test strain data, the short anchor test curve of the bamboo anchor rod is fitted.

[0031] Step 2: Based on the short anchor test curve of the anchor rod to be tested, and combined with the pre-constructed bond-slip model parameter identification model, obtain the multi-stage parameters of the bond-slip model. The pre-constructed bond-slip model parameter identification model is a decision tree model with pre-defined mathematical and physical constraints. Specifically, based on the short anchor test curve of the anchor rod to be tested, and using the test bond-slip model curve in the pre-determined short anchor test database as a standard, the bond-slip model parameters of the anchor rod to be tested are compared with those of the anchor rod using the decision tree model with pre-defined mathematical and physical constraints to obtain the multi-stage parameters of the bond-slip model.

[0032] More specifically, it includes the following steps: Step 21: Preprocess the short anchor test curve of the anchor rod to be tested to obtain the preprocessed short anchor test curve. The preprocessing process includes noise reduction, smoothing, and outlier removal. Specifically, the median filtering method is used to suppress the impulse noise of the original load-displacement data in the short anchor test curve. The Savitzky-Golay filtering method is used to smooth the short anchor test curve of the anchor rod to be tested to keep the curve inflection points and peak positions undistorted. According to the local slope change law of the short anchor test curve of the anchor rod to be tested, outliers are identified. For test points that suddenly jump or deviate from the trend, they are replaced by the neighborhood interpolation method, thereby obtaining a continuous, smooth, and physically reasonable short anchor test input curve as the preprocessed short anchor test curve.

[0033] It should be noted that when using the short anchor test curve of the anchor rod under test as input to the pre-constructed bond-slip model parameter identification model, preprocessing is first performed, including noise reduction, smoothing, and outlier removal, and key feature values ​​including the elastic segment start point, peak point, and residual segment are extracted. Since the bond-slip relationship is only related to the material properties and interface roughness of the anchor rod under test, and is independent of the geometric dimensions of the anchor rod under test, such as the anchorage length and radius, the short anchor test curve of the anchor rod under test can be directly used as a database for parameter identification and model training.

[0034] Step 21: Extract features from the preprocessed short anchor test curve to obtain key features of the short anchor test; among which, the key features of the short anchor test include the starting point of the elastic segment, the peak point of the elastic segment, and the residual segment of the load-displacement curve.

[0035] Step 23: Use the key features of the short anchor test as input to the pre-constructed bond-slip model parameter identification model, and output the multi-stage parameters of the bond-slip model. The multi-stage parameters of the bond-slip model include displacement parameters and stress parameters; specifically, the displacement parameters include the slip at the elastic limit, the slip between the end of the first softening stage and the beginning of the second softening stage, and the slip between the end of the second softening stage and the beginning of the friction stage; the stress parameters include the shear stress at the elastic limit, the shear stress between the end of the first softening stage and the beginning of the second softening stage, and the shear stress between the end of the second softening stage and the beginning of the friction stage.

[0036] It is worth noting that when obtaining the multi-stage parameters of the bond-slip model, the short anchor test curve of the anchor rod under test is used as the input to a decision tree model with pre-defined mathematical and physical constraints. Specifically, the curve characteristics of the short anchor test curve and the mechanical constraints are used as input to the decision tree model, and the multi-stage parameters of the bond-slip model are output. By introducing pre-defined mathematical and physical constraints into the decision tree model, the model can avoid the physical distortion problem caused by black-box prediction, ensuring the consistency of the output parameters in terms of statistical and physical laws. These pre-defined mathematical and physical constraints include parameter monotonicity constraints, compatibility constraints, energy consistency constraints, and physical boundary condition constraints.

[0037] The parameter monotonicity constraint is the order relationship between the stage displacement and shear stress of the anchor bolt, to force the multi-stage parameters of the bond-slip model to satisfy the following conditions:

[0038]

[0039] in, This represents the slip at the elastic limit. This refers to the amount of slippage between the end of the first softening stage and the beginning of the second softening stage. This refers to the amount of slippage at the end of the second softening stage and the beginning of the friction stage. This represents the shear stress at the elastic limit. The shear stress at the end of the first softening stage and the beginning of the second softening stage; This refers to the shear stress at the end of the second softening stage and the beginning of the friction stage.

