A method and system for long-term strength assessment of rock core samples based on rheological tests

Abstract

This invention relates to the fields of rock mechanics and building engineering, and discloses a method and system for long-term strength assessment of rock core samples based on rheological tests. The method includes preparing a standard cylindrical sample, testing the sample according to rheological tests to obtain a rheological curve, fitting the reciprocal of the steady-state rheological rate to the logarithm of the stress level to obtain a fitted curve, selecting the point of maximum curvature on the curve, performing a linear function fitting on the near-straight portion of the curve's end segment, drawing a horizontal line and a tangent line through the point of maximum curvature, plotting the angle bisectors of the horizontal line and the tangent line, performing a linear function fitting on the intersection point of the angle bisectors and the near-straight portion of the curve's end segment, and calculating the long-term strength. The system includes a curve fitting module, a function fitting module, and a strength calculation module. This invention achieves effective long-term strength assessment through quantitative analysis of the rheological properties of rock core samples; it also provides related technical means to ensure the accuracy and reliability of the results.

Description

Technical Field

[0001] This invention relates to the fields of rock mechanics and building engineering, and in particular to a method and system for long-term strength evaluation of rock core samples based on rheological testing. Background Technology

[0002] The long-term strength of rock refers to its resistance to failure under long-term loads. The long-term strength of rock is significantly affected by its structure and internal defects. When subjected to a load less than a constant value, the deformation of the rock increases over time, but the rate of increase decreases over time, eventually leading to a stable value where the rock does not fail. However, when the load exceeds a certain constant value, the deformation of the rock mass increases over time, and the rate of increase increases sharply, eventually leading to deformation and failure. Currently, determining accurate long-term strength values ​​using existing theoretical methods is difficult. Based on rheological tests, common methods include the isochronous curve method and the steady-state rheological rate curve method. However, these methods are more applicable when the rock's rheological properties are obvious. When the rock's rheological properties are not obvious, it is difficult to determine the early straight segment and the turning point of the curve. Therefore, an effective method for determining long-term strength is of significant practical importance for the design of engineering structures such as underground caverns, slopes, and dam foundations.

[0003] Prior art 1, application number: CN201711453978.3, discloses a method for determining long-term strength in rock creep tests, including: core sampling of rock samples from the field; processing the rock cores into specimens; installing and adjusting axial-radial displacement sensors on the specimens; applying axial-radial loads to the specimens until specimen failure; collecting test data and converting the data for output; plotting the axial-radial creep curve of the specimens; calculating the creep Poisson's ratio at each time point; and determining the long-term strength of the rock. Although this method is based on the actual ductile expansion deformation of the rock, comprehensively considers the influence of axial-radial deformation on rock properties during creep, segments the creep time, plots the creep Poisson's ratio time curve, and determines the long-term strength of the rock based on the stress corresponding to the inflection point data of the curve, making the calculated long-term strength better reflect the aging of the rock, eliminating subjective judgment, and is simple, reliable, and highly accurate, making it easy to promote and apply to practical rock engineering, it can easily lead to inaccurate results in determining the long-term strength when the rheological characteristics of the rock sample are not obvious.

[0004] Prior art two, application number: CN 201510369199.X, discloses a method for determining the long-term strength parameters of rocks based on the intersection of steady-state rheological rates. Rock core samples are processed into standard cylindrical specimens, and triaxial rheological mechanical property tests are performed on these specimens. Two steady-state rheological rate curves are obtained by fitting the axial and volumetric rheological rates during the steady-state rheological stage. The intersection of these two curves is used to quantitatively determine the long-term strength parameters of the rock. While comparing the axial and volumetric steady-state rheological rate curves calculated from the rock rheological mechanical property test results, and using the critical value of rock compression deformation and volume expansion—that is, the intersection of the two steady-state rheological rate curves—to quantitatively determine the long-term strength parameters overcomes the problem of ambiguous inflection points in rock samples with indistinct rheological properties using traditional stress-strain isochronous curve cluster methods and steady-state rheological rate methods, and has reference value for accurately evaluating the long-term stability of rocks, the determination of the early straight segment and the inflection point of the curve is cumbersome, resulting in a long calculation process.

[0005] Prior art three, application number: CN 201510272530.6, discloses a method for determining the long-term strength of rock through multi-level stress graded loading creep mechanical test, including the following steps: on-site sampling and preparation of rock core specimens; installation of the specimens into a rock triaxial rheological mechanical testing instrument, and adjustment of the axial strain and circumferential strain measurement systems to their initial values; conducting multi-level stress graded loading creep mechanical tests on the specimens according to the stress load control mode until the specimens are destroyed, during which the changes in axial compressive strain and circumferential expansion strain over time under different stresses throughout the test are measured; the change in volumetric strain of the specimen over time is calculated; the rock creep curve is plotted, and the decay creep stage and steady-state creep stage of the creep curve under each level of stress load are determined; the steady-state creep rate under each level of stress load is calculated, and the relationship curves of axial, circumferential, and volumetric steady-state creep rates with stress level are plotted, and their intersection points are determined. The stress corresponding to the intersection point is the long-term strength of the rock. Although the solution is based on the actual ductile dilatation deformation of the rock, comprehensively considering the axial, circumferential, and volumetric steady-state rheological rates, and objectively determined based on the intersection of these rates to ensure uniqueness and accuracy, the determination process is cumbersome and the calculation cycle is long, resulting in time-consuming and laborious calculations and significant time costs.

[0006] Current technologies 1, 2, and 3 suffer from the problem that when the rheological properties of the rock are not obvious, it is difficult to determine the early straight segment and the turning point of the curve at the end, resulting in the need for further improvement in the accuracy and precision of the calculation results. Therefore, this invention provides a method and system for long-term strength evaluation of rock core samples based on rheological tests. Summary of the Invention

[0007] The main objective of this invention is to provide a method and system for long-term strength evaluation of rock core samples based on rheological tests, in order to solve the problem in the prior art that when the rheological properties of the rock are not obvious, it is difficult to determine the early straight line segment and the turning point of the curve at the end of the curve, which leads to the need to further improve the accuracy and precision of the calculation results.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A method for long-term strength assessment of rock core samples based on rheological tests, the method comprising:

[0010] A standard cylindrical specimen was prepared, and the standard cylindrical specimen was tested according to the rheological test to obtain the rheological curve. The reciprocal of the steady-state rheological rate was fitted to the logarithm of the stress level to obtain the fitted curve.

[0011] Select the point of maximum curvature of the curve, and perform a linear function fitting on the near-straight part of the curve's end segment. Draw a horizontal line and a tangent line through the point of maximum curvature.

[0012] Draw the angle bisectors of the horizontal line and the tangents, combine the angle bisectors with the near-straight section of the end segment, and perform a linear function to obtain the x-coordinate of the intersection point. Calculate the long-term strength.

[0013] As a further improvement of the present invention, the process of testing a standard cylindrical specimen using rheological testing includes:

[0014] The selected rock core samples were processed into standard cylindrical samples with a size of φ50mm×100mm. The cylindrical samples were intact, undamaged, and without any missing parts.

[0015] The obtained rock core sample was placed on a rheological testing apparatus and a constant confining pressure of 5 MPa was applied. The loading was carried out in stages using a constant confining pressure and axial pressure increasing loading method. The first stress level was 0.5 times the instantaneous peak strength.

[0016] The rheological time for each stress level is 72 hours. Then, the next level of loading is applied. Under the last stress level, accelerated rheological failure occurs after 25.93 hours.

[0017] As a further improvement of the present invention, the process of obtaining the fitted curve includes:

[0018] The rheological test curves are divided into decay rheological, steady-state rheological, and accelerated rheological stages. The steady-state rheological rate is obtained by fitting a linear function to the test data of the steady-state rheological stage using a computer.

[0019] Plot a scatter plot of the reciprocal of the steady-state rheological rate versus the logarithm of the stress level;

[0020] The fitted curve was obtained by fitting a scatter plot of steady-state rheological rate versus logarithm of stress level using the Harris model.

[0021] As a further improvement of the present invention, the process of obtaining the steady-state rheological rate includes:

[0022] During the rheological test, timed automatic sampling was used to record more stress and strain data at regular intervals; outlier detection was performed on the collected data, and the 3σ rule was used to delete obviously deviating measurement values;

[0023] The system automatically identifies and classifies different rheological stages, including decay rheology, steady-state rheology, and accelerated rheology. After classifying the stages, the system dynamically evaluates the rationality of the classification by calculating the root mean square error of the data for each stage.

