Rock damage evaluation method and device

Abstract

The invention provides a rock damage evaluation method and device, and the method comprises the following steps: carrying out a compression test on a rock sample until the rock sample is damaged; treating the damaged rock sample to obtain a multi-scale damage fractal dimension of the damaged rock sample; based on the multi-scale damage fractal dimension, calculating a weight coefficient of each scale fractal dimension to the damage of the rock sample through an analytic hierarchy process; constructing a multi-scale rock damage evolution fractal model based on the weight coefficient; and evaluating the damage degree of the rock to be measured based on the rock damage evolution fractal model. The defect that the rock damage degree is determined from a single scale is overcome, rock damage can be more comprehensively and accurately quantified, long-term rock damage and stability evolution are effectively predicted, and reference is provided for comprehensively and accurately representing the rock damage degree and long-term evolution.

Description

Technical Field

[0001] The present invention relates to the technical field of rock damage mechanics, and in particular to a rock damage evaluation method and device. Background Art

[0002] In the safe exploitation of unconventional oil and gas resources, comprehensive, accurate, and quantitative assessment and prediction of rock damage levels are key to ensuring smooth and safe mining operations. Currently, there are a variety of methods for assessing rock damage, including classic damage models such as the Kachanov, Gurson, and Duncan damage models, as well as new damage models constructed based on experimental data to assess and predict the development of rock damage. The core of these methods lies in selecting appropriate parameters to construct damage variables and verifying the rationality and superiority of the methods and models. As a quantitative indicator for describing rock damage, an increase in the fractal dimension indicates the expansion of primary pores and cracks in the rock matrix, as well as the development and evolution of secondary cracks, ultimately leading to increased rock damage. This provides a new perspective for understanding rock damage.

[0003] However, most current methods for calculating rock damage are limited to a single scale. For example, they define rock damage variables using only a single parameter, such as macroscopic cracks, stress-strain parameters, or microscopic porosity. However, macroscopic rock damage is essentially the result of the gradual accumulation and development of microscopic pores and cracks, and the contribution of rock damage at different scales to rock failure varies. Therefore, single-scale assessment methods are unable to comprehensively and accurately evaluate the evolution of rock damage and fail to fully reflect the true extent of rock damage. Summary of the Invention

[0004] In order to solve the above technical problems, the present application provides a rock damage assessment method based on a multi-scale fractal method to solve or alleviate the problems existing in the above-mentioned prior art.

[0005] In order to achieve the above objectives, this application provides the following technical solutions:

[0006] In a first aspect of the present application, a rock damage assessment method is provided, comprising the following steps:

[0007] Conduct compression tests on rock samples until they fail;

[0008] Processing the damaged rock samples to obtain the multi-scale damage fractal dimension of the damaged rock samples;

[0009] Based on the multi-scale damage fractal dimension, the weight coefficient of each scale fractal dimension on the damage of the rock sample is calculated by the hierarchical analysis method;

[0010] Constructing a multi-scale rock damage evolution fractal model based on the weight coefficients;

[0011] The damage degree of the rock to be tested is evaluated based on the rock damage evolution fractal model.

[0012] Optionally, the compression test on the rock sample is specifically performed by using a uniaxial rock mechanics testing machine or a triaxial rock mechanics testing machine to perform a compression test on the rock sample.

[0013] Optionally, the rock sample is a rock sample made into a standard cylinder, and the size of the standard cylinder is 25×50 mm or 50×100 mm.

[0014] Optionally, the processing of the damaged rock sample to obtain a multi-scale damage fractal dimension of the damaged rock sample specifically includes:

[0015] Scanning the damaged rock sample using CT to obtain CT scanning results, and reconstructing the damaged rock sample in three dimensions using three-dimensional reconstruction software in combination with the CT scanning results to calculate the three-dimensional fractal dimension of macroscopic centimeter-level cracks;

[0016] The fracture surface of the rock sample after destruction was scanned and image binarized using SEM scanning combined with two-dimensional image processing software, and the fractal dimension of the micron-level fracture surface was calculated.

[0017] Liquid nitrogen adsorption experiments combined with the FrenkelHalseyHill (FHH) model were used to obtain the pore structure of the crushed rock samples and calculate the micro-nanoscale pore fractal dimension.

[0018] Optionally, the three-dimensional reconstruction software is Avizo software, and the two-dimensional image processing software is ImageJ software.

[0019] Optionally, the step of determining the weight coefficient of the fractal dimension at each scale on the damage of the rock sample by the analytic hierarchy process comprises:

[0020] Analyze the correlation between the fractal dimension at each scale and the mechanical parameters obtained from the rock sample during its destruction, including compressive strength and elastic modulus;

[0021] Determine the relative importance of fractal dimensions at each scale based on the degree of correlation;

[0022] Establish an initial matrix according to the AHP criteria;

[0023] The validity of the matrix is ​​verified by a consistency index test, wherein the consistency test requires a consistency ratio of < 0.1;

[0024] If the consistency test is satisfied, the weight coefficient of the contribution of each scale fractal dimension to rock damage is calculated;

[0025] According to the weight coefficient, a comprehensive fractal damage calculation formula D=a1D1+a2D2+a3D3 is established, where D1 is the macroscopic crack fractal dimension, D2 is the microscopic fracture fractal dimension, and D3 is the microscopic pore fractal dimension.

[0026] Optionally, when establishing the initial matrix, the relative importance values ​​of the fractal dimensions at each scale are determined through historical experimental data, and the values ​​are used as matrix elements.

[0027] Optionally, the multi-scale rock damage evolution fractal model is constructed based on the weight coefficients, specifically in the following steps:

[0028] Based on the comprehensive fractal damage calculation formula, the rock fractal damage variable formula is established:

[0029]

[0030] get:

[0031]

[0032] Where DF is the damage variable;

[0033] ΔF N0 It is the difference in the comprehensive fractal dimension between the state of the rock after being soaked in ScCO2 for N hours and its undried state;

[0034] F0 is the comprehensive fractal dimension of the untreated rock;

[0035] FN is the comprehensive fractal dimension of shale after soaking in ScCO2 for N hours;

[0036] The fractal damage variables and rock loading time are fitted with polynomial functions to obtain a multi-scale rock damage evolution fractal model.

[0037] Optionally, before evaluating the damage degree of the rock to be tested based on the rock damage evolution fractal model, the rock damage evolution fractal model is compared and verified with a traditional rock damage model.

[0038] Optionally, the traditional rock damage model includes an elastic modulus damage model and a porosity damage model;

[0039] The damage variable calculation formula of the elastic modulus damage model is:

[0040]

[0041] Where DE is the damage variable; E0 is the initial elastic modulus of unsoaked shale;

[0042] EN is the elastic modulus of shale after soaking in ScCO2 for N hours.

[0043] The damage variable calculation formula of the porosity damage model is:

[0044]

[0045] Where DP represents the damage variable;

[0046] P0 represents the porosity of shale before immersion;

[0047] PN represents the porosity after immersion for N hours;

[0048] PS represents the porosity after shale is completely destroyed.

[0049] Optionally, the comparison and verification of the rock damage evolution fractal model and the traditional rock damage model is achieved by comparing damage evolution curves, including:

[0050] According to the elastic modulus damage calculation formula, the elastic modulus damage evolution model is established, and the elastic modulus damage model curve is drawn;

[0051] According to the damage calculation formula defined by porosity, a porosity damage evolution model is established, and a porosity damage model curve is drawn;

[0052] The rock damage evolution fractal model curve drawn according to the rock damage evolution fractal model is compared with the elastic modulus damage evolution model curve and the porosity damage evolution model curve to verify the effectiveness of the rock damage evolution fractal model.

[0053] Optionally, the evaluation of the damage degree of the rock to be tested based on the rock damage evolution fractal model is specifically as follows: parameters such as the loading time, loading method, and loading rate of the rock to be tested are input into the rock damage evolution fractal model, and the damage degree of the rock to be tested under corresponding conditions is output.

[0054] Optionally, during the process of compressing the standard rock sample until failure, a stress-strain curve and mechanical parameters of the compression process are obtained, wherein the mechanical parameters include compressive strength and elastic modulus.

[0055] Optionally, the fractal dimension is calculated using the box dimension method.

[0056] The present application also provides a rock damage assessment device, which is used to implement a rock damage assessment method, including:

[0057] Mechanical testing module, used to perform compression tests on rock samples;

[0058] A multi-scale detection module, including a CT scanner, a SEM microscope, and a liquid nitrogen adsorption instrument, is used to process the damaged rock samples to obtain the multi-scale damage fractal dimension of the damaged rock samples;

[0059] A data processing module is used to calculate the weight coefficient of each scale fractal dimension on the damage of the rock sample through the hierarchical analysis method based on the multi-scale damage fractal dimension;

[0060] A model building module for building a multi-scale rock damage evolution fractal model based on the weight coefficients

[0061] The evaluation output module is used to evaluate the damage degree of the rock to be tested based on the rock damage evolution fractal model and output the damage evaluation result.

[0062] Optionally, the device further includes a model verification module, and the model verification module is configured to:

[0063] Receive prediction data from fractal models and benchmark data from traditional damage models;

[0064] Comparison of damage evolution curves of fractal model and traditional damage model;

[0065] Output verification results, which include curve fitting indicators and error analysis data.