[0040] Compatibility constraints are the compatibility conditions for the piecewise solution of the anchor bolt, ensuring the continuity of the piecewise governing equations at the boundaries; for example, continuity conditions, boundary adjustment, and first derivative continuity conditions; among which, the continuity conditions, boundary adjustment, and first derivative continuity conditions are as follows:

[0041]

[0042]

[0043] in, Radial strain; This represents the slippage at different locations along the length of the anchor rod being measured. This is the sliding length of the first softening segment; The length of the anchor rod to be measured; The location point is along the length of the anchor rod to be measured; For strain combination.

[0044] The energy consistency constraint is the consistency relationship between the area under the constraint prediction curve of the anchor bolt from the origin to the peak value and the energy of the experimental data; specifically, each micro-segment on the constraint prediction curve of the anchor bolt multiplied by the corresponding slip is approximately equal to the area under the analytical load-displacement curve; the specific energy consistency constraint is as follows:

[0045] in, The bearing capacity of the anchor rod to be tested; Along the length of the anchor rod to be measured The slip function at the point; Along the length of the anchor rod to be measured The shear stress function at that point.

[0046] The physical boundary conditions are as follows:

[0047]

[0048] at

[0049]

[0050] in, These are parameters related to the properties of the anchor bolt material being tested; The elastic modulus of the anchor rod to be tested; Let be the radius of the anchor rod to be measured; This represents the bearing capacity of the anchor rod to be tested.

[0051] Step 3: Substitute the multi-stage parameters of the bond-slip model into the four-line bond-slip control equations to generate the load-slip curve of the anchor to be tested. Specifically, substitute the multi-stage parameters of the bond-slip model into the four-line bond-slip control equations, and combine the length and radius of the anchor to be tested to calculate the analytical solutions of the anchor in the elastic segment, the first softening segment, the second softening segment, and the friction segment in sequence; then, stitch the analytical solutions of the anchor in the elastic segment, the first softening segment, the second softening segment, and the friction segment to obtain the load-slip curve of the anchor to be tested.

[0052] The four-line bond-slip control equation is as follows:

[0053] in, This represents the shear stress at different locations along the length of the anchor rod to be measured. This is the bonding stiffness coefficient at the elastic limit; This represents the slippage at different locations along the length of the anchor rod being measured. The bonding stiffness coefficient is located at the end of the first softening stage and the beginning of the second softening stage. It represents the bonding stiffness coefficient at the end of the second softening stage and the beginning of the friction stage.

[0054] The analytical solutions for the anchor bolt under test in the elastic section, the first softening section, the second softening section, and the friction section are as follows:

[0055]

[0056]

[0057]

[0058]

[0059] in, This is the analytical solution for the anchor rod under test in the elastic section; These are parameters related to the elastic characteristics of the anchor bolt under test; This is the analytical solution for the first softened section of the anchor bolt under test; These are parameters related to the characteristics of the first softened section of the anchor bolt under test; This represents the maximum sliding length of the first softening segment; This is the analytical solution for the second softened section of the anchor bolt under test; This represents the maximum sliding length of the second softening section; These are parameters related to the characteristics of the second softened section of the anchor bolt under test. This is the analytical solution for the anchor rod under test in the friction section; These are parameters related to the characteristics of the friction section of the anchor bolt under test. These are performance indicators used to evaluate the energy dissipation of the friction section.

[0060] It should be noted that in the process of generating the load-slip curve of the anchor rod under test, the multi-stage parameters of the bond-slip model are substituted into the four-line bond-slip control equation. The analytical solutions of the elastic segment, the first softening segment, the second softening segment, and the friction segment of the anchor rod under test are calculated sequentially and then spliced ​​to complete the generation of the load-slip curve of the anchor rod under test. Therefore, given the anchorage length and radius of the anchor rod under test, the load-slip curve of the anchor rod under test can be obtained. In particular, by obtaining different anchorage lengths and radii, prediction results under different working conditions can be obtained in real time.

[0061] Step 4: Based on the load-slip curve of the anchor to be tested, obtain the preset bearing capacity index of the anchor to be tested, which serves as the predicted bearing capacity result of the anchor to be tested. The predicted bearing capacity result of the anchor to be tested includes the peak bearing capacity, peak slip, and energy dissipation index; specifically, the preset bearing capacity index of the anchor to be tested can be obtained by feature recognition of the load-slip curve.