[0024] The optimal fitting parameters were determined through gray wolf optimization; a linear regression model was selected, and the training effect of the model was tested through cross-validation and hold-out method. The linear function fitting model reproduced the actual situation of steady-state rheological rate; during the linear function fitting process, an iterative scheme was implemented, and the fitting parameters were adjusted according to the preliminary fitting results, and the slope and intercept were re-evaluated until the error within the set tolerance range was reached; the Bootstrap method was used to perform multiple resampling to obtain the distribution of stable steady-state rheological rate.

[0025] As a further improvement of the present invention, the process of automatically identifying and classifying different rheological stages specifically includes the following steps:

[0026] The acquired stress and strain data are organized in chronological order to form a complete dataset; smoothing is performed using the moving average method or wavelet transform to remove noise; the second derivative of the stress-strain curve is calculated to identify regions of large variation; and the slopes of stress and strain are calculated to identify changes in rheological behavior.

[0027] A dynamic threshold is set to identify abrupt changes when stress increases or decreases rapidly; the boundaries between decaying rheology, steady-state rheology, and accelerated rheology are determined by combining changes in curvature and slope; the end point of decaying rheology is marked when stress and strain changes reach the set threshold; the start and end points of steady-state rheology are marked when the slope stabilizes and the change amplitude is less than the threshold; the start point of accelerated rheology is marked when stress or strain increases significantly again and exceeds the threshold.

[0028] Within each rheological stage, the root mean square error of each stage is calculated to evaluate the rationality of the cutting points. If the root mean square error of a certain stage is too high, the cutting points are re-evaluated and the division is optimized. The division results are dynamically adjusted. If the division error of the rheological segment is higher than the set value, the smoothing curve generation algorithm is automatically called to re-smooth the original data.

[0029] As a further improvement of the present invention, the process of obtaining the fitting curve includes:

[0030] In a two-dimensional coordinate system, the reciprocal of the calculated steady-state rheological rate is used as the vertical axis, and the logarithm of the corresponding stress level is used as the horizontal axis to draw a scatter plot; by visualizing the scatter plot, the distribution trend of the scatter points can be observed initially.

[0031] We chose to initialize the Harris model parameters using empirical rules and then used a nonlinear optimization algorithm to minimize the sum of squared errors between the predicted and actual values.

[0032] The system dynamically records the parameter adjustments and corresponding fitting errors at each step. Based on the determined Harris model parameters, it generates the corresponding fitting curves, which are then superimposed onto the scatter plot to form the final fitting plot.

[0033] As a further improvement of the present invention, the process of fitting the tangent line to the horizontal line and the point of maximum curvature includes:

[0034] Based on the curvature formula, the second and first derivatives of the fitted curve are calculated using numerical software to obtain the curvature value corresponding to the stress difference; from the curvature change curve, the numerical data are analyzed to determine the maximum curvature value and its corresponding coordinate point.

[0035] In a two-dimensional coordinate system, draw a line parallel to the vertical axis to represent the rheological rate at the point of maximum curvature; based on the first derivative of the fitted curve, perform local linearization at the point of maximum curvature to calculate the slope of the tangent; based on the slope of the tangent and the known rheological rate value, calculate the equation of the tangent and draw the tangent.

[0036] Calculate the slope of the bisector using the slopes of the tangent and the horizontal line, and apply trigonometric functions to determine the angle change of the true bisector; using the determined slope, draw the upward-sloping bisector.

[0037] As a further improvement of the present invention, the process of calculating the long-term strength includes:

[0038] Before performing least squares fitting, the terminal part of the fitting curve is selected as the target data; the least squares method is used to perform linear fitting on the selected terminal part to obtain a linear relationship equation, which describes the relationship between rheological rate and stress in the high stress range.

[0039] Based on the rheological rate coordinates at the point of maximum curvature, a horizontal line parallel to the vertical axis is drawn to clearly indicate the rheological rate under that specific stress difference. Combining the first derivative of the fitted curve, local linearization is performed at the point of maximum curvature, the slope of the tangent is calculated, and the equation of the tangent is obtained. This tangent is then plotted in the figure to visually display the instantaneous response characteristics of the rheological rate with stress changes.

[0040] By performing an intersection analysis between the tangent and the new fitted straight line, the intersection point is found, and the x-coordinate of the intersection point represents the long-term strength of the material.

[0041] As a further improvement of the present invention, the process of linearly fitting the selected endpoint portion using the least squares method includes:

[0042] For each data point, select a window size, center on the data point, and select N points around it as reference points for local regression; calculate the distance between each neighboring data point and the current data point;

[0043] A Gaussian kernel function is selected to assign weights to each data point within a local region; the weights are normalized during calculation; a weight matrix is ​​created for each target point, with the diagonal elements representing the weights of each reference point; a linear model is constructed to obtain the target of the least squares method; based on the theory of weighted least squares, the standard least squares method is used to solve for the parameters using weighted data.

[0044] The above steps are repeated for each input point. For each stress value for which the rheological rate needs to be estimated, a weighted linear regression based on its neighborhood data is performed. By uniformly performing local regression, a set of local models is generated, and combined with the obtained weights, a global fitting curve is finally formed.

[0045] To achieve the above objectives, the present invention also provides the following technical solution:

[0046] A long-term strength assessment system for rock core samples based on rheological testing is applied to the aforementioned long-term strength assessment method for rock core samples based on rheological testing. The long-term strength assessment system for rock core samples based on rheological testing includes:

[0047] The curve fitting module is used to prepare standard cylindrical specimens, test the standard cylindrical specimens according to the rheological test, obtain the rheological curve, and fit the reciprocal of the steady-state rheological rate with the logarithm of the stress level to obtain the fitted curve;

[0048] The function fitting module is used to filter the point of maximum curvature of the curve, and to perform a linear function fitting on the near-straight part of the curve's end segment, drawing a horizontal line and a tangent line through the point of maximum curvature.

[0049] The strength calculation module is used to draw the angle bisectors of the horizontal line and the tangent line, combine the angle bisectors with the near-straight part of the end segment, perform a linear function to obtain the x-coordinate of the intersection point, and calculate the long-term strength.

[0050] This invention prepares standard cylindrical specimens and conducts rheological tests. By preparing standard cylindrical specimens with a diameter of 50 mm and a height of 100 mm, sample consistency is ensured, providing comparability and repeatability for experimental data. Rheological tests are performed on the standard cylindrical specimens to obtain the relationship between steady-state rheological rate and stress level, and rheological curves are plotted, allowing researchers to clarify the flow behavior of the samples under different stress levels. Significance: This test obtains fundamental rheological characteristic data, which will be used for subsequent analysis. The rheological curves reveal the material's flow characteristics, which are crucial for understanding its long-term behavior. The fitting of the reciprocal of the steady-state rheological rate to the logarithm of the stress level provides a preliminary mathematical model for subsequent analysis, facilitating further numerical processing and analysis. The maximum curvature point of the curve is selected and a linear function is fitted. Through analysis of the fitted curves, the maximum curvature point is selected. This key information reflects the inflection point of the material's rheological behavior, usually corresponding to a significant change in the internal stress state of the sample. Fitting a linear function to the final segment of the rheological curve simplifies complex rheological behavior, thereby extracting important information related to long-term strength. Significance: The point of maximum curvature is usually a key point for evaluating the rheological properties of materials, providing important physical significance for subsequent strength assessment. Fitting a linear function clarifies and makes subsequent geometric calculations more feasible, effectively solving data processing problems under complex models. Plotting angle bisectors and calculating long-term strength: By plotting the angle bisectors of the horizontal line and tangent, and finding the intersection point with the near-straight portion of the linear function at the end, the parameters corresponding to long-term strength are precisely located, providing an analytical method combining geometry and algebra. The logarithm of the long-term strength can be calculated using the x-coordinate of the intersection point, and then converted to obtain the specific long-term strength value. Significance: This provides a new quantitative analysis method for evaluating the long-term strength of rock core samples, overcoming some of the shortcomings of traditional methods. The intuitive geometric method enhances the understanding of material mechanical properties, allowing researchers to more intuitively grasp the strength performance of samples under different conditions, which is of great significance for practical applications in geology and civil engineering. Attached Figure Description

[0051] Figure 1 This is a schematic flowchart of an embodiment of the long-term strength assessment method for rock core samples based on rheological testing according to the present invention.

[0052] Figure 2 This is a schematic diagram of the steps for testing a standard cylindrical sample using a rheological test, according to an embodiment of the long-term strength assessment method for rock core samples based on rheological testing of the present invention.