[0066] The technical solution in the present application has at least the following beneficial effects: traditional rock damage assessment methods are mostly limited to a single scale, which makes it difficult to fully reflect the overall picture of rock damage. However, the present application processes the rock samples after compression tests to obtain multi-scale damage fractal dimensions, covering three scales: macro, micro and micro. This multi-scale assessment method can fully consider the process of rock gradually accumulating from microscopic pores and cracks to macroscopic destruction, comprehensively quantify the degree of damage to the loaded rock, avoid the one-sidedness of single-scale assessment, and be more in line with the actual situation of rock damage evolution. Secondly, the technical solution of the present application enhances the accuracy of rock damage assessment. Based on the multi-scale damage fractal dimension, the hierarchical analysis method is used to calculate the weight coefficient of each scale fractal dimension on the damage of the rock sample, and construct a multi-scale rock damage evolution fractal model. This process comprehensively considers the difference in the contribution of fractal dimensions of different scales to rock damage through scientific analysis methods. Compared with the traditional method of defining damage variables with a single parameter, it can more accurately describe the degree of rock damage. At the same time, before evaluating the damage degree of the rock to be tested, the model is compared and verified with the traditional rock damage model, and the damage evolution curve is compared to further ensure the accuracy and reliability of the evaluation results. Furthermore, this application combines the theory of fractal damage mechanics and the hierarchical analysis method. By constructing a multi-scale rock damage evolution fractal model, only the loading time, loading method, loading rate and other parameters of the rock to be tested need to be input to output the damage degree under the corresponding conditions. The operation is simple and quantifiable. This has important practical value and guiding significance for the real-time and accurate assessment of rock damage in the exploitation of unconventional oil and gas resources, and for ensuring the safety and smooth progress of the mining operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] The drawings that constitute part of this application are used to provide a further understanding of this application and make other features, objects and advantages of this application more apparent. The illustrative embodiment drawings of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0068] Figure 1 This is a schematic flow chart of a rock damage assessment method according to an embodiment of the present application;

[0069] Figure 2a This is a schematic diagram of a rock sample according to an embodiment of the present application;

[0070] Figure 2b This is a schematic diagram of a rock sample after destruction according to an embodiment of the present application;

[0071] Figure 3 is a stress-strain curve diagram obtained according to an embodiment of the present application;

[0072] Figure 4 It is a schematic diagram of the box dimension method according to an embodiment of the present application;

[0073] Figure 5 This is a comparison diagram of the correlation between fractal dimensions and elastic modulus at three scales according to the embodiment of the present application;

[0074] Figure 6a It is a multi-scale rock damage evolution fractal model according to an embodiment of the present application;

[0075] Figure 6b It is an elastic modulus damage model according to an embodiment of the present application;

[0076] Figure 6c It is a porosity damage model according to an embodiment of the present application. DETAILED DESCRIPTION

[0077] In order to enable those skilled in the art to better understand the present invention, the following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work should fall within the scope of protection of the present invention.

[0078] It should be noted that the term "including" in the specification and claims of this application and the above-mentioned drawings is intended to cover non-exclusive inclusions. In this application, the directions or positional relationships indicated by the terms "upper", "lower", "front", "rear", etc. are based on the directions or positional relationships shown in the drawings. These terms are mainly used to better describe this application and its embodiments, and are not used to limit the indicated components to having specific directions. For those of ordinary skill in the art, the specific meanings of these terms in this application can be understood according to the specific circumstances.

[0079] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0080] Figure 1 This is a flow chart of a rock damage evaluation method according to an embodiment of the present application. Figure 1 As shown, the present application provides a rock damage assessment method, comprising the following steps:

[0081] Perform compression tests on rock samples until they fail;

[0082] Processing the damaged rock samples to obtain the multi-scale damage fractal dimension of the damaged rock samples;

[0083] Based on the multi-scale damage fractal dimension, the weight coefficient of each scale fractal dimension on the damage of the rock sample is calculated by the hierarchical analysis method;

[0084] Constructing a multi-scale rock damage evolution fractal model based on the weight coefficients;

[0085] The damage degree of the rock to be tested is evaluated based on the rock damage evolution fractal model.

[0086] In this embodiment, by processing the damaged rock samples, multi-scale damage fractal dimensions are obtained, covering the macroscopic, microscopic and microscopic levels. The macroscopic damage of rocks is the result of the gradual accumulation and development of microscopic pores and cracks. Damage at different scales contributes differently to the final damage of the rock. Multi-scale assessment can capture the characteristics of rock damage from multiple dimensions, fully present the entire process of rock from microscopic defect initiation and development to macroscopic damage, and comprehensively reflect the nature of rock damage. Compared with single-scale assessment, it can more realistically and comprehensively display the damage state of the rock, avoiding errors caused by one-sided assessment. In addition, the hierarchical analysis method is used to determine the weights and scientifically quantify the contributions of each scale. Based on the obtained multi-scale damage fractal dimension, the hierarchical analysis method is used to calculate the weight coefficients of the fractal dimensions of each scale on the damage of the rock sample. The hierarchical analysis method is a systematic analysis method that can decompose complex problems into multiple levels and determine the weights by analyzing the relative importance of each factor. In rock damage assessment, fractal dimensions at different scales have varying degrees of influence on rock damage. Using the analytic hierarchy process (AHP) and combined with mechanical parameters during rock failure, the weights of each fractal dimension are scientifically and rationally determined, quantifying the contribution of each scale to rock damage. This makes the assessment results more scientific and accurate, avoiding bias caused by arbitrary weighting. Furthermore, a fractal model is constructed to achieve precise prediction and assessment. Based on the calculated weight coefficients, a multi-scale fractal model of rock damage evolution is constructed, and the damage extent of the rock under test is evaluated based on this model. Fractal theory effectively describes complex, self-similar phenomena in nature, and rock damage processes exhibit fractal characteristics. By constructing a fractal model, the evolution of rock damage can be accurately characterized. Incorporating multi-scale fractal dimensions and weight coefficients into the model allows it to comprehensively consider the influence of factors at all scales on rock damage. When assessing the rock under test, simply inputting the relevant parameters allows the model to output the damage extent, achieving accurate prediction and quantitative assessment of rock damage. This provides a reliable and effective tool for rock damage assessment in engineering practices such as unconventional oil and gas resource extraction, facilitating the rational planning of extraction plans and ensuring project safety.

[0087] Optionally, the rock sample is a rock sample made into a standard cylinder, and the size of the standard cylinder is 25×50 mm or 50×100 mm in diameter×height.

[0088] In this embodiment, Figure 2a According to the rock sample schematic diagram in the embodiment of the present application, the rock samples are uniformly made into Figure 2a The standard cylinders shown, with a diameter and height of 25 × 50 mm or 50 × 100 mm, provide a foundation for comparing results between different experiments. In rock mechanics experiments, sample size significantly influences experimental results, and unified standard sizes standardize experimental conditions. When rock damage assessment experiments are conducted using standard cylindrical samples of the same specifications, the data obtained are highly comparable, effectively avoiding deviations in experimental results caused by differences in sample size. This ensures experimental repeatability, makes research results more credible and universal, and promotes academic exchange and technological advancement. Furthermore, the design of these standard sizes fully considers the performance and operating requirements of experimental equipment such as uniaxial and triaxial rock mechanics testing machines, allowing for adaptation to experimental equipment and optimization of experimental results. The appropriate size ensures stable sample installation on the equipment, ensuring uniform and precise loading, and avoiding problems such as samples that are too large and exceed the equipment's loading range, or samples that are too small and lead to uneven stress distribution. Furthermore, when using CT scanning, scanning electron microscopy (SEM), and other methods to obtain multi-scale fractal dimensions of rock damage, standard-sized samples facilitate scanning and imaging, facilitating the acquisition of high-quality image data. This provides a strong foundation for accurate calculation of fractal dimensions and analysis of rock damage characteristics, thereby enhancing the accuracy and reliability of the entire rock damage assessment method. Finally, the standardized cylinder dimensions align with industry norms and promote technical application. The 25×50mm or 50×100mm standard cylinder dimensions align with industry norms and standards in rock mechanics, facilitating the widespread application of this rock damage assessment method in practical engineering and academic research. In practical engineering scenarios such as unconventional oil and gas resource extraction, the unified sample standard enables companies and research institutions to rapidly apply this assessment method, accurately assessing the extent of rock damage and providing a scientific basis for mining plan design and engineering safety assurance. In academic research, standardized sample preparation facilitates the integration and summarization of research results, promoting the overall development of the field of rock damage mechanics.

[0089] Optionally, before the compression test is performed on the rock samples, the method further includes the steps of: soaking part of the rock samples in supercritical carbon dioxide (ScCO2) for different lengths of time, and retaining another part of the rock samples without soaking.

[0090] In this embodiment, some rock samples are immersed in supercritical carbon dioxide (ScCO2) for different lengths to simulate the real engineering environment and improve the practicality of the research. In actual projects such as unconventional oil and gas production and geological storage, rocks are often in a complex fluid environment. Supercritical carbon dioxide (ScCO2) immersion can simulate the interaction between rocks and fluid media in these engineering scenarios. By immersing some rock samples in ScCO2 for different lengths, the damage evolution process of rocks under long-term fluid erosion can be studied, making the experimental results closer to actual working conditions. Compared with the control group samples that were not immersed, the influence of ScCO2 on the mechanical properties and structure of rocks can be intuitively reflected, providing a more practical reference for the formulation of oil and gas production plans and the safety assessment of geological storage, effectively reducing the gap between theoretical research and practical application. In addition, the damage mechanism can be further explored and theoretical cognition can be enriched. Some rock samples are immersed in supercritical carbon dioxide (ScCO2) for different lengths to form immersion group samples, and another part of the rock samples are not immersed as control group samples; setting the immersion group and control group rock samples provides a comparative basis for studying the rock damage mechanism. Different durations of ScCO2 immersion trigger various physical and chemical processes, including changes in the rock's microscopic pore structure, dissolution and reaction of mineral components, and crack propagation. The control group, however, retains its original rock state. By comparing the multi-scale damage fractal dimensions and mechanical parameters of the two groups of samples after compression testing, we can deeply analyze the initiation, development, and evolution of rock damage under ScCO2, clarify the contribution of various factors to rock damage, fill a gap in the study of rock damage mechanisms in specific fluid environments, enrich the theoretical system of rock damage mechanics, and provide new perspectives and data support for academic research in this field. Furthermore, this embodiment optimizes the damage assessment model and enhances prediction accuracy. The multi-scale rock damage evolution fractal model constructed based on samples from the immersion and control groups comprehensively considers the impact of ScCO2 immersion on rock damage. During model construction, the data differences between the two groups of samples can be used to more accurately determine the weight coefficients of the fractal dimensions at each scale and optimize the model parameters. Compared with traditional models, this model can more comprehensively describe the damage characteristics of rocks in complex fluid environments. By inputting different immersion conditions and loading parameters, the degree of rock damage can be accurately predicted. In the model verification phase, by comparing the results of the immersion group, the control group and the traditional damage model, the effectiveness and superiority of the model were further verified, providing a reliable tool for the accurate assessment of rock damage and long-term evolution prediction in engineering practice.

[0091] Optionally, the compression test is performed on the rock samples in the immersion group and the control group, specifically, a uniaxial rock mechanics testing machine or a triaxial rock mechanics testing machine is used to perform the compression test on the rock samples.