[0062] Explanation of prediction principles: As attached Figure 2 As shown in Example 1, the anchor bearing capacity prediction method based on data-driven and physical constraints takes the physical nature of material / geometry separation as its starting point. It follows the rule that the interface bonding-slip relationship is mainly determined by material properties and surface roughness, and does not change with the anchor length and radius. Therefore, it can identify model parameters that are independent of geometry using short anchor test data, and then extrapolate and predict the load-slip curve under any geometric condition. Compared with the traditional approach that relies on long anchor tests, Example 1 can significantly reduce the test cost and engineering disturbance of obtaining parameters without reducing the mechanical authenticity. Especially in scenarios such as the protection of earthen sites where large-scale or deep sampling is not suitable, it can complete the reliable characterization of the target material-interface under small disturbance and low cost conditions, achieving the goal of fewer tests and strong extrapolation.

[0063] In this embodiment 1, during the acquisition of multi-stage parameters of the bond-slip model, a decision tree model with mathematical and physical constraints is introduced to incorporate curve features and mechanical constraints into the recognition process. By setting parameter monotonicity constraints, compatibility constraints, energy consistency constraints, and physical boundary condition constraints, the learning process simultaneously satisfies statistical fitting and physical interpretability. Compared with black-box methods lacking physical constraints, this approach effectively avoids results that violate mechanical common sense, such as disjointed stage splicing, peak position drift, and residual segment distortion. At the same time, the decision tree model has readable splitting rules in its structure, which facilitates review and engineering verification, reduces the risk of opacity that is usable but not explainable, and can improve the stability of recognition while taking into account the traceability and interpretability of the results.

[0064] In this embodiment 1, a unified four-line bond-slip control equation is used in the process of generating the load-slip curve of the anchor rod under test. The analytical solution of the piecewise control equation ensures that the displacement / shear stress at the boundary point of each stage is compatible. This can cover the typical evolution of elasticity, two-stage softening and friction residue, and avoid the contradiction between peak accuracy and residual rationality that is difficult to balance in bilinear / trilinear models. Since the multi-stage parameters of the bond-slip model do not change with geometry, the load-slip curve of the corresponding working condition can be directly generated given any anchorage length and radius, and the peak bearing capacity, peak slip and energy dissipation index are output simultaneously. This allows the bearing difference of the same material-interface under different geometric and constraint conditions to be quickly and uniformly evaluated, which significantly improves the portability and consistency from test to design.

[0065] The method described in Embodiment 1 integrates data, identification, modeling, and indicators into a single system. By simply importing short anchor test curves or selecting material-interface conditions, parameter identification and curve prediction can be automatically completed. The anchorage length and radius can be adjusted in real time via a slider to observe changes in the results. This reduces human error and time overhead associated with cross-software and multi-step manual splicing. It supports batch processing and standardized export, facilitating scientific research reproduction and engineering archiving. Optionally, the method incorporates a built-in result verification and fault tolerance strategy, automatically correcting identification results that do not meet energy consistency or compatibility thresholds, thus improving robustness under practical conditions such as noisy data and limited samples.

[0066] Performance verification results: (1) Using a decision tree model with pre-defined mathematical and physical constraints, the multi-stage parameters of the bond-slip model are inverted based on the short anchor test curve of the anchor rod to be tested, and compared with the actual test values. This yields the prediction accuracy curve of the pre-constructed bond-slip model parameter identification model, as shown in the attached figure. Figure 3 As shown.

[0067] From the appendix Figure 3As can be seen, the predicted values ​​of the multi-stage parameters of the bond-slip model show a strong linear correlation with the actual values; among them, the slip at the elastic limit... The amount of slip at the end of the first softening stage and the beginning of the second softening stage. and the amount of slip at the end of the second softening stage and the beginning of the friction stage. The determination coefficients reached 0.9157, 0.9443, and 0.9296, respectively, and the root mean square errors (RMSE) were all controlled within the order of 0.05, at 0.0418, 0.0463, and 0.1919, respectively; this indicates that the predicted slip characteristic points have high accuracy; regarding the stress parameters, i.e., the peak shear stress, i.e., the shear stress in the softened segment, the shear stress at the elastic limit... The prediction accuracy is the highest, with a coefficient of determination of 0.9472 and a root mean square error of 0.0743; the shear stress at the end of the first softening stage and the beginning of the second softening stage. The good fit was good, with a coefficient of determination of 0.8005 and a root mean square error of 0.1343; the shear stress at the end of the second softening stage and the beginning of the friction stage. The coefficient of determination is 0.6723 and the root mean square error is 0.1110, which is slightly lower due to the influence of experimental discreteness but still maintains reasonable consistency. In summary, the decision tree model with pre-set mathematical and physical constraints can reliably invert the multi-stage parameters of the bond-slip model, laying a good foundation for the subsequent prediction of the mechanical behavior of long anchors.