[0053] Figure 3 This is a schematic diagram of stress level levels in an embodiment of the long-term strength assessment method for rock core samples based on rheological testing according to the present invention.

[0054] Figure 4 This is a schematic diagram illustrating the steps of fitting a horizontal line and a tangent line through the point of maximum curvature in an embodiment of the long-term strength assessment method for rock core samples based on rheological tests according to the present invention.

[0055] Figure 5 This is a schematic diagram of the curvature curve of an embodiment of the long-term strength evaluation method for rock core samples based on rheological testing according to the present invention;

[0056] Figure 6 This is a schematic diagram of the steps for calculating long-term strength in a core sample long-term strength assessment method based on rheological testing according to an embodiment of the present invention.

[0057] Figure 7 This is a schematic diagram of the functional modules of an embodiment of the long-term strength evaluation system for rock core samples based on rheological testing according to the present invention.

[0058] Figure 8 This is a schematic diagram of the structure of an embodiment of the electronic device of the present invention;

[0059] Figure 9 This is a schematic diagram of the structure of one embodiment of the storage medium of the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention 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 the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0061] The terms "first," "second," and "third" used in this invention are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first," "second," or "third" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified. All directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of this invention are only used to explain the relative positional relationships and movements between components in a specific orientation (as shown in the figures). If the specific orientation changes, the directional indications also change accordingly. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0062] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0063] like Figure 1 As shown, this embodiment provides an example of a method for long-term strength assessment of rock core samples based on rheological tests. In this embodiment, the method for long-term strength assessment of rock core samples based on rheological tests specifically includes the following steps:

[0064] Step S1: Prepare a standard cylindrical specimen, test the standard cylindrical specimen according to the rheological test, obtain the rheological curve, fit the reciprocal of the steady-state rheological rate with the logarithm of the stress level, and obtain the fitted curve;

[0065] Step S2: Filter the point of maximum curvature of the curve, and perform a linear function fitting on the near-straight part of the end segment of the curve, drawing a horizontal line and a tangent line through the point of maximum curvature;

[0066] Step S3: Draw the angle bisector of the horizontal line and the tangent line. Combine the angle bisector with the near-straight part of the end segment and perform a linear function to obtain the x-coordinate of the intersection point. Calculate the long-term strength.

[0067] Preferably, in step S1 of this embodiment, a standard cylindrical specimen is prepared and a rheological test is performed. Preparing standard cylindrical specimens with a diameter of 50 mm and a height of 100 mm ensures sample consistency and provides comparability and repeatability for experimental data. The rheological test is performed on the standard cylindrical specimens to obtain the relationship between the steady-state rheological rate and the stress level, and a rheological curve is plotted, allowing researchers to clarify the flow behavior of the sample under different stress levels. Significance: This test obtains basic rheological characteristic data, which will be used for subsequent analysis. The rheological curve reveals the material's flow characteristics and is crucial for understanding its long-term behavior. The fitting of the reciprocal of the steady-state rheological rate to the logarithm of the stress level provides a preliminary mathematical model for subsequent analysis, facilitating further numerical processing and analysis. Step S2 involves screening the point of maximum curvature of the curve and performing a linear function fitting. By analyzing the fitted curve, the point of maximum curvature is screened. This key information reflects the inflection point of the material's rheological behavior, usually corresponding to a significant change in the internal stress state of the sample. Performing a linear function fitting on the final segment of the rheological curve simplifies complex rheological behavior, thereby extracting important information related to long-term strength. Significance: The point of maximum curvature is usually a key point for evaluating the rheological properties of materials, providing important physical significance for subsequent strength assessment. Fitting a linear function clarifies and makes subsequent geometric calculations more feasible, effectively solving data processing problems under complex models. Step S3 involves drawing the angle bisector and calculating the long-term strength. By drawing the angle bisector of the horizontal line and tangent, and finding the intersection point with the near-straight section of the linear function at the end, the parameters corresponding to the long-term strength are precisely located, providing an analytical method combining geometry and algebra. The logarithm of the long-term strength can be calculated using the x-coordinate of the intersection point, and then converted to obtain the specific long-term strength value. Significance: This provides a new quantitative analysis method for evaluating the long-term strength of rock core samples, overcoming some of the shortcomings of traditional methods. The intuitive geometric method enhances the understanding of material mechanical properties, allowing researchers to more intuitively grasp the strength performance of samples under different conditions, which is of great significance for practical applications in geology and civil engineering.

[0068] In this embodiment, the selected rock core sample is processed into a standard cylindrical sample with a size of φ50mm×100mm. Rheological tests are performed on the obtained sample, and the steady-state rheological rate under various stress levels is calculated. A scatter plot of the reciprocal of the steady-state rheological rate and the logarithm of the stress level is plotted. The scatter plot is fitted, and the curvature K of the fitted curve is solved by computer. The point of maximum curvature is selected, and a horizontal line and a tangent line to the fitted curve are drawn through this point. The bisector of the angle formed by the two line segments is drawn. The end line of the curve is fitted with a linear function. The bisector and the linear function form an intersection point. The x-coordinate of this intersection point is the logarithm of the long-term strength. After conversion, the long-term strength value can be obtained.

[0069] This embodiment, based on rock rheological tests, uses a computer to determine the inflection point of the fitted curve of the reciprocal of the steady-state rheological rate and the logarithm of the stress level. A horizontal line is drawn through this point, and the tangent to the fitted curve is also drawn. The bisector of the angle formed by these two line segments is then constructed. A linear function is used to fit the final line portion of the curve. The bisector intersects the linear function at a point, and the x-coordinate of this intersection point is the logarithm of the long-term strength. After conversion, the long-term strength value is finally obtained. This method overcomes the problem of difficulty in determining the early straight segment and the inflection point of the curve when the rheological properties of the rock (mass) are not obvious. It has reference value for accurately evaluating the long-term stability of rocks. The long-term strength evaluation calculation process in this embodiment is completed by computer, which greatly reduces errors and can accurately obtain the corresponding coordinate values. It overcomes the shortcomings of traditional methods, such as large errors and ambiguous inflection points, and provides a reliable basis for long-term stability problems in geotechnical engineering.

[0070] This embodiment can be used for the design of underground caverns, which need to consider the long-term stability of the soil or rock mass after excavation. Evaluating the long-term strength of rock core samples based on rheological tests helps to provide quantitative strength parameters, thereby analyzing and predicting the deformation and stability of the cavern under long-term loads. By optimizing the evaluation of long-term strength, the potential risk of collapse during construction and operation can be effectively reduced, ensuring the safety and service life of the cavern.

[0071] Slope stability analysis reveals that slopes are at significant risk of sliding under long-term environmental changes and mechanical loads. Accurate long-term strength assessments allow for the calculation of slope safety factors to determine their stability under various conditions. When slope instability is identified, this analysis provides a scientific basis for designing reinforcement and modification schemes, such as anchoring, drainage, and gravity protection measures.

[0072] Dam foundation stability assessment requires long-term strength evaluation of the water and earth pressures exerted on the dam foundation to ensure its safety and stability under any operating conditions. Rheological testing provides a method for effectively assessing the shear strength of the dam foundation; by evaluating the long-term strength of the dam foundation and dam body materials, the design of seepage prevention measures can be optimized, thereby reducing the impact of seepage on dam foundation stability.

[0073] In civil engineering, the selection of materials based on long-term strength assessment results can help engineers choose appropriate construction materials according to the specific requirements of the project. Properties such as compactness, flowability, and cohesion are particularly important. Based on the assessed long-term strength, the impact of different construction methods (such as vibration compaction, repeated loading, etc.) on material strength can be analyzed to optimize construction technology and improve the overall quality of the project.

[0074] Monitoring and maintenance are crucial because the strength of building materials changes with age over long-term use. Long-term strength assessment methods can be used to monitor these changes, enabling timely repair or reinforcement measures. For example, natural events such as earthquakes and rainfall can affect the stability of engineering structures; monitoring the extent of this impact using long-term strength assessment methods provides a basis for subsequent risk assessments and post-disaster recovery.

[0075] Geological hazard early warning, through long-term strength monitoring of soil and rock masses combined with rheological properties, can identify potential risks of geological hazards such as landslides and collapses in advance, helping to establish an effective early warning mechanism and ensuring the safety of surrounding residents. The long-term strength assessment method for rock core samples based on rheological tests has demonstrated significant practical value in multiple engineering fields. By improving the accuracy of strength assessment of soil and rock materials, it provides a scientific basis for engineering design, construction, maintenance, and disaster early warning, thereby effectively ensuring the safety and stability of buildings and infrastructure.