[0092] In this embodiment, a uniaxial rock mechanics testing machine or a triaxial rock mechanics testing machine is used to perform compression tests on rock samples to accurately simulate different stress states, close to actual working conditions. Figure 2bThis is a schematic diagram of a rock sample after destruction according to an embodiment of the present application. Uniaxial rock mechanics testing machines and triaxial rock mechanics testing machines can simulate the stress state that rocks are subjected to in different engineering environments. Uniaxial testing machines can be used to simulate the damage characteristics of rocks under unidirectional stress conditions and are suitable for studying some rock scenes subjected to simple stress; triaxial testing machines can accurately simulate the actual stress state of underground rocks in complex stress fields by applying confining pressure and axial pressure. For example, in scenes such as deep oil and gas extraction and underground engineering construction, rocks are often subjected to multi-directional stress. By performing compression tests on rock samples in the immersion group and the control group on these two testing machines, it is possible to comprehensively study the effect of supercritical carbon dioxide (ScCO2) immersion on the damage characteristics of rocks under different stress environments, making the test results more consistent with actual engineering conditions and providing a more reliable basis for engineering design and decision-making. In addition, the test parameters can be accurately controlled to ensure data reliability. Both types of testing machines are equipped with high-precision loading control systems and data acquisition systems. During the compression test, parameters such as loading rate and stress magnitude can be accurately controlled with a very small error range. For example, the loading rate can be stably controlled within a very small variation range to ensure the consistency of each test condition. At the same time, highly sensitive sensors collect real-time data on stress and strain during the compression process, with high frequency and accuracy. For rock samples in the immersion and control groups, this precise parameter control and data acquisition effectively reduces experimental error, enhances the reliability of comparative analysis results, and accurately reflects the impact of ScCO2 immersion on rock mechanical properties and damage severity, providing a solid data foundation for further research into rock damage mechanisms. Furthermore, multidimensional mechanical parameters can be obtained to deepen damage research. During compression tests, uniaxial and triaxial rock mechanics testing machines can acquire a rich set of rock mechanical parameters. In addition to common parameters such as compressive strength and elastic modulus, multidimensional data such as Poisson's ratio and peak strain can also be obtained based on experimental requirements. Combining these multidimensional mechanical parameters with multiscale damage fractal dimensions for both immersion and control groups enables in-depth analysis of the impact mechanisms of ScCO2 immersion on rock damage from multiple perspectives. By comparing the differences in mechanical parameters between the two groups, the contributions of various factors to rock damage can be further clarified, providing comprehensive data support for the construction of more accurate rock damage assessment models and contributing to a deeper understanding of the nature and evolution of rock damage. Finally, this embodiment demonstrates broad applicability and versatility, facilitating technology dissemination. Uniaxial and triaxial rock mechanics testing machines are widely used in rock mechanics research, demonstrating their high versatility and standardization. These machines are widely available in both scientific research institutions and engineering companies. Using these two types of testing machines to conduct tests on immersion and control rock samples in rock damage assessment studies facilitates understanding and replication by other researchers and engineering technicians, promoting the exchange and dissemination of research findings.At the same time, the data obtained based on widely used equipment are easier to compare and analyze with existing research results and industry standards, which helps to integrate the rock damage evaluation method into the existing research system and engineering practice, and promote the development and application of rock damage mechanics technology.

[0093] Optionally, during the process of compressing the standard rock sample until it is destroyed, a stress-strain curve and mechanical parameters of the compression process are obtained, wherein the mechanical parameters include compressive strength and elastic modulus.

[0094] In this embodiment, a uniaxial or triaxial rock mechanics testing machine is used, and a comprehensive calibration step is required before testing. In one alternative, the loading system uses a high-precision pressure sensor (accuracy up to ±0.1% FS) and a displacement sensor (resolution up to 0.001 mm), calibrated using standard weights and gauge blocks to ensure the accuracy of load force and displacement measurements. The data acquisition system uses a 24-bit high-speed data acquisition card with a sampling frequency of 1000 Hz to capture subtle mechanical changes during rock compression. Simultaneously, the testing machine's temperature and humidity control systems are debugged to maintain the test environment temperature at (20±2)°C and the relative humidity at (60±5)% to minimize environmental interference with the test results. Furthermore, during sample installation and testing, a standard cylindrical rock sample (diameter x height: 25 x 50 mm or 50 x 100 mm) is placed at the center of the upper and lower pressure plates of the testing machine. A level is used to ensure the sample is installed vertically to avoid eccentric loading. A rigid pad and lubricating film are placed between the sample and the pressure plate to minimize the impact of friction on the test results. In an optional embodiment, the test uses a displacement-controlled loading mode with a loading rate set at 0.05 mm / min. During the loading process, the data acquisition system collects real-time load data from the pressure sensor and displacement data from the displacement sensor. The stress is calculated using the formula σ = F / A, where F is the load and A is the cross-sectional area of ​​the sample. The strain is calculated using the formula ε = ΔL / L0, where ΔL is the displacement change and L0 is the initial sample height, generating a stress-strain data array.

[0095] Figure 3This is a stress-strain curve diagram obtained according to an embodiment of the present application, which shows the stress-strain curve of the rock under different immersion times. The figure contains multiple sub-graphs, corresponding to immersion times of 0h, 24h, 48h, 72h and 96h respectively. In each sub-graph, there are multiple curves representing the stress-strain relationship of different rock samples under corresponding immersion times, with the horizontal axis being strain (%) and the vertical axis being compressive strength (MPa). In this embodiment, the collected stress-strain data is also pre-processed after the compression test. A digital filtering algorithm, such as a Butterworth low-pass filter, is used to remove high-frequency noise, and the cutoff frequency is set to 50Hz. By analyzing the stress-strain curve, the peak stress point is determined, and the stress value corresponding to this point is the compressive strength. In the elastic stage of the curve, the straight line segment of the stress-strain curve is generally taken, and the data is linearly fitted using the least squares method. The slope of the fitting line is the elastic modulus. At the same time, the processed data and the calculated mechanical parameters are stored in a database to establish an association index between the rock sample information and the mechanical parameters.

[0096] The stress-strain curve obtained in this embodiment intuitively shows the mechanical behavior of the rock from elastic deformation, plastic deformation to failure. By analyzing the slope change, inflection point location and other characteristics of the curve, combined with mechanical parameters such as compressive strength and elastic modulus, it is possible to deeply study the initiation, expansion and penetration of microcracks in the rock. In addition, the accuracy of the rock damage assessment model is improved. Compressive strength and elastic modulus are important indicators for rock damage assessment. When constructing a multi-scale rock damage evolution fractal model, these mechanical parameters are combined with the multi-scale damage fractal dimension. The weight of each parameter is determined by the hierarchical analysis method, which can more accurately quantify the degree of rock damage. The rock mechanical response characteristics reflected by the stress-strain curve help optimize the relationship between damage variables and mechanical parameters in the model, making the model more consistent with the actual damage evolution law of the rock, thereby improving the accuracy and reliability of the model's prediction of rock damage degree, and providing more accurate rock damage assessment results for engineering practice. Furthermore, it can guide engineering design and construction. In unconventional oil and gas extraction, underground tunnel construction and other projects, the compressive strength and elastic modulus of rock directly affect the stability and safety of the engineering structure. By obtaining accurate stress-strain curves and mechanical parameters, engineers can rationally design mining plans and support structures. For example, by determining a reasonable mining pressure based on the compressive strength of the rock and selecting appropriate support materials and parameters based on the elastic modulus, they can effectively avoid engineering accidents caused by inaccurate assessments of rock mechanical properties, reduce engineering risks, and improve engineering economic benefits and safety. Finally, it can promote academic exchanges and technology sharing, unify standardized stress-strain curve and mechanical parameter acquisition methods, and make experimental data from different research institutions and engineering teams comparable. In academic research, researchers can exchange results and conduct comparative analysis based on data of the same standard, promoting academic development in the field of rock mechanics. In engineering practice, standardized data acquisition methods facilitate the sharing and promotion of technical experience, accelerate the application of new technologies and methods within the industry, and enhance the entire industry's understanding of rock mechanical properties and engineering application level.

[0097] Optionally, the processing of the damaged rock sample to obtain a multi-scale damage fractal dimension of the damaged rock sample specifically includes:

[0098] Scanning the damaged rock sample using CT to obtain a CT scan result, and reconstructing the damaged rock sample in three dimensions using three-dimensional reconstruction software in combination with the CT scan result to calculate the three-dimensional fractal dimension D1 of the macroscopic centimeter-level crack;

[0099] The fracture surface of the rock sample after destruction was scanned and image binarized using SEM scanning combined with two-dimensional image processing software, and the fractal dimension D2 of the micron-level fracture surface was calculated.

[0100] Liquid nitrogen adsorption experiments combined with the FrenkelHalseyHill (FHH) model were used to obtain the pore structure of the crushed rock sample and calculate the micro-nanoscale pore fractal dimension D3.

[0101] Optionally, the three-dimensional reconstruction software is Avizo software, and the two-dimensional image processing software is ImageJ software.

[0102] Optionally, the fractal dimension is calculated using the box dimension method.

[0103] In this embodiment, before using CT to scan the damaged rock sample to obtain the CT scan results, in an optional solution, the CT scan parameters can be set. An industrial microfocus CT scanner is used with the tube voltage set to 130 kV, the tube current set to 200 μA, the voxel resolution set to 50 μm, the rotation step size set to 0.5°, and the scanning time set to approximately 30 minutes to obtain a three-dimensional data set of the internal structure of the rock.

[0104] In the step of using 3D reconstruction software to reconstruct the damaged rock sample using the CT scan results, the original CT data is first imported. The 3D dataset of the rock's internal structure, acquired by the CT scanner, is imported in a format supported by Avizo software, such as DICOM or TIFF. During the import process, the software automatically identifies parameters such as the spatial resolution and number of scan slices, constructing an initial 3D data volume. This data volume contains grayscale differences between different structures and defects within the rock, providing a foundation for subsequent processing.

[0105] The data is then subjected to noise reduction using anisotropic diffusion filtering, a nonlinear filtering method that smooths the image while preserving edge information. In rock CT images, noise can arise from electronic interference from the scanning equipment, environmental factors, and other sources, interfering with the accurate identification of damage features such as cracks. Anisotropic diffusion filtering selectively smoothes pixels based on their gradient information. In areas of the image with small gradients (i.e., pixel values ​​change gently), the filter applies a greater degree of diffusion to remove noise. In areas with larger gradients (i.e., edges and details), the filter applies a lesser degree of diffusion, preserving important structural information such as cracks.

[0106] In the Avizo software's filtering interface, select the anisotropic diffusion filtering algorithm, set the diffusion coefficient to 15, and the number of iterations to 3. The diffusion coefficient determines the degree of diffusion of pixel values ​​during the filtering process; a larger value indicates a stronger diffusion effect. The number of iterations indicates how many times the filtering operation is repeated. Three iterations effectively remove noise while avoiding loss of detail due to oversmoothing. Based on the set parameters, the software performs voxel-by-voxel calculations on the imported 3D data volume, updating the pixel values ​​to complete the noise reduction process.