[0068] (2) Compare the analytical results of the four-line bond-slip control equation with the predetermined publicly available experimental data, as shown in the appendix. Figure 4 As shown; among them, the predetermined publicly available test data comes from the pull-out test results of Ren et al. (2010) on fully grouted anchor bolts with circular cross sections.

[0069] From the appendix Figure 4 As can be seen, the analytical curve of the model and the pull-out test results of Ren et al. (2010) on the fully grouted anchor rod with circular cross-section show a high degree of consistency throughout the slip process. This indicates that the four-line bond-slip control equation can accurately capture the key features including the initial elastic stage rise, peak plateau, post-peak softening process, and residual friction stage. It is particularly worth emphasizing that the analytical solution has extremely high prediction accuracy for the peak load index, while maintaining a good fit in other stages as well. Quantitative analysis shows that the mean absolute error (MAE) and root mean square error (RMSE) between the predicted and experimental values ​​are 5.3 kN and 5.7 kN, respectively, with a coefficient of determination of 0.9904. The error relative to the peak load is less than 3%, indicating that the model fit is extremely high.

[0070] The anchor bearing capacity prediction method based on data-driven and physical constraints described in Example 1 uses the short anchor test curve of the anchor under test, introduces a decision tree model with preset mathematical and physical constraints, and a four-line bond-slip control equation to achieve the unification of automatic parameter identification and curve prediction. This not only overcomes the shortcomings of traditional methods such as strong reliance on experiments, difficulty in parameter inversion, and lack of physical interpretation in intelligent methods, but also maintains universality under various material and interface conditions, providing a reliable basis for anchor design and optimization. Specifically, the parameter identification method based on the material / geometry separation principle utilizes the short anchor test... The bond-slip model parameters, independent of geometric dimensions, are obtained through inversion of experimental data. A decision tree model with physical constraints is constructed, embedding parameter monotonicity, compatibility conditions, and energy consistency into the identification process to achieve a unified intelligent identification and physical interpretability of parameters. A unified four-line bond-slip control equation framework is introduced to ensure the compatibility of curve segment splicing and to predict the complete load-slip curve under different anchorage lengths and radii. The system supports the import of short anchor data and, by adjusting geometric parameters, outputs predicted curves, peak bearing capacity, and energy indicators in real time, achieving the integration of parameter identification and curve prediction.

[0071] Example 2 As attached Figure 5 As shown in the figure, this embodiment 2 provides a data-driven and physical constraint-based anchor bolt bearing capacity prediction system, including a data acquisition module, a parameter identification module, a curve generation module, and an index identification module.

[0072] The data acquisition module is used to acquire the short anchor test curve of the anchor rod under test; the parameter identification module is used to obtain the multi-stage parameters of the bond-slip model based on the short anchor test curve of the anchor rod under test and in combination with the pre-constructed bond-slip model parameter identification model; wherein, the pre-constructed bond-slip model parameter identification model is a decision tree model with preset mathematical and physical constraints; the curve generation module is used to substitute the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation to generate the load-slip curve of the anchor rod under test; the index identification module is used to obtain the preset bearing performance index of the anchor rod under test based on the load-slip curve of the anchor rod under test, as the bearing performance prediction result of the anchor rod under test.

[0073] Example 3 As attached Figure 6 As shown, this embodiment 3 provides an electronic device, including: a memory for storing a computer program; a processor for executing the computer program to implement the steps of the anchor bolt bearing capacity prediction method based on data-driven and physical constraints; or, the processor executing the computer program to implement the functions of each module in the above-mentioned anchor bolt bearing capacity prediction system based on data-driven and physical constraints.

[0074] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a preset function, the instruction segments describing the execution process of the computer program in the electronic device.

[0075] The electronic device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The electronic device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above are examples of electronic devices and do not constitute a limitation on the electronic device. It may include more components than described above, or combine certain components, or different components. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0076] The processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor, or any conventional processor, etc. The processor is the control center of the electronic device, connecting various parts of the entire electronic device through various interfaces and lines.

[0077] The memory can be used to store the computer program and / or module. The processor implements various functions of the electronic device by running or executing the computer program and / or module stored in the memory and by calling the data stored in the memory.