[0076] In summary, this embodiment achieves effective long-term strength assessment through quantitative analysis of the rheological properties of rock core samples. Each step not only accumulates experimental data but also provides relevant technical means and mathematical tools, ensuring the accuracy and reliability of the results. This not only provides new ideas for materials science research but also has significant implications for practical engineering applications, effectively guiding the selection and application of geotechnical engineering materials.

[0077] Furthermore, such as Figure 2 As shown, the process of testing the standard cylindrical specimen using rheological methods in step S1 specifically includes the following steps:

[0078] Step S11: The selected rock core sample is processed into a standard cylindrical sample with a size of φ50mm×100mm. The cylindrical sample is intact, undamaged, and without any missing parts.

[0079] Step S12: Place the obtained core sample on a rheological testing apparatus and apply a constant confining pressure of 5 MPa. Use a constant confining pressure graded axial pressure loading method to perform graded loading. The first stress level is 0.5 times the instantaneous peak strength.

[0080] Among them, the specific stress level is as follows: Figure 3 As shown in the figure, ε1 represents the axial strain of the rock, ε3 represents the circumferential strain of the rock, and ε v Let t be the volumetric strain of the rock and t be the rheological time of the rock, in order to ensure a relatively stable steady-state rheological stage;

[0081] Step S13: The rheological time for each stress level is 72 hours. Then, the next level of loading is applied. Under the action of the last stress level, accelerated rheological failure occurs after 25.93 hours.

[0082] Preferably, in step S11 of this embodiment, a standard cylindrical specimen is prepared, processed into a cylindrical specimen with a diameter of 50 mm and a height of 100 mm, so that the specimen size is uniform, thereby ensuring the consistency and comparability of the test results; ensuring that the specimen is not damaged or missing during processing, so as to facilitate accurate measurement of the material's rheological properties. Significance: Standardized specimens can better eliminate errors caused by sample differences during testing, thereby improving the reliability of the experiment; intact specimens can truly reflect the inherent properties of rocks, ensuring the accuracy of subsequent stress application and deformation observation. Step S12 applies a constant confining pressure and loads the material. Applying a constant confining pressure of 5 MPa on the rheological testing instrument can better simulate the compression environment of rocks under geological conditions; the use of a constant confining pressure graded axial pressure loading method realizes the gradual examination of steady-state rheology. Significance: The application of confining pressure can more accurately simulate the stress state of rock strata, providing data support for evaluating the material's performance in real geological environments; through the graded loading method, the material's response at various stress levels can be observed, providing a systematic observation for obtaining rheological properties, and helping to reveal the evolution stages of the material's long-term mechanical behavior. Step S13 records the rheological time and rheological failure at each stress level. Each stress level is applied continuously for 72 hours to ensure the sample reaches the steady-state rheological stage, providing favorable conditions for accurate measurement. Accelerated rheological failure occurs after 25.93 hours under the final stress level, clearly recording the material's failure characteristics and rheological behavior. Significance: Long-term stress application allows observation of material performance changes under long-term stress, which is important for both scientific research and engineering applications. Observing accelerated rheological failure provides a deeper understanding of the material's deformation mechanism and failure mode, offering a scientific basis for subsequent design and reinforcement measures.

[0083] In summary, this embodiment, through the detailed steps described above, demonstrates that rheological testing not only provides information on the mechanical behavior of rocks under high pressure and long-term loads, but also offers crucial theoretical and data support for engineering practice. Each step, through precise operation and long-term observation, ensures reliable experimental data, laying the foundation for geotechnical engineering design and material safety assessment. It has significant reference value for practical engineering applications and materials research.

[0084] Furthermore, the process of obtaining the fitted curve in step S1 specifically includes the following steps:

[0085] Step S14: Divide the rheological test curve into decay rheological, steady-state rheological and accelerated rheological stages, and use a computer to perform a linear function fitting on the test data of the steady-state rheological stage to obtain the steady-state rheological rate;

[0086] Step S15: Plot a scatter plot of the reciprocal of the steady-state rheological rate versus the logarithm of the stress level;

[0087] Step S16: Fit the scatter plot of steady-state rheological rate versus logarithm of stress level using the Harris model to obtain the fitted curve.

[0088] Preferably, step S14 of this embodiment, the segmentation of the rheological test curve stages and the fitting of a linear function, which divides the rheological, steady-state, and accelerated rheological stages, can clearly identify the behavioral characteristics of rocks under different loading conditions, providing a foundation for subsequent data processing. By fitting the experimental data of the steady-state rheological stage to a linear function using a computer, the steady-state rheological rate can be accurately determined, reflecting the flow characteristics of the material under constant stress. Significance: Effective segmentation of the rheological stages ensures the accuracy of subsequent fitting data and avoids confusion of results due to different rheological behaviors; the steady-state rheological rate is an important parameter for evaluating the long-term performance of rock materials, laying the foundation for constructing mathematical models and analyzing material behavior. Step S15, plotting a scatter plot and fitting the data, plots the reciprocal of the steady-state rheological rate against the logarithm of the stress level, clearly showing the relationship between the two, making the data distribution and trend readily apparent; fitting the scatter plot using the Harris model obtains the correlation between the two, and the model's description of rheological characteristics is relatively universal. Significance: Scatter plots and their fitted curves help researchers visually observe and analyze rheological behavior, making the relationship between rheological properties and external stress levels clearer. This is an important foundation for subsequent research and applications. Using the Harris model for fitting improves the model's applicability and predictive ability, providing more credible theoretical support for practical applications. Step S16, Harris model fitting, involves again using the Harris model to fit the data, systematically determining the mathematical relationship between rheological rate and stress, forming a fitted curve that can be used for analysis. The obtained fitted curve provides a quantitative description of the relationship between steady-state rheological rate and stress level, helping to understand the behavior of materials under dynamic loading conditions. Significance: The fitted curve transforms rheological properties into a mathematical model, allowing engineers to use these results in practical engineering design and risk assessment. It can be referenced by other materials research and engineering applications, promoting in-depth research and theoretical development in related disciplines.

[0089] In summary, this embodiment, through these steps, provides important insights into the rheological behavior of rock materials by demonstrating the process of fitting curves in rheological experiments. Each step not only improves the accuracy of experimental data processing but also provides theoretical basis and data support for practical applications in materials science, civil engineering, and other fields. This method not only enhances the understanding of the long-term properties of rock materials but also provides a solid foundation for future research.

[0090] In this embodiment, the rheological test curve is divided into three stages: decaying rheology, steady-state rheology, and accelerated rheology. A computer is used to fit a linear function to the test data of the steady-state rheological stage to obtain a relatively accurate steady-state rheological rate. A scatter plot of the reciprocal of the steady-state rheological rate versus the logarithm of the stress level is plotted. The well-known Harris model is used to fit the scatter plot to obtain the fitted curve i. The Harris model is as follows:

[0091]

[0092] In the formula, y represents the reciprocal of the steady-state rheological rate; A represents a constant in the Harris model, indicating the baseline or intercept affecting the rheological rate, the specific value of which may be affected by factors such as material properties and the initial state of flow; B represents another constant in the Harris model, indicating the sensitivity of the rheological rate to changes in stress level, its value reflecting the flow characteristics of the material, such as its response to external stress; x represents the logarithm of the stress level, usually the shear stress applied in the experiment; C represents a constant in the Harris model, indicating the nonlinearity of the effect of stress on the steady-state rheological rate, reflecting the sensitivity of the material's flow behavior to stress changes; the fitted curve i is obtained by fitting a scatter plot of steady-state rheological rate versus logarithm of stress level using the Harris model.

[0093] Furthermore, the process of obtaining the steady-state rheological rate in step S14 specifically includes the following steps:

[0094] Step S141: During the rheological test, timed automatic sampling is used to record more stress and strain data at regular intervals (e.g., within 1 hour); outlier detection is performed on the collected data, and the 3σ rule is used to delete obviously deviating measurement values;

[0095] Step S142: Automatically identify and classify different rheological stages, including decay rheology, steady-state rheology, and accelerated rheology stages; after classifying the stages, dynamically evaluate the rationality of the classification by calculating the root mean square error of the data for each stage.

[0096] Step S143: Determine the optimal fitting parameters through gray wolf optimization; select a linear regression model, and test the training effect of the model through cross-validation and hold-out method. The linear function fitting model reproduces the actual situation of steady-state rheological rate; during the linear function fitting process, implement an iterative scheme, adjust the fitting parameters according to the preliminary fitting results, and re-evaluate the slope and intercept until the error reaches the set tolerance range; use the Bootstrap method to perform multiple resampling to obtain the distribution of stable steady-state rheological rate.