[0107] The method also includes a step for performing threshold segmentation based on the Otsu algorithm, an automatic threshold segmentation method based on the image grayscale histogram. Its goal is to find an optimal grayscale threshold to separate image pixels into foreground (e.g., fractures) and background (e.g., rock matrix) components, maximizing the inter-class variance between the two components. In rock CT images, fractures and the rock matrix exhibit different grayscale distributions due to differences in physical properties such as density. The Otsu algorithm exploits this difference to automatically determine the optimal threshold for distinguishing the two.

[0108] After selecting the Otsu threshold segmentation function in Avizo software, the software automatically analyzes the grayscale distribution of all pixels in the 3D data volume, calculates the inter-class variance curve as it changes with different thresholds, and finds the threshold that maximizes the inter-class variance. Based on this threshold, the software classifies the pixels in the data volume. Pixels with grayscale values ​​above the threshold are marked as foreground (fracture areas), while pixels with grayscale values ​​below the threshold are marked as background. This initially separates the fractures from the rock matrix, resulting in a preliminary binary image with foreground values ​​of 1 and background values ​​of 0.

[0109] Finally, morphological processing is performed. Morphological processing is an image processing method based on mathematical morphology. It operates on images by defining structuring elements to enhance, extract, or repair image features. Closing operations consist of two basic operations: dilation and erosion. First, dilation is performed on the image, expanding the boundaries of foreground pixels outward according to the defined structuring element. Then, erosion is performed, contracting the expanded boundaries inward. For rock CT images, the binary image after threshold segmentation may contain small holes and discontinuities in the fractured region. Closing operations can fill these holes and connect discontinuous fracture segments, making the fracture model more complete and smooth, facilitating the subsequent accurate calculation of the fracture fractal dimension. In the morphological processing module of Avizo software, the closing operation is selected and the structuring element radius is set to 3 voxels. The structuring element radius determines the range of the dilation and erosion operations. A radius of 3 voxels effectively repairs the fracture model while avoiding distortion of the fracture morphology caused by excessive processing. The software will perform dilation and erosion calculations on each voxel of the binary image after threshold segmentation based on the set structural elements, update the image pixel values, and ultimately obtain a complete and clear binary three-dimensional crack model, providing an accurate data basis for subsequent box dimension calculations.

[0110] In this embodiment, a Python script can be written in Avizo to implement the three-dimensional box dimension calculation. The exemplary code snippet provided is as follows:

[0111] importnumpyasnpfromscipy.ndimageimportlabel

[0112] defbox_counting_3d(binary_volume,min_box_size=2,max_box_size=None):

[0113] ifmax_box_sizeisNone:

[0114] max_box_size=min(binary_volume.shape) / / 2

[0115] box_sizes=np.logspace(np.log2(min_box_size),np.log2(max_box_size),

[0116] num=10, base=2, dtype=int)

[0117] counts=[]

[0118] forsizeinbox_sizes:

[0119] #Divide the grid and count the number of non-empty boxes

[0120] non_empty=0

[0121] foriinrange(0,binary_volume.shape[0],size):

[0122] forjinrange(0,binary_volume.shape[1],size):

[0123] forkinrange(0,binary_volume.shape[2],size):

[0124] ifnp.any(binary_volume[i:i+size,j:j+size,k:k+size]):

[0125] non_empty+=1

[0126] counts.append(non_empty)

[0127] #Linear fitting to find the slope

[0128] slope,_=np.polyfit(np.log(1 / box_sizes),np.log(counts),1)

[0129] returnslope

[0130] In an alternative embodiment, a scanning electron microscope (SEM) is used to scan the fracture surface of the damaged rock sample and perform image binarization processing in combination with two-dimensional image processing software to calculate the fractal dimension D2 of the micron-level fracture surface, including image import and bit depth conversion steps. The original image obtained by the SEM is imported into ImageJ, and the image bit depth is confirmed and converted to 8-bit through the menu command. This step maps the pixel grayscale value to the range of 0-255 to establish a unified numerical space for subsequent processing. Grayscale normalization processing is then performed to perform grayscale normalization operations to adjust the grayscale value range of the pixels in the image to between 0-255 to enhance the contrast of the image and other effects. This process is achieved through the grayscale normalization formula:

[0131]

[0132] in,

[0133] NormalizedValue: The normalized value, that is, the new grayscale value obtained after calculation, which ranges from 0 to 255;

[0134] OriginalValue: original value, that is, the original grayscale value of the pixel in the image;

[0135] MinValue: minimum value, which refers to the minimum value of all pixel grayscale values ​​in the image;

[0136] MaxValue: Maximum value, which refers to the maximum value of all pixel grayscale values ​​in the image;

[0137] This operation enhances image contrast and highlights differences in microscopic features on the fracture surface.

[0138] Median filtering is then used to reduce image noise, with a filter radius of 2 pixels. This algorithm takes the median grayscale value of all pixels within a 5×5 neighborhood centered on the current pixel and replaces the original pixel value. Median filtering effectively suppresses salt and pepper noise while preserving edge detail. Its mathematical expression is:

[0139] Filtered(x,y)=median{I(i,j)|(i,j)∈N(x,y)}

[0140] in,

[0141] Filtered(x,y) represents the pixel value obtained after median filtering at coordinates (x,y). In an image, each pixel has its corresponding horizontal and vertical coordinates. After the median filter operation, the pixel value at that location will be updated to the median value of the pixels in the specific neighborhood.

[0142] Median is a function that finds the median of a set of values ​​within the curly brackets. In the context of image filtering, it sorts the grayscale values ​​of pixels in a specified neighborhood and takes the grayscale value in the middle as the filtered result.

[0143] In I(i,j), I represents the image, and I(i,j) represents the pixel value at coordinates (i,j) in image I, usually the grayscale value of that pixel. When performing median filtering, the grayscale values ​​of all pixels (i,j) in a neighborhood centered on the currently processed pixel (x,y) are considered.

[0144] In (i,j)∈N(x,y), N(x,y) represents a neighborhood centered at coordinate (x,y). (i,j)∈N(x,y) means that (i,j) is a coordinate point in the neighborhood N(x,y). This means that the grayscale values ​​of all pixels in the neighborhood must be considered to calculate the median value to update the pixel value at (x,y). For example, when the filter radius is 2 pixels, the neighborhood is a 5×5 pixel area, and (i,j) represents the coordinates of each pixel in this 5×5 area.

[0145] Again, the optimal threshold is automatically calculated based on the Otsu algorithm to segment the image into foreground and background. The algorithm determines the threshold by maximizing the variance between classes.

[0146]

[0147] Among them, this formula is used in the Otsu algorithm to calculate the between-class variance The Otsu algorithm is often used for image threshold segmentation to automatically determine the optimal threshold for dividing an image into foreground and background. The following are the meanings of the parameters in the formula:

[0148] It represents the inter-class variance when the threshold is T. The inter-class variance is used to measure the difference between the foreground and background classes in an image. The larger the value, the better the distinction between the foreground and background. The goal of the Otsu algorithm is to find the threshold T that maximizes the inter-class variance.

[0149] P0(T) represents the probability of a pixel in the image having a grayscale value less than or equal to the threshold T, that is, the probability of the background pixel appearing. It is obtained by counting the number of pixels with a grayscale value less than or equal to T and dividing it by the total number of pixels in the image.

[0150] P1(T) represents the probability of a pixel in the image having a grayscale value greater than the threshold T, that is, the probability of the foreground pixel appearing. It is also obtained by counting the corresponding pixels and dividing it by the total number of pixels, and satisfies P0(T) + P1(T) = 1.

[0151] μ0(T) represents the average grayscale value of pixels (i.e., background pixels) whose grayscale values ​​are less than or equal to the threshold T. When calculating, the grayscale values ​​of all pixels with grayscale values ​​less than or equal to T are added together and then divided by the number of these pixels.

[0152] μ1(T) represents the average grayscale value of pixels (i.e., foreground pixels) whose grayscale values ​​are greater than the threshold T. The calculation method is similar to μ0(T), which is to add the grayscale values ​​of all pixels with grayscale values ​​greater than T and divide it by the number of such pixels.

[0153] The Otsu algorithm calculates the corresponding inter-class variance by traversing different thresholds T Select The maximum value of T is used as the optimal threshold for image segmentation, thereby dividing the image into foreground and background.

[0154] After the threshold is determined, the image is converted into binary form

[0155] Binary(x,y) represents the binary pixel value at coordinates (x,y). In a binary image, a pixel has only two possible values: 0 or 1, corresponding to different states in the image (such as background and foreground).

[0156] In I(x,y), I represents the original image, and I(x,y) represents the pixel value at coordinates (x,y) in the original image, usually the grayscale value of that pixel. In a grayscale image, each pixel has a specific grayscale value to represent its brightness.

[0157] T represents the threshold, a key parameter used to distinguish different areas in an image. During the binarization process, the grayscale value I(x,y) of each pixel is compared with the threshold T to determine the value of the pixel in the binary image.

[0158] Conditional judgment part ifI(x,y)≥T: If the grayscale value I(x,y) of the pixel at the coordinate (x,y) in the original image is greater than or equal to the threshold T, then in the binarized image, the pixel value Binary(x,y) at that position is assigned a value of 1, which usually represents the foreground part of the image.

[0159] Otherwise means that if the grayscale value I(x,y) of the pixel at the coordinate (x,y) in the original image is less than the threshold T, then in the binarized image, the pixel value Binary(x,y) at that position is assigned to 0, which usually represents the background part of the image.

[0160] In this way, the original grayscale image can be converted into a binary image consisting only of 0 and 1, achieving preliminary separation of different areas in the image for subsequent analysis and processing.

[0161] Morphological noise removal optimizes binary image quality through a series of morphological operations:

[0162] Open operation, first erosion and then expansion, to remove small bright spots;

[0163] Closing operation, first dilation and then corrosion, to fill small holes;

[0164] Isolated point elimination, based on connected region analysis, removes regions with an area smaller than a threshold.

[0165] The morphological operation transforms the image based on the structural elements, removes small noise points, and obtains a clear binary image of the fracture surface.

[0166] Finally, after the result verification and export processing is completed, the binarization quality is evaluated through statistical analysis, and indicators such as the proportion of foreground pixels and the number of connected regions are calculated. Finally, the processed binary image is saved for subsequent fractal dimension calculations.

[0167] This process systematically converts the original SEM images into high-quality binary images through mathematical transformation and algorithmic processing, laying the foundation for the fractal feature analysis of the fracture surface.

[0168] The box dimension was calculated using the FracLac plugin in ImageJ.