[0078] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function (such as sound playback, image playback, etc.). The data storage area may store data created based on the use of the mobile phone (such as audio data, phonebook, etc.). Furthermore, the memory may include high-speed random access memory and non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart memory cards, secure digital cards, flash memory cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0079] Example 4 This embodiment 4 also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the data-driven and physical constraint-based anchor bearing capacity prediction method.

[0080] If the modules / units integrated by the data-driven and physical constraint-based anchor bearing capacity prediction system are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0081] Based on this understanding, the present invention can implement all or part of the processes in the above-mentioned data-driven and physical constraint-based anchor bolt bearing capacity prediction method. This can also be accomplished by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium. When executed by a processor, the computer program can implement the steps of the above-mentioned data-driven and physical constraint-based anchor bolt bearing capacity prediction method. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or a preset intermediate form, etc.

[0082] The computer-readable storage medium may include any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electrical carrier signal, telecommunication signal, and software distribution medium, etc.

[0083] Example 5 This embodiment 5 provides a computer product, which includes a computer program stored in a computer-readable storage medium. The processor of the electronic device reads the computer program from the computer-readable storage medium and executes the computer program, so that the electronic device can execute the anchor bolt bearing performance prediction method based on data-driven and physical constraints described in embodiment 1, which will not be repeated here.

[0084] It should be noted that those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above methods.

[0085] The data-driven and physically constrained anchor bearing capacity prediction method described in this invention is used for modeling and predicting the bond-slip relationship at the anchor interface, and is particularly suitable for complex scenarios such as earthen heritage preservation, underground engineering, and slope protection. Since complex scenarios typically do not allow for large-scale long anchor tests, this invention can complete parameter identification and long anchor performance prediction using short anchor test data, significantly reducing test disturbance. It employs a decision tree model with mathematical and physical constraints, taking short anchor test curve features such as initial stiffness, peak point, and residual slope as input, and outputting multi-stage parameters of the bond-slip model. This differs from ordinary regression trees. This invention embeds pre-defined mathematical and physical constraints in both the splitting and prediction stages to ensure that the results satisfy the governing equations and energy consistency. The load-slip curve prediction is based on a four-line bond-slip model, including an elastic segment, a first softening segment, a second softening segment, and a friction segment. The equations of each segment are continuously spliced ​​at the boundary points, and the derivative continuity is ensured when necessary. Compared with traditional bilinear or trilinear models, it can more accurately describe the softening and residual characteristics of the interface. Optionally, in the specific implementation, the parameter identification algorithm can not only use a decision tree, but can also be extended to a gradient boosting tree, random forest, or lightweight neural network, but all of them must embed the same physical constraint logic.

[0086] This invention uses physical principles to ensure parameter extrapolation, constrained decision trees to ensure interpretable identification, a four-line analytical framework to ensure compatibility of splicing, and an integrated platform to ensure the feasibility of the process. It fundamentally overcomes the problems of strong experimental dependence, unstable inversion, physical distortion, and fragmented tools in existing technologies. It can obtain more reliable interface parameters with lower experimental perturbation and cost; it covers different materials and interface conditions with a unified framework; it provides design indicators such as peak value and energy in an interpretable and verifiable manner; and it achieves rapid trade-off and optimization between anchor volume and bearing capacity through geometric extrapolation, making it suitable for the dual needs of scientific research verification and engineering design.

[0087] The above embodiments are merely one of the implementation methods for achieving the technical solution of the present invention. The scope of protection claimed by the present invention is not limited to this embodiment, but also includes any variations, substitutions and other implementation methods that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention.