[0097] Preferably, in step S141 of this embodiment, data acquisition and outlier detection, through timed automatic sampling, can obtain dense stress and strain data, making the experimental data more comprehensive and continuous; using the 3σ rule for outlier detection can effectively identify and eliminate erroneous data caused by equipment or operation during the measurement process, ensuring the reliability and accuracy of the data. Significance: Improved data quality lays a good foundation for subsequent analysis, avoiding inaccurate fitting and misjudgment caused by erroneous data; ensures the scientific validity and credibility of experimental results, contributing to the accuracy and efficiency of subsequent processes. Step S142, rheological stage division and evaluation, automatically identifies and divides different rheological stages, reducing manual intervention and improving processing efficiency; through dynamic evaluation of the root mean square error (RMSE), the rationality of the division can be quantitatively verified, ensuring the accuracy of the division. Significance: Ensures more detailed analysis of the rheological process, enabling more accurate research on different stages and grasping key rheological characteristics; through reasonable rheological stage division, more accurate samples can be provided for subsequent fitting and optimization, improving the overall efficiency and accuracy of the analysis. Step S143 determines the optimal fitting parameters and model training. The optimal fitting parameters are determined using the Grey Wolf optimization algorithm, improving the accuracy and efficiency of the fitted model. A linear regression model combined with cross-validation and hold-out methods is used for training and evaluation, effectively avoiding overfitting and improving the model's generalization ability. An iterative approach is implemented to gradually adjust the fitting parameters, ensuring the fitting results are as close as possible to the real data. Significance: By accurately determining the fitting parameters, the established model can better reproduce the actual steady-state rheological rate, providing reliable data support for subsequent applications; it deepens the understanding of rheological properties, promotes research and development in the field of rheology, and provides a scientific basis for industrial applications.

[0098] In summary, this embodiment, through the implementation of the above steps, can systematically acquire high-quality rheological data and accurately identify and optimize rheological properties through effective calculation and analysis techniques. This not only improves the research efficiency of rheological processes but also enhances the credibility of research results, providing crucial support for in-depth analysis and optimization in fields such as materials science and chemical engineering. Ultimately, it achieves dynamic monitoring and optimization in static rheological processes, providing an advanced and feasible solution for practical industry applications.

[0099] Furthermore, the process of automatically identifying and classifying different rheological stages in step S142 specifically includes the following steps:

[0100] Step S1421: Organize the acquired stress and strain data in chronological order to form a complete dataset; perform smoothing processing using the moving average method or wavelet transform to remove noise; calculate the second derivative of the stress-strain curve to identify regions of large change (the parts of the stress-strain curve with significant characteristic changes. These characteristic changes may be graphically represented by sharp slope changes, local maxima or minima, inflection points of different rheological behaviors, etc.; specifically, when the applied stress or strain increases or decreases significantly in a short period of time, such rapidly changing regions are key rheological behavior transition points. For example, the material changes from a plastic rheological state to a brittle rheological state); calculate the slope of stress and strain (i.e., the rheological rate) to identify changes in rheological behavior;

[0101] Step S1422: Set a dynamic threshold to identify abrupt changes when stress increases or decreases rapidly; determine the boundaries between decaying rheology, steady-state rheology, and accelerated rheology by combining changes in curvature and slope; mark the end point of decaying rheology when stress and strain changes reach the set threshold; mark the start and end points of steady-state rheology when the slope is stable and the change amplitude is less than the threshold; mark the start point of accelerated rheology when stress or strain increases significantly again and exceeds the threshold.

[0102] Step S1423: Within each rheological stage, calculate the root mean square error of each stage and evaluate the rationality of the cutting points; if the root mean square error of a certain stage is too high, re-evaluate the cutting points and optimize the division; dynamically adjust the division results; if the division error of the rheological segment is higher than the set value, automatically call the smoothing curve generation algorithm to re-smooth the original data.

[0103] Preferably, in step S1421 of this embodiment, data organization and preprocessing involves organizing the acquired stress and strain data in chronological order to form a continuous and complete dataset, ensuring that subsequent analysis is orderly and logical. Smoothing methods such as moving averages or wavelet transforms are used to effectively reduce noise in the data and improve data quality. The second derivative of the stress-strain curve and the slope of the rheological rate are calculated to automatically identify specific points and regions of rheological behavior changes, ensuring that key features are accurately captured. Significance: Through refined data processing, the data quality and integrity of subsequent steps are guaranteed, avoiding analytical errors caused by data problems. Extracting feature information helps to gain a deeper understanding of changes in the material's rheological behavior, providing necessary basis for subsequent stage division. Step S1422: Dynamic Threshold Setting and Rheological Stage Division. Setting dynamic thresholds allows for adaptation to stress and strain changes under different rheological states, flexibly identifying abrupt changes. By combining curvature and slope analysis, the boundaries between decaying rheology, steady-state rheology, and accelerated rheology are accurately marked, clearly defining the start and end points of each stage. When stress or strain reaches the set threshold, the transition point of the rheological stage is automatically marked, improving the automation level of the analysis. Significance: Dynamic threshold setting makes the stage division process more flexible and adaptable, capable of handling rheological characteristics under various material and environmental conditions. Clear rheological stage division facilitates subsequent analysis and model building, resulting in higher efficiency in resource and time utilization and supporting comprehensive process optimization. Step S1423: Root Mean Square Error Calculation and Dynamic Adjustment. The root mean square error (RMSE) is calculated within each rheological stage to quantify the rationality of the cutting points and ensure the scientific nature of the division. Based on RMSE feedback, if the error of a certain stage is too high, a smoothing curve generation algorithm is automatically invoked to re-smooth the data, thereby optimizing the stage division. Significance: Quantitative error assessment can effectively determine the rationality of the division and ensure the reliability of the analysis results; the dynamic adjustment mechanism enables the entire rheological analysis process to be intelligent and adaptive, promoting the scientific and efficient development of the method and facilitating comprehensive material performance analysis.

[0104] In summary, this embodiment, through the implementation of the above steps, not only effectively improves the accuracy and efficiency of data processing and rheological stage identification, but also enhances the system's flexibility and adaptability. The implementation of this methodology provides reliable technical support for materials science, engineering practice, and rheological property analysis, promoting cutting-edge research in related fields. The ultimate goal is to optimize material properties and improve the effectiveness and economy of industrial applications.

[0105] Furthermore, the process of obtaining the fitted curve in step S16 specifically includes the following steps:

[0106] Step S161: In a two-dimensional coordinate system, plot a scatter plot by using the reciprocal of the calculated steady-state rheological rate as the vertical axis and the logarithm of the corresponding stress level as the horizontal axis; through visualization of the scatter plot, observe the distribution trend of the scatter points.

[0107] Step S162: Initialize the Harris model parameters using empirical rules, and minimize the sum of squared errors between the predicted and actual values ​​using a nonlinear optimization algorithm;

[0108] Step S163: Dynamically record the parameter adjustments and corresponding fitting errors at each step. Based on the determined Harris model parameters, generate the corresponding fitting curves and overlay them onto the scatter plot to form the final fitting plot.

[0109] Preferably, in step S161 of this embodiment, the scatter plot is drawn and initially observed. By drawing a scatter plot of the reciprocal of the steady-state rheological rate and the logarithm of the stress level in a two-dimensional coordinate system, the data is presented in a visual form, facilitating intuitive analysis. The distribution trend of the scatter points is initially observed, identifying concentrated areas, outliers, and possible linear or nonlinear relationships, laying the foundation for subsequent model fitting. Significance: Through visualization analysis, researchers can initially determine the appropriate model type (linear or nonlinear) and the initial settings of model parameters based on the distribution trend of the scatter points. Visualization provides a visual basis for team discussions and promotes understanding of data characteristics, which is of great significance in scientific exploration and engineering decision-making. Step S162, Harris model parameter initialization and optimization, selects appropriate initial parameters through rules of thumb to ensure a reasonable starting point for the fitting process, thereby guaranteeing the efficiency and convergence of the optimization process. A nonlinear optimization algorithm is used to automatically adjust the model parameters by minimizing the sum of squared errors between the predicted and actual values, achieving accurate data fitting. Significance: Reasonable initial parameters can significantly improve the convergence speed of the algorithm, avoid ineffective iterations, and provide better utilization efficiency in terms of time and resources. The optimization process ensures the reliability and accuracy of the fitting results, forming an effective model of the experimental data and strengthening the foundation for scientific analysis. Step S163, parameter adjustment recording and fitting curve generation, dynamically records the parameter adjustments and fitting errors at each step during the iteration process, forming a feedback mechanism and providing detailed process data for subsequent analysis. Based on the determined Harris model parameters, the fitting curve is generated and superimposed on a scatter plot to form the final fitting plot, achieving integrated display of data and model. Significance: The dynamically recorded process not only provides transparency in model optimization but also provides detailed information for subsequent research and result analysis, helping to verify the credibility of the results. Superimposing the fitting curve on the scatter plot allows the model's fitting effect to be presented visually, facilitating an intuitive understanding of model performance and providing a strong visual reference for subsequent research on material rheological properties.