[0169] In an alternative solution, the box dimension calculation is implemented through a Python script. An example code is provided below:

[0170] fromskimageimportioimportnumpyasnp

[0171] defbox_counting_2d(binary_image,min_box_size=2,max_box_size=None):

[0172] ifmax_box_sizeisNone:

[0173] max_box_size=min(binary_image.shape) / / 2

[0174] box_sizes=np.logspace(np.log2(min_box_size),np.log2(max_box_size),

[0175] num=10, base=2, dtype=int)

[0176] counts=[]

[0177] forsizeinbox_sizes:

[0178] non_empty=0

[0179] foriinrange(0,binary_image.shape[0],size):

[0180] forjinrange(0,binary_image.shape[1],size):

[0181] ifnp.any(binary_image[i:i+size,j:j+size]):

[0182] non_empty+=1

[0183] counts.append(non_empty)

[0184] slope,_=np.polyfit(np.log(1 / box_sizes),np.log(counts),1)

[0185] returnslope

[0186] The liquid nitrogen adsorption experiment combined with the FrenkelHalseyHill (FHH) model is used to obtain the pore structure of the crushed rock sample and calculate the micro-nanoscale pore fractal dimension. One embodiment includes: using a fully automatic gas adsorption analyzer, performing adsorption-desorption experiments at liquid nitrogen temperature (-196°C), with a relative pressure range of 0.01-0.99, and sample pretreatment conditions of vacuum degassing at 150°C for 12 hours. The adsorption data is processed based on the FHH model, and the model expression is:

[0187]

[0188] This formula is an expression of the Frenkel-Halsey-Hill (FHH) model, which is often used to describe the relationship between the adsorption amount and relative pressure during the adsorption process to obtain information such as the fractal dimension of the pore structure of the adsorbent (such as crushed rock samples).

[0189] V: Indicates the relative pressure The adsorption capacity is the actual amount of adsorbate adsorbed on the surface or in the pores of the adsorbent, and the unit is usually volume cm 3 / g or amount of substance mol / g.

[0190] Vm stands for the monolayer saturated adsorption capacity, which refers to the adsorption capacity when the adsorbent surface is completely covered by a monomolecular layer of adsorbate, and its unit is the same as V. It represents the ratio of the actual adsorption capacity to the monolayer saturated adsorption capacity. is to take the natural logarithm of the ratio.

[0191] D3: represents the fractal dimension of micro- and nano-scale pores, a parameter that describes the complexity and irregularity of the adsorbent's pore surface. D3 values ​​range from 2 to 3. D3 values ​​closer to 3 indicate a more complex and irregular pore surface; D3 values ​​closer to 2 indicate a relatively smoother pore surface. is a coefficient in the formula and is related to the pore fractal dimension.

[0192] P: is the actual pressure during the adsorption process.

[0193] P0: is the saturated vapor pressure of the adsorbate at the experimental temperature. It is called relative pressure and its value is between 0 and 1. is the natural logarithm of the reciprocal of the relative pressure, It is right Then take the natural logarithm.

[0194] C is the constant term in the formula, which includes factors related to the specific properties of the adsorption system (such as adsorbate-adsorbent interaction, adsorption heat, etc.). In practical applications, the value of C can be determined by fitting experimental data.

[0195] By processing the experimentally measured adsorption data at different relative pressures and using this formula for linear fitting, the pore fractal dimension D3 can be calculated based on the slope of the fitting line, thereby obtaining information about the fractal characteristics of the adsorbent's pore structure.

[0196] The adsorption data is converted into an equivalent "pore surface" and the fractal dimension is calculated by the following steps. The example code is as follows:

[0197] deffhh_fractal_dimension(pressure_ratio,volume):

[0198] #Convert to FHH model coordinates

[0199] x=np.log(np.log(1 / pressure_ratio))

[0200] y=np.log(volume / volume.max())

[0201] #Linear fitting (take the middle linear area)

[0202] valid_indices=(pressure_ratio>0.05)&(pressure_ratio<0.5)

[0203] slope,_=np.polyfit(x[valid_indices],y[valid_indices],1)

[0204] #Calculate fractal dimension

[0205] fractal_dim=3-1 / slope

[0206] returnfractal_dim

[0207] Figure 4 This is a schematic diagram of the box dimension method according to an embodiment of the present application, which shows the process of using the box dimension method. From left to right, the original image of the rock sample is presented, as well as the situation of covering the rock image with grids of different side lengths r = 5mm, r = 10mm, r = 15mm, and r = 20mm. In this way, the fractal dimension of the rock structure can be calculated to describe the complexity and irregularity of the rock structure. This embodiment uses the box dimension method to calculate the fractal dimension. The box dimension method counts the number of boxes required to cover the target by changing the measurement scale (box size). It can process fractal objects of different dimensions such as three-dimensional crack networks, two-dimensional fracture surfaces, and one-dimensional pore structures under the same mathematical framework, ensuring the consistency of multi-scale analysis. For the massive three-dimensional data (usually containing millions of voxels) and high-resolution SEM images generated by CT scanning, the box dimension method uses a box size that varies on a logarithmic scale, which can significantly reduce the amount of calculation while ensuring calculation accuracy. By setting an appropriate box size range (usually 2-100 voxels / pixel), a stable fractal dimension estimate can be obtained. The box dimension directly reflects the spatial filling ability and complexity of the research object. In rock damage assessment, the higher the three-dimensional fractal dimension of macroscopic cracks, the more complex the crack network; the larger the fractal dimension of the fracture surface, the more tortuous the energy dissipation path during the fracture process; and the pore fractal dimension reflects the roughness of the pore surface and is closely related to the fluid migration capacity.

[0208] This example uses CT, SEM, and liquid nitrogen adsorption experiments to obtain structural information at the centimeter, micrometer, and nanometer scales, respectively. Combined with the box dimension method to calculate fractal dimension, it can comprehensively quantify the multi-scale damage characteristics of rocks from macro to micro. This breaks through the limitations of traditional methods that only focus on a single scale and more accurately reflects the complexity and hierarchy of rock damage. In addition, fractal dimension, as a quantitative indicator of damage degree, can intuitively reflect the damage evolution process of rocks under different loading stages or different immersion conditions. For example, by comparing the changes in fractal dimension of the immersion group and the control group, the damage mechanism of supercritical CO2 on rock structure can be clearly revealed, providing theoretical support for CO2 geological storage and unconventional oil and gas extraction. Furthermore, multi-scale fractal dimension provides rich parameters for constructing rock damage evolution models. The fractal dimension calculated by the box dimension method has a good correlation with rock mechanical parameters (such as compressive strength and elastic modulus), further improving the predictive ability of the model. Finally, this technical solution integrates multidisciplinary methods such as materials science, geology, and computational mathematics, providing a new technical means for rock mechanics research. Standardized experimental procedures and calculation methods facilitate result comparison and technology sharing among different research teams, and promote the widespread application of rock damage assessment technology in fields such as energy development, geological engineering, and materials science.

[0209] Optionally, the step of determining the weight coefficient of the fractal dimension at each scale on the damage of the rock sample by the analytic hierarchy process comprises:

[0210] Analyze the correlation between the fractal dimension at each scale and the mechanical parameters obtained from the rock sample during its destruction, including compressive strength and elastic modulus;

[0211] Determine the relative importance of fractal dimensions at each scale based on the degree of correlation;

[0212] Establish an initial matrix according to the AHP criteria;

[0213] The validity of the matrix is ​​verified by a consistency index test, wherein the consistency test requires a consistency ratio of < 0.1;

[0214] If the consistency test is satisfied, the weight coefficient of the contribution of each scale fractal dimension to rock damage is calculated;

[0215] According to the weight coefficient, a comprehensive fractal damage calculation formula D=a1D1+a2D2+a3D3 is established, where D1 is the macroscopic crack fractal dimension, D2 is the microscopic fracture fractal dimension, and D3 is the microscopic pore fractal dimension.

[0216] Figure 5 This is a comparison of the correlation between the fractal dimension and elastic modulus at three scales according to the embodiment of the present application. This figure is a three-dimensional scatter plot with the elastic modulus (GPa) as the horizontal axis and the fractal dimension D as the vertical axis. The figure shows the fractal dimensions at three scales, marked with red D1, blue D2 and black D3 respectively. The fractal dimension data points at each scale are fitted by linear fitting to obtain a fitting line, and the determination coefficient R is marked. 2 , such as R corresponding to D1 2 =0.7919, R corresponding to D2 2 =0.8831, R corresponding to D3 2 = 0.1682. This figure is used to compare the correlation between the three scales of fractal dimension and elastic modulus, the coefficient of determination R 2 The closer it is to 1, the stronger the linear correlation between the fractal dimension and the elastic modulus. In this embodiment, an optional solution for determining the weight coefficient of the fractal dimension at each scale on the damage of the rock sample by the hierarchical analysis method includes: first, performing data preprocessing and multi-source data fusion to construct a three-dimensional tensor data structure:

[0217]

[0218] Where, D{i,j}: the j-th fractal dimension of the i-th sample;

[0219] n: sample size;

[0220] j=1, 2, 3: correspond to the fractal dimensions of macro cracks, micro fractures, and micro pores, respectively.

[0221] Secondly, perform feature standardization. The Z-score standardization formula is as follows:

[0222]

[0223] in,

[0224] x norm : Standardized data values, that is, new data values ​​obtained after Z-score standardization processing, are used to convert the original data into a distribution range with a specific mean and standard deviation to facilitate subsequent data processing and analysis.

[0225] x: The original data value, that is, a data point in the original data set that has not been normalized.

[0226] μ: Data set mean, which is the average value of all data in the data set and reflects the central tendency of the data. Its calculation formula is in:

[0227] n: The number of data in the dataset.

[0228] The i-th data value in the xi data set, i ranges from 1 to n, and the mean μ is obtained by summing these n data values ​​and dividing by n.

[0229] σ: Standard deviation of the data set, which measures the degree of dispersion of the data in the data set. The larger the standard deviation, the more dispersed the data; the smaller the standard deviation, the more concentrated the data. Its calculation formula is

[0230]

[0231] in:

[0232] n: the number of data in the dataset;

[0233] x i : the i-th data value in the data set;

[0234] μ: The mean of the data set. The formula first calculates each data value x i The square of the difference from the mean μ, sum these squared values ​​and divide by the number of data n, and finally take the square root to get the standard deviation σ;

[0235] Through Z-score standardization, the original data is converted into standardized data with a mean of 0 and a standard deviation of 1, so that data of different magnitudes or distributions can be compared and analyzed on the same scale.

[0236] Thirdly, correlation analysis and importance ranking were performed, and the Spearman correlation coefficient was used to calculate the correlation between the fractal dimensions of each scale and the mechanical parameters, thereby providing a basis for determining the relative importance of the fractal dimensions of each scale.