Claims

1. A method for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints, characterized in that, include: Obtain the short anchor test curve of the anchor rod to be tested; Based on the short anchor test curve of the anchor rod to be tested, and combined with the pre-constructed bond-slip model parameter identification model, the multi-stage parameters of the bond-slip model are obtained; among them, the pre-constructed bond-slip model parameter identification model is a decision tree model with preset mathematical and physical constraints. Substitute the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation to generate the load-slip curve of the anchor rod under test; Based on the load-slip curve of the anchor rod to be tested, the preset bearing capacity index of the anchor rod to be tested is obtained as the bearing capacity prediction result of the anchor rod to be tested; The process of obtaining the multi-stage parameters of the bond-slip model based on the short anchor test curve of the anchor rod under test and combined with the pre-constructed bond-slip model parameter identification model is as follows: The short anchor test curve of the anchor rod to be tested is preprocessed to obtain the preprocessed short anchor test curve; Feature extraction was performed on the preprocessed short anchor test curves to obtain key features of the short anchor test; among which, the key features of the short anchor test include the starting point of the elastic segment, the peak point of the elastic segment, and the residual segment of the load-displacement curve; The key features of the short anchor test are used as input to the pre-constructed bond-slip model parameter identification model, and the multi-stage parameters of the bond-slip model are output. The pre-defined mathematical and physical constraints include parameter monotonicity constraints, compatibility constraints, energy consistency constraints, and physical boundary condition constraints. The constraints include: parametric monotonicity constraints, specifically the order relationship between the stage displacement and shear stress of the anchor bolt; compatibility constraints, specifically the compatibility conditions of the piecewise solution of the anchor bolt; energy consistency constraints, specifically the consistency relationship between the integral area of ​​the constraint prediction curve of the anchor bolt from the origin to the peak value and the energy of the experimental data; and physical boundary condition constraints, as follows: at in, Along the length of the anchor rod to be measured The slip function at the point; These are parameters related to the properties of the anchor bolt material being tested; Along the length of the anchor rod to be measured The shear stress function at the location; The elastic modulus of the anchor rod to be tested; Let be the radius of the anchor rod to be measured; The bearing capacity of the anchor rod to be tested; The length of the anchor rod to be measured; The multi-stage parameters of the bond-slip model include displacement parameters and stress parameters; among which, the displacement parameters include the slip at the elastic limit, the slip at the end of the first softening stage and the beginning of the second softening stage, and the slip at the end of the second softening stage and the beginning of the friction stage; the stress parameters include the shear stress at the elastic limit, the shear stress at the end of the first softening stage and the beginning of the second softening stage, and the shear stress at the end of the second softening stage and the beginning of the friction stage. The four-line bond-slip control equations are as follows: in, This represents the shear stress at different locations along the length of the anchor rod to be measured. This is the bonding stiffness coefficient at the elastic limit; This represents the slippage at different locations along the length of the anchor rod being measured. The bonding stiffness coefficient is located at the end of the first softening stage and the beginning of the second softening stage. This represents the slip at the elastic limit. This represents the shear stress at the elastic limit. This is the bonding stiffness coefficient at the end of the second softening stage and the beginning of the friction stage; This refers to the amount of slippage between the end of the first softening stage and the beginning of the second softening stage. The shear stress at the end of the first softening stage and the beginning of the second softening stage; This refers to the shear stress at the end of the second softening stage and the beginning of the friction stage.

2. The method for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints according to claim 1, characterized in that, The process of substituting the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation to generate the load-slip curve of the anchor rod under test is as follows: Substituting the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation, and combining the length and radius of the anchor rod under test, the analytical solutions of the anchor rod under test in the elastic segment, the first softening segment, the second softening segment and the friction segment are calculated in sequence, and then spliced ​​into a complete curve to obtain the load-slip curve of the anchor rod under test.

3. The anchor bolt bearing capacity prediction method based on data-driven and physical constraints according to claim 1, characterized in that, The preset bearing capacity indicators of the anchor bolt to be tested include the peak bearing capacity, peak slip, and energy dissipation index of the anchor bolt to be tested.

4. A data-driven and physically constrained anchor bolt bearing capacity prediction system, characterized in that, The method for predicting the bearing capacity of anchor bolts based on data-driven and physical constraints as described in claim 1 includes: The data acquisition module is used to acquire the short anchor test curve of the anchor rod under test; The parameter identification module is used to obtain the multi-stage parameters of the bond-slip model based on the short anchor test curve of the anchor rod under test and in combination with the pre-constructed bond-slip model parameter identification model; wherein, the pre-constructed bond-slip model parameter identification model is a decision tree model with preset mathematical and physical constraints. The curve generation module is used to substitute the multi-stage parameters of the bond-slip model into the four-line bond-slip control equation to generate the load-slip curve of the anchor rod to be tested. The index recognition module is used to obtain the preset bearing capacity index of the anchor rod under test based on the load-slip curve of the anchor rod under test, and use it as the bearing capacity prediction result of the anchor rod under test.

5. An electronic device, characterized in that, include: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, performs the anchor bolt bearing capacity prediction method based on data-driven and physical constraints as described in any one of claims 1-3.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the anchor bolt bearing capacity prediction method based on data-driven and physical constraints as described in any one of claims 1-3.

7. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the anchor bolt bearing capacity prediction method based on data-driven and physical constraints as described in any one of claims 1-3.

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