[0110] In summary, this embodiment, through the implementation of these three steps, not only effectively improves the accuracy and scientific rigor of the fitted curves but also ensures the visualization and transparency of model building and data analysis. This methodology helps researchers gain a deeper understanding of rheological properties and provides a reliable theoretical foundation and experimental guidance for the practical application of different materials. Furthermore, the establishment of a systematic process will facilitate the development and optimization of similar research in the future.

[0111] Furthermore, such as Figure 4 As shown, the process of fitting the horizontal line and the tangent line through the point of maximum curvature in step S2 specifically includes the following steps:

[0112] Step S21: Based on the curvature formula, use numerical software to calculate the second and first derivatives of the fitted curve to obtain the curvature value corresponding to the stress difference; analyze the numerical data from the curvature change curve to determine the maximum curvature value and its corresponding coordinate point.

[0113] Step S22: In a two-dimensional coordinate system, draw a line parallel to the vertical axis to represent the rheological rate at the maximum curvature; based on the first derivative of the fitted curve, perform local linearization at the maximum curvature point, calculate the slope of the tangent line, and calculate the tangent line equation based on the slope of the tangent line and the known rheological rate value, and draw the tangent line.

[0114] Step S23: Calculate the slope of the bisector using the slope of the tangent and the slope of the horizontal line, and use trigonometric functions to determine the angle change of the true bisector; use the determined slope to draw the upward-sloping bisector.

[0115] Preferably, in step S21 of this embodiment, the curvature value calculation and maximum curvature location utilize the curvature formula and numerical software to accurately calculate the first and second derivatives of the fitted curve, thereby obtaining the curvature value. This step ensures a scientific and quantitative analysis of the changes in rheological properties; from the calculated curvature change curve, the numerical data is analyzed and the maximum curvature value and its corresponding coordinate point are determined, providing key information for further analysis. Significance: Through precise numerical calculation and analysis methods, important points of change in rheological properties can be effectively identified, providing a clear starting basis for subsequent research; the location of the maximum curvature point helps to identify how the material rheological behavior changes significantly when the stress difference changes, which provides a basis for designing corresponding material property research strategies. Step S22: Drawing the horizontal line and tangent line. A horizontal line parallel to the vertical axis is drawn in the two-dimensional coordinate system, specifically representing the rheological rate corresponding to the maximum curvature point. This line serves as a reference benchmark, helping to better understand the rheological properties under this specific stress level; based on the first derivative of the fitted curve, local linearization is performed at the maximum curvature point to determine the slope of the tangent line and calculate the tangent line equation, thereby drawing the tangent line. Significance: The drawing of horizontal lines and tangents forms an important geometric reference, clearly showing the changes in rheological rate at the point of maximum curvature, providing visual support for in-depth analysis. The slope of the tangent intuitively reflects the sensitivity of the rheological rate to stress changes around a specific point, providing important insights for predicting material behavior. Step S23 calculates and draws the bisector. The slope of the bisector is calculated using the slopes of the tangent and horizontal lines. Trigonometric functions are used to determine the true angle change of the bisector. This calculation process ensures that the bisector accurately reflects the angular relationship between the tangent and horizontal lines. Based on the determined slope, an upward-sloping bisector BD is drawn starting from the point of maximum curvature. Significance: The drawing of the bisector not only supplements the relationship between the tangent and horizontal lines but also shows a more complex balance between rheological rate and stress at the point of maximum curvature, contributing to a comprehensive understanding of rheological behavior. As an isogonal line of the tangent and horizontal lines, the bisector provides an intermediate reference, helping researchers consider more factors when analyzing the rheological properties of materials, promoting a multi-level understanding and analysis of rheological properties.

[0116] In summary, this embodiment, through the implementation of these three steps, significantly improves the accuracy and depth of rheological property analysis. It enables researchers not only to pinpoint key changes in material behavior but also to clearly visualize the material's response and properties under stress conditions. This systematic analytical method enhances research quality and is of great significance in materials science and engineering applications.

[0117] This embodiment uses numerical software to calculate and plot the curvature change curve of the fitted curve based on the curvature calculation formula, such as... Figure 5The curvature curve (K) is used to filter out the maximum curvature value;

[0118]

[0119] In the formula

[0120]

[0121] The coordinates of the maximum curvature point are (43.80, 69.86), as follows: Figure 5 At point B, draw the horizontal line BC and the tangent line BE to the fitted curve (i) through point B:

[0122]

[0123] Draw the horizontal line BC and the bisector BD of the fitted curve (i):

[0124]

[0125] Furthermore, such as Figure 6 As shown, the process of calculating the long-term strength in step S3 specifically includes the following steps:

[0126] Step S31: Before performing least squares fitting, select the terminal line portion of the fitting curve as the target data; use the least squares method to perform linear fitting on the selected terminal line portion to obtain a linear relationship equation, which describes the relationship between rheological rate and stress in the high stress range.

[0127] Step S32: Based on the rheological rate coordinates of the maximum curvature point, draw a horizontal line parallel to the vertical axis to clearly indicate the rheological rate under the specific stress difference; combine the first derivative of the fitted curve to perform local linearization at the maximum curvature point, calculate the slope of the tangent and obtain the tangent equation, and draw this tangent in the figure to intuitively show the instantaneous response characteristics of the rheological rate with stress changes.

[0128] Step S33: By performing an intersection analysis between the tangent and the new fitted straight line, the intersection point is found. The x-coordinate of the intersection point represents the long-term strength of the material.

[0129] Preferably, in step S31 of this embodiment, the end-line portion is selected and least-squares fitting is performed. The end-line portion of the fitted curve is selected as the target data. By focusing on the linear characteristics within the high-stress range, the accuracy of the analysis is ensured. By selecting data within a specific range, its importance in the study is emphasized. The least-squares method is applied to linearly fit the selected data to obtain an accurate linear relationship equation describing the relationship between the rheological rate and the stress difference. Significance: Through linear fitting, the rheological characteristics within the high-stress range are expressed as a concise mathematical relationship, providing a definite foundation for further analysis and research. Through clearly marked linear equations, researchers can identify important trends and characteristics of material behavior under high-stress conditions, helping to guide future experimental design and theoretical research. Step S32: A horizontal line and tangent are drawn. Based on the rheological rate coordinates of the maximum curvature point, a horizontal line parallel to the vertical axis is created to indicate the rheological rate under this specific stress condition, forming a visual reference benchmark. Combining the first derivative of the fitted curve, local linearization is performed at the maximum curvature point, the slope of the tangent is calculated, and the tangent equation is obtained, thereby drawing the tangent in the figure. Significance: The visualization of horizontal lines and tangents provides researchers with an intuitive benchmark for comparison, helping to understand the variation and characteristics of rheological rates under different stress conditions. The slope of the tangent reflects the sensitivity of the rheological rate to stress changes at the point of maximum curvature, allowing researchers to analyze the nonlinear behavior of the material near that point and its impact. Step S33: Intersection analysis of the tangent and the fitted straight line. By analyzing the intersection of the tangent and the newly fitted straight line (FG), the intersection point 'a' is found, and the coordinates of this intersection point are calculated, especially the abscissa (long-term strength). Significance: The abscissa of the intersection point represents the long-term strength of the material, which is a direct experimental measurement that can be used to evaluate the material's durability and performance in practical applications. Through the intersection of the tangent and the fitted straight line, researchers can correlate rheological behavior with long-term strength, making the analysis results more comprehensive and enhancing the understanding of the material's overall properties.

[0130] In this embodiment, the least squares method is used to perform a linear function fitting on the terminal line portion of the fitted curve (i) to obtain the straight line FG:

[0131]

[0132] Line BD and line FG intersect at point a, and the x-coordinate of a is the long-term strength.