[0237] The formula for calculating the Spearman correlation coefficient is:

[0238]

[0239] Parameter explanation:

[0240] ρ: Spearman correlation coefficient. In this scheme, it represents the degree of correlation between a fractal dimension at a certain scale and a mechanical parameter. Its value range is [-1, 1]. When ρ is close to 1, it indicates that there is a strong positive monotonic correlation between the fractal dimension at that scale and the corresponding mechanical parameter, that is, as the fractal dimension increases, the value of the mechanical parameter also tends to increase; when ρ is close to -1, it means that there is a strong negative monotonic correlation, that is, as the fractal dimension increases, the value of the mechanical parameter tends to decrease; when ρ is close to 0, it indicates that the monotonic correlation between the two is weak. For example, ρD1-compressive strength represents the Spearman correlation coefficient between the fractal dimension of the macro crack and the compressive strength.

[0241] d i : The difference between the rankings of two variables. In this scheme, for each rock sample, the data of a certain scale fractal dimension and a certain mechanical parameter are sorted and ranked. For example, the macroscopic crack fractal dimension D1 of all rock samples is sorted from large to small (or from small to large), and the corresponding compressive strength of these samples is also sorted. For the i-th rock sample, the difference between its ranking in the D1 ranking and its ranking in the compressive strength ranking is di. By calculating di, the relative position difference of the two variables in each sample can be reflected.

[0242] n: Sample number. In this technical solution, n refers to the number of rock samples analyzed. These rock samples were subjected to a destructive process, and data such as fractal dimensions and mechanical parameters at various scales were obtained. The size of the sample number n affects the reliability and stability of the correlation coefficient calculation. Generally speaking, the larger n, the more accurately the calculated Spearman correlation coefficient reflects the true correlation between the fractal dimension and the mechanical parameters.

[0243] By calculating the Spearman correlation coefficient between the fractal dimensions at each scale and the mechanical parameters, a set of numerical values ​​reflecting the degree of correlation between them can be obtained. These correlation coefficients are then used to determine the relative importance of the fractal dimensions at each scale. For example, the fractal dimension-mechanical parameter combination with the larger absolute value of the correlation coefficient is likely to be more important in assessing rock damage. This provides important basic information for subsequent steps such as establishing the initial matrix and determining the weight coefficients in the hierarchical analysis method.

[0244] Optionally, analyzing the correlation between the fractal dimensions at each scale and the mechanical parameters includes establishing a feature importance matrix importance_matrix:

[0245]

[0246] Among them, ρD j , M j : represents the correlation coefficient between the i-th fractal dimension and the j-th mechanical parameter.

[0247] i=1, 2, 3, corresponding to the macro crack fractal dimension D1, micro fracture fractal dimension D2, and micro pore fractal dimension D3 in the technical solution, respectively.

[0248] j=1,2, where M1 corresponds to the compressive strength in the mechanical parameters, and M2 corresponds to the elastic modulus.

[0249] Specifically, ρD1,M1 represents the correlation coefficient between the macroscopic crack fractal dimension and the compressive strength, and ρD2,M2 represents the correlation coefficient between the microscopic fracture fractal dimension and the elastic modulus.

[0250] The correlation between the fractal dimensions at each scale and the mechanical parameters is analyzed by calculating and arranging the correlation coefficients between the fractal dimensions D1, D2, and D3 at each scale and different mechanical parameters (compressive strength M1, elastic modulus M2) to form a structured matrix importance_matrix. This matrix can intuitively display the close relationship between each fractal dimension and different mechanical parameters, providing a quantitative basis for the subsequent "determining the relative importance of fractal dimensions at each scale based on the degree of correlation." If the absolute value of ρD1,M1 is large, it means that the correlation between the fractal dimension of macroscopic cracks and compressive strength is high. When assessing rock damage, D1 is relatively more important, which in turn affects the construction of the initial matrix and the determination of the weight coefficient in the hierarchical analysis method. Integrating multiple groups of correlation coefficients in matrix form lays the foundation for the subsequent determination of the relative importance of fractal dimensions and weight calculation.

[0251] Optionally, establishing an initial matrix according to the analytic hierarchy process criteria includes constructing a judgment matrix:

[0252]

[0253] The matrix is ​​a 3×3 square matrix, corresponding to the three fractal dimensions in the technical solution: macro crack fractal dimension D1, micro fracture fractal dimension D2, and micro pore fractal dimension D3. The matrix row and column numbers 1, 2, and 3 correspond to D1, D2, and D3 respectively. The element 1 in the first row and first column indicates that the importance ratio of D1 to itself is 1; the element a in the first row and second column indicates that the importance ratio of D1 to itself is 1. 12 Indicates the importance ratio of D1 to D2.

[0254] When calculating matrix elements,

[0255] in,

[0256] a ij It represents the importance ratio of fractal dimension i to j and is an element of the judgment matrix. For example, a12 represents the importance ratio of macro crack fractal dimension D1 to micro fracture fractal dimension D2. This ratio is expressed by weight i and weight j The ratio calculation of reflects the relative importance of the two fractal dimensions in rock damage assessment.

[0257] weight i It represents the comprehensive weight value of the i-th fractal dimension i=1,2,3, corresponding to D1,D2,D3. It is obtained by the absolute value of the correlation coefficient between the fractal dimension and the two mechanical parameters, compressive strength M1 and elastic modulus M2 |ρD i , M j For example, weight1 is the sum of |ρD1,M1| of D1 and compressive strength M1, and |ρD1,M2| of D1 and elastic modulus M2, multiplied by the corresponding mechanical parameter weights w1 and w2, respectively. That is, weight1 = w1·|ρD1,M1|+w2·|ρD1,M2|.

[0258] w j : represents the jth mechanical parameter, j = 1, 2, corresponding to the weights of compressive strength M1 and elastic modulus M2. This can be determined using the entropy weighting method. The entropy weighting method determines the weight based on the degree of dispersion of the mechanical parameter data. The greater the dispersion (the lower the information entropy), the higher the weight, reflecting the importance of the mechanical parameter in the assessment. For example, if the data for compressive strength M1 is highly dispersed, its weight w1 will be relatively high.

[0259] |ρD i , M j| represents the absolute value of the correlation coefficient between the i-th fractal dimension and the j-th mechanical parameter. In the technical solution, the Spearman correlation coefficient ρD between the fractal dimensions D1, D2, D3 and the mechanical parameters compressive strength M1 and elastic modulus M2 is calculated. i , M j For example, |ρD2,M1| reflects the absolute value of the correlation between the microscopic fracture fractal dimension D2 and the compressive strength M1. The larger the absolute value, the closer the correlation between the two. i The greater the contribution to the comprehensive weight of D2.

[0260] weight j It represents the comprehensive weight of one of the j-th fractal dimension, such as the macroscopic crack fractal dimension D1, the microscopic fracture fractal dimension D2, and the microscopic pore fractal dimension D3. The comprehensive weight is obtained by calculating the absolute value of the correlation coefficient between the j-th fractal dimension and the mechanical parameters compressive strength M1 and elastic modulus M2. j , M k |(k=1,2) is weighted summed to obtain

[0261] where w k is the weight of the corresponding mechanical parameter, weight j Calculation method and weight i same.

[0262] Thus, the initial matrix is ​​established according to the criterion of the hierarchical analysis method, which includes the following steps: First, by calculating |ρD i ,M j | Quantify the correlation between fractal dimension and mechanical parameters. Then, the entropy weight method is used to determine the mechanical parameter weight w j and through Calculate the comprehensive weight of each fractal dimension i , in order to determine the relative importance of each fractal dimension. Finally, by Calculate the judgment matrix elements and construct the initial matrix.

[0263] For the entropy weight method, the mechanical parameter weight w is determined j ,

[0264] in,

[0265] in,

[0266] x ij : represents the jth mechanical parameter value of the i-th rock sample. For example, when j = 1, x i1represents the compressive strength of the i-th rock sample; when j = 2, x i2 represents the elastic modulus of the i-th rock sample.

[0267] p ij :To x ij Normalized data. Data normalization is achieved by dividing the jth mechanical parameter value of the i-th sample by the sum of the jth mechanical parameter values ​​of all samples. For example, calculate the sum of the compressive strength of all rock samples Then use the compressive strength x of each sample i1 Dividing by this sum, we get p i1 , which reflects the proportion of the mechanical parameter value of a single sample in the total.

[0268]

[0269] e j : represents the entropy value of the jth mechanical parameter, used to measure the degree of data dispersion. For example, when j = 1, e1 represents the entropy value of the mechanical parameter compressive strength. The smaller the entropy value, the greater the degree of data dispersion of the mechanical parameter, and the higher the discrimination and the greater its importance in assessing rock damage.

[0270]

[0271] w j : represents the weight of the jth mechanical parameter. When j = 1, w1 is the weight of the compressive strength; when j = 2, w2 is the weight of the elastic modulus. j Perform "reverse transformation" on the entropy value (the entropy value is small, 1-e j Large), and then divided by the two mechanical parameters (1-e k ) is normalized to obtain the final weight.

[0272] In an optional solution, the step of determining the relative importance of the fractal dimensions of each scale according to the degree of correlation further includes the following steps:

[0273] Data preparation: Get the mechanical parameter value x of each rock sample ij (such as compressive strength, elastic modulus).

[0274] Normalization: By The mechanical parameter values ​​are normalized to make mechanical parameters of different magnitudes comparable.

[0275] Calculating entropy: Using Calculate the entropy value e of each mechanical parameter j , to evaluate the degree of data dispersion.

[0276] Determine weight: by Calculate the mechanical parameter weight w j The mechanical parameter with large discreteness and small entropy value has a weight w j Higher, indicating more importance in rock damage assessment.

[0277] Apply weight: w j Substitution Calculate the comprehensive weight of the fractal dimension at each scale i , and then determine the relative importance of fractal dimension, providing a basis for constructing the judgment matrix of hierarchical analysis method.

[0278] The entropy weight method formula converts the discrete characteristics of the mechanical parameters of rock samples into evaluation weights by quantifying the weights of mechanical parameters. It is a key link in determining the relative importance of fractal dimensions and constructing a judgment matrix, which ultimately affects the accurate calculation of the rock damage weight coefficient.

[0279] The weight coefficients of the contribution of fractal dimensions at each scale to rock damage are calculated, including the calculation of eigenvectors based on the power iteration method. The formula is as follows:

[0280]

[0281] where w (k) is the eigenvector of the kth iteration. A random eigenvector can be given initially (it must meet certain conditions, such as each element is non-negative and the sum is 1, etc.); A is the judgment matrix constructed previously; ||·|| is the vector norm used to calculate Aw (k) Normalize. Through multiple iterations, the eigenvector w (k) It gradually converges to a stable weight coefficient vector w, whose elements are the estimated values ​​of the weight coefficients of the contribution of fractal dimensions at various scales to rock damage.

[0282] After obtaining the weight coefficient vector w, use the maximum eigenvalue formula Calculate the maximum eigenvalue λ of the judgment matrix A max Where n is the order of the judgment matrix A (n = 3 in this solution, (Aw) i is the i-th element of the vector obtained by multiplying the matrix A by the eigenvector w, i is the i-th element of the eigenvector w.

[0283] Verifying the validity of the matrix through consistency index testing includes calculating a consistency index, and obtaining a consistency test result based on the comparison between the consistency index and a consistency threshold.

[0284] According to the calculated maximum eigenvalue λ max , using the consistency index formula Calculate the consistency index CI. CI is used to quantify the consistency of the judgment matrix. The smaller the value, the better the consistency.

[0285] By using the consistency ratio formula Calculate the consistency ratio (CR). RI is the random consistency index, which can be obtained by looking up the table based on the order n of the judgment matrix. Compare the calculated CR with the specified threshold of 0.1. If CR < 0.1, the judgment matrix is ​​considered to have acceptable consistency and the previously calculated weight coefficients are reliable. If CR ≥ 0.1, the judgment matrix needs to be readjusted and the above steps of calculating the weight coefficients and checking consistency need to be repeated.

[0286] Establish a comprehensive fractal damage calculation formula. If the judgment matrix passes the consistency test, the calculated weight coefficient w i , calculate the normalized weight coefficient And establish a comprehensive fractal damage calculation formula Where D is the comprehensive fractal damage value, D i is the i-th fractal dimension. This formula can be used to calculate the comprehensive damage degree of a rock sample based on the values ​​of fractal dimensions at different scales. Specifically, in this embodiment, the formula for calculating comprehensive fractal damage can be written as D = a1D1 + a2D2 + a3D3, where D1 is the macroscopic crack fractal dimension, D2 is the microscopic fracture fractal dimension, and D3 is the microscopic pore fractal dimension.

[0287] The weight coefficients of the three scale fractal dimensions calculated in this embodiment for the contribution of rock damage are a1=0.375, a2=0.562, and a3=0.063;

[0288] The established fractal damage calculation formula D=0.375D1+0.562D2+0.063D3 is obtained.

[0289] The calculation results of matrix A in this embodiment are as follows:

[0290] Importance value D1 D2 D3 D1 1 1 / 2 8 D2 2 1 7 D3 1 / 8 1 / 7 1

[0291] When the consistency test is performed in this embodiment, the n matrix order is equal to 3, the random consistency index (RI) is calculated to be 0.58, and the consistency ratio (CR) is calculated to be 0.0665, which is less than 0.1, indicating that the consistency is acceptable.

[0292] Optionally, when establishing the initial matrix, the relative importance values ​​of the fractal dimensions at each scale are determined through historical experimental data, and the values ​​are used as matrix elements.

[0293] In this example, relative importance values ​​were determined using historical experimental data, providing objective data support. This historical experimental data reflects the actual conditions of rock samples from past studies. Scientific data analysis methods can reveal the inherent connection between fractal dimensions at various scales and rock damage, making the conclusions more objective and reliable. This improves the accuracy of determining the relative importance of fractal dimensions at various scales, thereby constructing a more reasonable initial matrix and laying a solid foundation for the subsequent analytic hierarchy process. This approach allows the model to better adapt to different research scenarios and data characteristics.

[0294] Optionally, the multi-scale rock damage evolution fractal model is constructed based on the weight coefficients, specifically in the following steps:

[0295] Based on the comprehensive fractal damage calculation formula, the rock fractal damage variable formula is established:

[0296]

[0297] get:

[0298]

[0299] Where DF is the damage variable;

[0300] ΔF N0 It is the difference in the comprehensive fractal dimension between the state of the rock after being soaked in ScCO2 for N hours and its undried state;

[0301] F0 is the comprehensive fractal dimension of the untreated rock;

[0302] FN is the comprehensive fractal dimension of shale after soaking in ScCO2 for N hours;

[0303] The fractal damage variables and rock loading time are fitted with polynomial functions to obtain a multi-scale rock damage evolution fractal model.

[0304] In this embodiment, it is necessary to first clarify the comprehensive fractal damage calculation formula D = a1D1 + a2D2 + a3D3 established after determining the weight coefficients of the fractal dimensions of each scale on the damage of the rock sample through the hierarchical analysis method, where D1 is the macro crack fractal dimension, D2 is the micro fracture fractal dimension, D3 is the micro pore fractal dimension, and a1, a2, and a3 are the corresponding weight coefficients.

[0305] When calculating the fractal dimension, the calculation of F0 is: for the unsoaked rock, obtain its macro crack fractal dimension D 10 , micro-fracture fractal dimension D 20 , microscopic pore fractal dimension D 30 , and then calculate its comprehensive fractal dimension according to the comprehensive fractal damage calculation formula

[0306] F0=a1D 10 +a2D 20 +a3D 30

[0307] F N Calculation: After the shale is soaked in ScCO2 for N hours, the macroscopic fracture fractal dimension D of the rock is obtained. 1N , micro-fracture fractal dimension D 2N , microscopic pore fractal dimension D 3N Then, according to the comprehensive fractal damage calculation formula, the comprehensive fractal dimension F after immersion for N hours is obtained. N =a1D 1N +a2D 2N +a3D 3N .

[0308] ΔF N0 Calculation: By F N Calculate the comprehensive fractal dimension difference between F0 and ΔF N0 =F N -F0.

[0309] Establish the rock fractal damage variable formula, according to the formula or Calculate the damage variable D F .

[0310] Obtain rock loading time data. During the experiment, accurately record relevant information of the rock from the beginning of loading to different time points to ensure the accuracy and continuity of the loading time data.

[0311] Fitting the polynomial function, the calculated fractal damage variable D F The corresponding rock loading time data is collected and collated, and a polynomial function is fitted using mathematical software. An appropriate polynomial order is selected so that the fitted polynomial function can better reflect the relationship between the fractal damage variables and the rock loading time, thereby obtaining a multi-scale rock damage evolution fractal model.

[0312] The multi-scale rock damage evolution fractal model of this embodiment is constructed based on multi-scale fractal dimensions (macro, micro, and micro), fully considering the damage characteristics of rocks at different scales. It can more comprehensively and accurately describe the damage evolution process of rocks and capture more detailed information about rock damage compared to single-scale analysis. By establishing a fractal damage variable formula, the degree of rock damage is quantified, making the description of damage more accurate and intuitive. Combined with the fitting of a polynomial function to the rock loading time, the evolution law of damage over time is further clarified, providing a quantitative basis for predicting the damage state of rocks under different loading times. In addition, the influence of the environmental factor of rock immersion in ScCO2 on the comprehensive fractal dimension of the rock is taken into account. It can simulate the damage evolution of rocks under specific environments in actual projects. It has important guiding significance for engineering fields involving the interaction between ScCO2 and rocks, such as geological storage and oil and gas production, and helps to evaluate the safety and stability of the project.

[0313] Optionally, before evaluating the damage degree of the rock to be tested based on the rock damage evolution fractal model, the rock damage evolution fractal model is compared and verified with a traditional rock damage model.

[0314] Optionally, the traditional rock damage model includes an elastic modulus damage model and a porosity damage model;

[0315] The damage variable calculation formula of the elastic modulus damage model is:

[0316]

[0317] Among them D E is the damage variable; E0 is the initial elastic modulus of unsoaked shale;

[0318] E N is the elastic modulus of shale after being soaked in ScCO2 for N hours.

[0319] The damage variable calculation formula of the porosity damage model is:

[0320]

[0321] Among them, D P represents the damage variable;

[0322] P0 represents the porosity of shale before immersion;

[0323] P N represents the porosity after immersion for N hours;

[0324] P S Represents the porosity after the shale is completely destroyed.

[0325] Optionally, the comparison and verification of the rock damage evolution fractal model and the traditional rock damage model is achieved by comparing damage evolution curves, including:

[0326] According to the elastic modulus damage calculation formula, the elastic modulus damage evolution model is established, and the elastic modulus damage model curve is drawn;

[0327] According to the damage calculation formula defined by porosity, a porosity damage evolution model is established and a porosity damage model curve is drawn;

[0328] The rock damage evolution fractal model curve drawn according to the rock damage evolution fractal model is compared with the elastic modulus damage evolution model curve and the porosity damage evolution model curve to verify the effectiveness of the rock damage evolution fractal model.

[0329] In this embodiment, a certain number and type of shale samples were selected and divided into two groups. One group served as a non-immersed control group, and the other group was immersed in ScCO2 for different lengths of time (e.g., N = 1, 24, 48, 72, 96 hours, etc.).

[0330] Mechanical parameters and porosity measurement: the initial elastic modulus E0, the elastic modulus E0 after soaking for N hours, and the porosity of the shale samples before and after soaking were measured. N , porosity P0 before immersion, porosity P after immersion for N hours N And the porosity P after shale is completely destroyed S . And obtain the relevant data of fractal dimensions at each scale (macro crack fractal dimension, micro fracture fractal dimension, micro pore fractal dimension) to construct a fractal model of rock damage evolution.

[0331] The process of establishing the traditional rock damage model and drawing the curve is as follows:

[0332] Establish the elastic modulus damage evolution model and draw the curve:

[0333] Elastic modulus is an important mechanical parameter that measures the ability of rock to resist elastic deformation. The change of its value can reflect the degree of rock damage. In, D E is the initial elastic modulus of unsoaked shale, E N is the elastic modulus of shale after N hours of immersion in ScCO2. This formula quantifies the damage variable D based on the change in elastic modulus before and after immersion. E .

[0334] refer to Figure 3The stress-strain curve shown in the figure shows that the mechanical properties of the rock change under different immersion times, including the change of elastic modulus. By conducting mechanical tests on rock samples at different immersion times, the corresponding elastic modulus data E0 and E N .

[0335] According to the elastic modulus damage calculation formula, calculate the damage variable D under different immersion times N E With immersion time N as the horizontal axis, damage variable D E Using the vertical axis, the elastic modulus damage model curve is plotted using the drawing tool. This curve shows the evolution of rock damage over time based on the change of elastic modulus.

[0336] Establish a porosity damage evolution model and draw a curve

[0337] Porosity is a parameter that describes the internal pore structure characteristics of rocks. During the ScCO2 soaking process, the pore structure of rocks will change, thus affecting the porosity. In the figure, P0 represents the porosity of shale before immersion, P N Indicates the porosity after soaking for N hours, P S Represents the porosity after shale is completely destroyed. This formula determines the damage variable D by the difference in porosity under different states. P .

[0338] The porosity of rock samples was measured by experiments to obtain the P0 and P N and P S data.