[0133] (σ1-σ3) s =49.34

[0134] In summary, this embodiment, through the implementation of these three steps, enables a clear analysis and calculation of the long-term strength of materials, enhancing our understanding of their rheological behavior. This process provides crucial data support for subsequent research, contributing to the optimization of material design and applications, and improving their reliability and effectiveness in engineering and practical applications.

[0135] Furthermore, the process of linearly fitting the selected endpoint portion using the least squares method in step S31 specifically includes the following steps:

[0136] Step S311: For each data point, select a window size, center on the data point, and select N points around it as reference points for local regression; calculate the distance between each neighboring data point and the current data point;

[0137] Step S312: Select a Gaussian kernel function to assign weights to each data point within a local region; normalize the weights when calculating them; create a weight matrix for each target point, with the diagonal elements representing the weights of each reference point; construct a linear model to obtain the target of the least squares method; based on the theory of weighted least squares, use the standard least squares method to solve for the parameters using weighted data.

[0138] Step S313: Repeat the above steps for each input point in sequence, and perform a weighted linear regression based on its neighborhood data for each stress value for which the rheological rate needs to be estimated; by uniformly performing local regression, a set of local models is generated, and combined with the obtained weights, a global fitting curve is finally formed.

[0139] Preferably, in step S311 of this embodiment, data point selection and distance calculation involves selecting a window size for each data point and choosing N neighboring points to construct a local dataset. This ensures that the regression analysis is based on relevant data, enhancing the specificity and accuracy of the fit. Calculating the distance between each neighboring data point and the current data point allows for the assessment of the relative positions between data points, providing a basis for subsequent weight allocation. The significance is that by selecting nearby reference points, the relevance of the data used to the physical phenomena is ensured, thereby improving the practical significance of the fit. Constructing a local dataset based on distance makes the fit more closely reflect actual rheological characteristics, reducing bias caused by data point sparsity and improving model accuracy. Step S312, Weight Allocation and Weighted Least Squares, uses a Gaussian kernel function to assign weights to each neighboring point, ensuring that points closer to the target point have higher weights and vice versa. This non-uniform weighting allows the model to focus more on the data most important for predicting the current point. After calculating the weights, normalization is performed to ensure that the total weight is 1, avoiding excessive influence of any single data point on the fitting result and maintaining the stability of the model. Combined with the principle of weighted least squares, a weight-based linear model is formed, thereby generating more accurate and reliable parameter estimates. Significance achieved: Through the local weighting mechanism, the model can better reflect the complex but realistic response characteristics of rheological rate to stress changes, making the results more scientifically reasonable; by effectively utilizing surrounding relevant data, the accuracy of the model's prediction of unknown data points (such as rheological rate under Thomas stress) is improved, thus enabling effective evaluation of actual material properties. Step S313, Repeated Local Regression and Global Curve Generation, applies the local regression process sequentially to each target point, generating a series of local models. This iterative process ensures that optimal parameters are obtained at each point; by combining each local model and its corresponding weight, a global fitting curve is formed for the entire data range, thus describing the overall data. The significance is that by creating a global model through the accumulation of local regression models, the advantages of each local model are fully utilized, thereby enhancing the accuracy and rationality of the overall fit; the final global fitting curve can intuitively reflect the rheological properties of materials under different stress conditions, providing a solid data foundation for subsequent material performance analysis, design, and optimization.

[0140] In summary, this embodiment achieves greater flexibility and accuracy in the linear fitting process through these three steps. The fitting mechanism, from local to global, ensures that the fitting results not only effectively reflect the material's true response but also provide a deeper understanding and analytical foundation for the material's practical applications. The successful implementation of this process provides more precise tools and methodologies for research in materials science and engineering, promoting the advancement and application of related technologies.

[0141] like Figure 7As shown, this embodiment also provides an embodiment of a long-term strength evaluation system for core samples based on rheological tests. In this embodiment, the long-term strength evaluation system for core samples based on rheological tests is applied to the long-term strength evaluation method for core samples based on rheological tests as described in the above embodiment. The long-term strength evaluation system for core samples based on rheological tests includes a curve fitting module 1, a function fitting module 2, and a strength calculation module 3 that are electrically connected in sequence.

[0142] The curve fitting module 1 is used to prepare standard cylindrical specimens, test the standard cylindrical specimens according to the rheological test, obtain the rheological curve, and fit the reciprocal of the steady-state rheological rate with the logarithm of the stress level to obtain the fitted curve; the function fitting module 2 is used to screen the point of maximum curvature of the curve, and perform a linear function fitting on the near-straight part of the end segment of the curve to draw the tangent of the horizontal line and the curve through the point of maximum curvature; the strength calculation module 3 is used to draw the angle bisector of the tangent of the horizontal line and the curve, perform a linear function fitting on the near-straight part of the end segment to obtain the x-coordinate of the intersection point, and calculate the long-term strength.

[0143] Preferably, in this embodiment, the curve fitting module 1 ensures that the preparation of the standard cylindrical specimen and the implementation of the rheological test, from sample selection to control of the loading environment, are conducted under standardized conditions, ensuring the repeatability and consistency of the experiment. After the rheological test, the module can acquire rheological curve data and use this data, especially the relationship between steady-state rheological rate and stress level, to generate specific rheological characteristic images. By fitting the reciprocal of the rheological rate to the logarithm of the stress level, a fitted curve is generated, which lays the mathematical foundation for subsequent data analysis. The significance is that the preparation of the standard cylindrical specimen and the implementation of the corresponding rheological test ensure that the obtained rheological data has good standardization and comparability, facilitating subsequent research and application. Through the generation of rheological curves, researchers can better understand the fluidity and deformation characteristics of materials under different stress conditions, providing a scientific basis for subsequent strength assessment. After the function fitting module 2 completes the fitting, this module is responsible for screening the point with the largest curvature in the curve, which is an important indicator of the transition between material strength and rheological characteristics. This analysis reveals the material's variation characteristics under stress. By fitting a linear function to a selected key region, the linear approximation of that region is determined, allowing for a clearer interpretation of the curve shape and subsequent calculations. The module also calculates the tangent at the point of maximum curvature, providing crucial connection information for subsequent strength calculations. The significance is that the selected points of maximum curvature and their corresponding tangents provide key information, effectively helping researchers understand the critical points of material rheological behavior and supporting further analysis. Fitting the near-straight section at the end ensures the accuracy of the assessment, reducing the impact of nonlinearity on the final strength evaluation, thereby improving the reliability of judging the material's long-term strength. The strength calculation module 3 provides a geometric way to connect the material's rheological properties and long-term strength assessment by drawing the angle bisector between the horizontal line and the tangent. Fitting the angle bisector to the near-straight section at the end with a linear function and solving for the x-coordinate of the intersection point provides specific numerical basis for quantifying material strength. Finally, the long-term strength of the material is calculated using the x-coordinate of the intersection point; this output is the system's most important performance indicator. Significance achieved: The module provides a scientific basis based on engineering methods for calculating long-term strength, making the assessment results more credible; by providing specific values ​​for long-term strength, the module's output directly supports design and decision-making in the fields of geotechnical engineering and materials science, helping to improve engineering safety and economy.

[0144] In summary, this embodiment, through the close collaboration of these three modules, enables the long-term strength assessment system for rock core samples based on rheological testing to accurately extract key parameters from experimental data and derive the long-term strength standards that materials adhere to through scientific calculation methods. The system not only improves the accuracy of material performance assessment but also provides effective technical support and theoretical basis for application fields, promoting the progress of engineering practice.

[0145] like Figure 8 As shown, this embodiment provides an example of an electronic device 4, which includes a processor 41 and a memory 42 coupled to the processor 41. The memory 42 stores program instructions for implementing the long-term strength evaluation method for core samples based on rheological testing according to any of the above embodiments. The processor 41 is used to execute the program instructions stored in the memory 42 to perform long-term strength evaluation of core samples based on rheological testing. The processor 41 can also be referred to as a CPU (Central Processing Unit). The processor 41 may be an integrated circuit chip with signal processing capabilities. The processor 41 can also be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0146] Furthermore, Figure 9 This is a schematic diagram of the structure of a storage medium according to an embodiment of this application. The storage medium 5 of this embodiment stores program instructions 51 capable of implementing all the above methods. These program instructions 51 can be stored in the storage medium in the form of a software product, including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks, or terminal devices such as computers, servers, mobile phones, and tablets.

[0147] In the several embodiments provided by this invention, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0148] The specific embodiments of the invention have been described in detail above, but these are merely examples, and the invention is not limited to the specific embodiments described above. For those skilled in the art, any equivalent modifications or substitutions to the invention are also within the scope of this invention. Therefore, all equivalent transformations, modifications, and improvements made without departing from the spirit and principles of this invention should be included within the scope of this invention.

Claims

1. A method for evaluating long-term strength of a core sample based on a rheological test, characterized by, The core sample long-term strength evaluation method comprises: A standard cylindrical sample is prepared, the standard cylindrical sample is tested according to a rheological test, a rheological curve is obtained, and a fitting curve is obtained by fitting the steady-state rheological rate reciprocal and the stress level logarithm; A maximum curvature point of the fitting curve is screened, a horizontal line and a tangent line are fitted through the maximum curvature point of the curve end section near the straight line part, and an angle bisector of the horizontal line and the tangent line is drawn; An intersection point of the angle bisector and the end section near the straight line part is obtained by drawing the angle bisector and the end section near the straight line part according to a linear function, and the long-term strength is calculated; The process of obtaining the fitting curve comprises: The attenuation rheology, steady-state rheology and accelerated rheology stages of the rheological test curve are divided, the steady-state rheological rate is obtained by fitting the test data of the steady-state rheology stage according to a linear function by using a computer, a scatter plot of the steady-state rheological rate reciprocal and the stress level logarithm is drawn, and the fitting curve is obtained by fitting the scatter plot of the steady-state rheological rate and the stress level logarithm according to a Harris model; The process of obtaining the steady-state rheological rate comprises: During the rheological test, automatic sampling is performed at regular intervals, and more stress and strain data are recorded every interval; abnormal value detection is performed on the collected data, and the obviously deviated measured values are deleted according to the 3σ rule; Different rheological stages are automatically identified and divided, and the attenuation rheology, steady-state rheology and accelerated rheology stages are divided; after the stages are divided, the rationality of the division is dynamically evaluated by calculating the root mean square error of the data of each stage; Optimal fitting parameters are determined by using a grey wolf optimization; a linear regression model is selected, the training effect of the model is detected by cross-validation and leave-out method, and the actual situation of the steady-state rheological rate is reproduced by the linear function fitting model; in the linear function fitting process, the fitting parameters are adjusted according to the preliminary fitting result, the slope and intercept are reevaluated, and the error is adjusted until the error is within the set tolerance range; the Bootstrap method is used for multiple resampling to obtain the distribution of the stable steady-state rheological rate; The process of calculating the long-term strength comprises: Before least square fitting, the end line part of the fitting curve is selected as the target data; the selected end line part is linearly fitted by using the least square method, a linear relationship equation is obtained, and the relationship between the rheological rate and the stress in the high stress range is described; According to the rheological rate coordinate value of the maximum curvature point, a horizontal line parallel to the vertical axis is drawn, and the rheological rate under a specific stress difference is clearly marked; the slope of the tangent line is calculated by locally linearizing the fitting curve at the maximum curvature point, and the tangent line equation is obtained, and the tangent line is drawn in the graph to intuitively display the instantaneous response characteristics of the rheological rate with the stress; The intersection of the tangent line and the new fitting straight line is found by intersection analysis, and the horizontal coordinate of the intersection point represents the long-term strength of the material. The process of testing the standard cylindrical sample according to the rheological test comprises: The selected core sample is processed into a standard cylindrical sample, the sample size is φ50mm*100mm, the cylindrical sample is intact without damage, and there is no loss.

2. The method for evaluating long-term strength of a core sample based on a rheological test according to claim 1, characterized by, ​ ​ The obtained core sample was placed on a rheometer, a constant confining pressure value of 5 MPa was applied, and a constant confining pressure stepwise axial pressure loading mode was used, and the first stage stress level was 0.5 times the instantaneous peak strength; The rheological time of each stress level was 72 h, and the next stage loading was carried out, and under the action of the last stage stress level, accelerated rheological failure occurred after 25.93 h.

3. The method for evaluating long-term strength of a core sample based on a rheological test according to claim 1, characterized by, The process of automatically identifying and dividing different rheological stages specifically includes the following steps: The obtained stress and strain data were arranged in chronological order to form a complete data set; smoothing processing was performed, and a moving average method or wavelet transform was used to remove noise; the second derivative of the stress-strain curve was calculated to identify the region with large changes; the slope of stress and strain was calculated to identify the change of rheological behavior; A dynamic threshold was set to identify the sharp change when the stress rapidly increased or decreased; the boundaries of the decay rheology, steady rheology and accelerated rheology were determined by combining the changes of curvature and slope; when the stress and strain change reached the set threshold, it was marked as the end point of the decay rheology; when the slope was stable and the change amplitude was less than the threshold, it was marked as the starting and ending points of the steady rheology paragraph; when the stress or strain increased significantly again and exceeded the threshold, it was marked as the starting point of the accelerated rheology; In each rheological stage, the root mean square error of each stage was calculated to evaluate the rationality of the cutting point; if the root mean square error of a stage is too high, the cutting point is re-evaluated and optimized; the division result is dynamically adjusted, and if the division error of the rheological stage is higher than the set value, the original data is re-smoothed by calling the smoothing curve generation algorithm.

4. The method for evaluating long-term strength of a core sample based on a rheological test according to claim 1, characterized by, The process of obtaining the fitting curve includes: In a two-dimensional coordinate system, the reciprocal of the calculated steady-state rheological rate is taken as the vertical coordinate, and the logarithm of the corresponding stress level is taken as the horizontal coordinate to draw a scatter plot; the distribution trend of the scatter points is observed by visualizing the scatter plot; The Harris model parameters are initialized by an empirical rule, and a nonlinear optimization algorithm is used to minimize the sum of squared errors between the predicted value and the actual value; The parameter adjustment and corresponding fitting error of each step are dynamically recorded, the corresponding fitting curve is generated based on the determined Harris model parameters, and the fitting curve is superimposed on the scatter plot to form the final fitting graph.

5. The method for evaluating long-term strength of a core sample based on a rheological test according to claim 1, characterized by, The process of drawing a horizontal line and a tangent line through the maximum curvature point includes: According to the curvature formula, the second derivative and the first derivative of the fitting curve are calculated using numerical software to obtain the curvature value corresponding to the stress difference; from the curvature change curve, the numerical data is analyzed to determine the maximum curvature value and its corresponding coordinate point; In a two-dimensional coordinate system, a line parallel to the vertical axis is drawn, representing the rheological rate at the maximum curvature point; based on the first derivative of the fitting curve, the maximum curvature point is locally linearized to calculate the slope of the tangent line, and the tangent line equation is calculated based on the slope of the tangent line and the known rheological rate value to draw the tangent line; The slope of the bisector is calculated using the slope of the tangent line and the slope of the horizontal line, and the angle change of the true bisector is judged using trigonometric functions; the upward inclined bisector is drawn using the determined slope.

6. The method for evaluating long-term strength of a core sample based on a rheological test according to claim 1, characterized by, The process of linear fitting of the selected end line part by least square method comprises: For each data point, a window size is selected, with the data point as the center, and N points around it are selected as the reference points for local regression; the distance between each adjacent data point and the current data point is calculated; A Gaussian kernel function is selected to assign weights to each data point in the local area; the weights are normalized when calculating the weights; a weight matrix is created for each target point, with the diagonal elements being the weights of each reference point; a linear model is constructed to obtain the objective of least square method; according to the theory of weighted least square method, the standard least square method is used to solve the parameters obtained by weighted data; Each input point is repeated in turn, and weighted linear regression based on the neighborhood data of each stress value to be estimated is implemented; by uniformly performing local regression, a set of local models are generated, and finally a global fitting curve is formed by combining the obtained weights.

7. A system for evaluating long-term strength of a core sample based on a rheological test, which is applied to the method for evaluating long-term strength of a core sample based on a rheological test according to any one of claims 1 to 6, characterized by, The core sample long-term strength evaluation system based on rheological test comprises: A curve fitting module is configured to prepare a standard cylindrical sample, test the standard cylindrical sample according to a rheological test, obtain a rheological curve, fit the reciprocal of the steady-state flow rate and the logarithm of the stress level, and obtain a fitting curve; A function fitting module is configured to screen a maximum curvature point of the curve, and perform a first function fitting on a nearly straight part of the end segment of the curve to pass through the maximum curvature point to obtain a horizontal line and a tangent line; A strength calculation module is configured to draw an angle bisector of the horizontal line and the tangent line, combine the angle bisector with the nearly straight part of the end segment, and obtain an intersection point of the first function to calculate a long-term strength.

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