[0339] Based on the acquired data, the damage variable D under different immersion times N is calculated according to the porosity damage calculation formula. P With immersion time N as the horizontal axis, damage variable D P The porosity damage model curve is plotted on the vertical axis. This curve reflects the evolution of rock damage over time based on porosity changes.

[0340] According to the comprehensive fractal damage calculation formula, the comprehensive fractal dimension is obtained, and then the formula Calculate the fractal damage variable D F (where F0 is the comprehensive fractal dimension of unsoaked rock, F N is the comprehensive fractal dimension after immersion for N hours). With immersion time N as the horizontal axis, the fractal damage variable D F As the vertical coordinate, the fractal model curve of rock damage evolution is drawn.

[0341] The drawn rock damage evolution fractal model curve is compared with the elastic modulus damage evolution model curve and the porosity damage evolution model curve. Figure 6a The multi-scale rock damage evolution fractal model according to the embodiment of the present application shows the relationship between the damage degree and time of the rock damage evolution fractal model. The fitting equation is y=0.022ln(x)-0.0207, R 2 is the coefficient of determination, R 2 =0.9832; Figure 6b The elastic modulus damage model according to the embodiment of the present application shows the relationship between the damage degree and time of the elastic modulus model. The fitting equation is y=0.2563ln(x)-0.6542, R 2 is the coefficient of determination, R 2 =0.9811; Figure 6c The porosity damage model of the embodiment of the present application shows the relationship between the damage degree of the porosity model and time. The fitting equation is y=0.0806ln(x)-0.2683, R 2 is the coefficient of determination, R 2 =0.53. The figure shows the relationship curves between damage degree and time under different models and the corresponding fitting equations and determination coefficients R 2 By comparing the trend of the curve, the range of damage variables, the degree of fit (determination coefficient R 2 The ability and accuracy of the rock damage evolution fractal model in describing the rock damage evolution process were evaluated using factors such as the size of the rock damage evolution curve. The fractal model curve performed well in terms of fit and reflection of rock damage evolution trends, outperforming traditional model curves. This demonstrates the model's high effectiveness and ability to more accurately describe the damage evolution process of rock under ScCO2 immersion, providing a more reliable tool for rock damage assessment.

[0342] In this embodiment, the rock damage evolution fractal model is compared and verified with the traditional elastic modulus damage model and porosity damage model, and the fractal model is evaluated from different angles (mechanical properties and pore structure). The multi-dimensional verification method can more comprehensively test the accuracy and reliability of the model, reduce the limitations and errors that may exist in a single model, and ensure the credibility of the model when evaluating the degree of rock damage. Different damage models reflect different aspects of rock damage. The elastic modulus damage model focuses on the changes in the mechanical properties of the rock, the porosity damage model focuses on the changes in the pore structure inside the rock, and the rock damage evolution fractal model takes into account the fractal characteristics of the rock at multiple scales. By comparing the damage evolution curves of these models, we can gain an in-depth understanding of the damage mechanism of the rock under ScCO2 immersion, discover the influence of different factors on rock damage, and help further reveal the essential laws of rock damage. In addition, the existence of multiple damage models provides a variety of means for rock damage assessment. In actual engineering applications, the appropriate model can be selected according to specific needs and conditions. For example, if one is more concerned with changes in the mechanical properties of rock, the elastic modulus damage model can be used as a reference. If one focuses on the impact of rock pore structure on damage, the porosity damage model is more applicable. The rock damage evolution fractal model can comprehensively describe rock damage at multiple scales, providing a more comprehensive perspective for rock damage assessment in complex situations. Furthermore, by comparing it with traditional models, the scope and conditions of applicability of the rock damage evolution fractal model are clarified. This helps to accurately determine the model's effectiveness in actual engineering projects under different factors such as rock type, immersion time, and environmental conditions, thereby enabling more rational application of the model to evaluate the damage level of the rock under test and improving its application value and practicality in actual engineering projects.

[0343] Optionally, the evaluation of the damage degree of the rock to be tested based on the rock damage evolution fractal model is specifically as follows: parameters such as the loading time, loading method, and loading rate of the rock to be tested are input into the rock damage evolution fractal model, and the damage degree of the rock to be tested under corresponding conditions is output.

[0344] In this embodiment, specific parameters such as the loading time, loading method, and loading rate of the rock to be tested are taken into account. This allows the damage degree to be evaluated for the different working conditions faced by the rock in actual engineering, making the evaluation results more consistent with the actual stress damage of the rock. Compared with models that do not consider these parameters, it has stronger working condition targeting. In addition, different loading times, loading methods, and loading rates will significantly affect the damage process and degree of the rock. By inputting these parameters into the rock damage evolution fractal model, the model can integrate multi-scale fractal characteristics and these working condition parameters to more accurately simulate the damage evolution process of the rock, thereby outputting more accurate damage degree assessment results and providing a reliable basis for engineering decision-making. Furthermore, in actual engineering, parameters such as the loading time, loading method, and loading rate of the rock can be obtained in real time and input into the model to evaluate the damage degree in real time, providing strong support for real-time monitoring and safety early warning of rock structures, helping to promptly discover potential safety hazards and take appropriate measures to ensure engineering safety. Finally, accurate damage assessment results can help engineers better understand the changes in rock performance under different working conditions, thereby optimizing engineering design plans, rationally selecting construction parameters and protective measures, improving project reliability and durability, and reducing project risks and costs.

[0345] The present application also provides a rock damage assessment device, which is used to implement a rock damage assessment method, including:

[0346] Mechanical testing module, used to perform compression tests on rock samples;

[0347] A multi-scale detection module, including a CT scanner, a SEM microscope, and a liquid nitrogen adsorption instrument, is used to process the damaged rock samples to obtain the multi-scale damage fractal dimension of the damaged rock samples;

[0348] A data processing module is used to calculate the weight coefficient of each scale fractal dimension on the damage of the rock sample through the hierarchical analysis method based on the multi-scale damage fractal dimension;

[0349] A model building module for building a multi-scale rock damage evolution fractal model based on the weight coefficients

[0350] The evaluation output module is used to evaluate the damage degree of the rock to be tested based on the rock damage evolution fractal model and output the damage evaluation result.

[0351] Optionally, the device further includes a model verification module, and the model verification module is configured to:

[0352] Receive prediction data from fractal models and benchmark data from traditional damage models;

[0353] Comparison of damage evolution curves of fractal model and traditional damage model;

[0354] Output verification results, which include curve fitting indicators and error analysis data.

[0355] The above description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

Claims

1. A rock damage assessment method, characterized in that: The following steps are involved: Conduct compression tests on rock samples until they fail; Processing the damaged rock samples to obtain the multi-scale damage fractal dimension of the damaged rock samples; Based on the multi-scale damage fractal dimension, the weight coefficient of each scale fractal dimension on the damage of the rock sample is calculated by the hierarchical analysis method; Constructing a multi-scale rock damage evolution fractal model based on the weight coefficients; The damage degree of the rock to be tested is evaluated based on the rock damage evolution fractal model.

2. The rock damage assessment method according to claim 1, characterized in that: The processing of the damaged rock sample to obtain the multi-scale damage fractal dimension of the damaged rock sample specifically includes: Scanning the damaged rock sample using CT to obtain CT scanning results, and reconstructing the damaged rock sample in three dimensions using three-dimensional reconstruction software in combination with the CT scanning results to calculate the three-dimensional fractal dimension of macroscopic centimeter-level cracks; The fracture surface of the rock sample after destruction was scanned and image binarized using SEM scanning combined with two-dimensional image processing software, and the fractal dimension of the micron-level fracture surface was calculated. Liquid nitrogen adsorption experiments combined with the Frenkel-Halsey-Hill model were used to obtain the pore structure of the crushed rock samples and calculate the micro-nanoscale pore fractal dimension.

3. The rock damage assessment method according to claim 1, characterized in that: The method of determining the weight coefficient of each scale fractal dimension on the damage of the rock sample by the hierarchical analysis method specifically includes the following steps: Analyze the correlation between the fractal dimension at each scale and the mechanical parameters obtained from the rock sample during its destruction, including compressive strength and elastic modulus; Determine the relative importance of fractal dimensions at each scale based on the degree of correlation; Establish an initial matrix according to the AHP criteria; The validity of the matrix is ​​verified by a consistency index test, wherein the consistency test requires a consistency ratio of < 0.1; If the consistency test is satisfied, the weight coefficient of the contribution of each scale fractal dimension to rock damage is calculated; According to the weight coefficient, a comprehensive fractal damage calculation formula D=a1D1+a2D2+a3D3 is established, where D1 is the macroscopic crack fractal dimension, D2 is the microscopic fracture fractal dimension, and D3 is the microscopic pore fractal dimension.

4. The rock damage assessment method according to claim 1, characterized in that: The multi-scale rock damage evolution fractal model is constructed based on the weight coefficients, and the specific steps are: Based on the comprehensive fractal damage calculation formula, the rock fractal damage variable formula is established: get: Where DF is the damage variable; ΔF N0 It is the difference in the comprehensive fractal dimension between the state of the rock after being soaked in ScCO2 for N hours and its undried state; F0 is the comprehensive fractal dimension of the untreated rock; F N is the comprehensive fractal dimension of shale after being soaked in ScCO2 for N hours; The fractal damage variables and rock loading time are fitted with polynomial functions to obtain a multi-scale rock damage evolution fractal model.

5. The rock damage assessment method according to claim 1, characterized in that: Before evaluating the damage degree of the rock to be tested based on the rock damage evolution fractal model, the rock damage evolution fractal model is compared and verified with a traditional rock damage model.

6. The rock damage assessment method according to claim 5, characterized in that: The traditional rock damage model includes an elastic modulus damage model and a porosity damage model; The damage variable calculation formula of the elastic modulus damage model is: Among them D E is the damage variable; E0 is the initial elastic modulus of unsoaked shale; E N is the elastic modulus of shale after being immersed in ScCO2 for N hours; The damage variable calculation formula of the porosity damage model is: Among them, D P represents the damage variable; P0 represents the porosity of shale before immersion; P N represents the porosity after soaking for N hours; P S Represents the porosity after the shale is completely destroyed.

7. The rock damage assessment method according to claim 6, characterized in that: The comparison and verification of the rock damage evolution fractal model and the traditional rock damage model is achieved by comparing damage evolution curves, including: According to the elastic modulus damage calculation formula, the elastic modulus damage evolution model is established, and the elastic modulus damage model curve is drawn; According to the damage calculation formula defined by porosity, a porosity damage evolution model is established, and a porosity damage model curve is drawn; The rock damage evolution fractal model curve drawn according to the rock damage evolution fractal model is compared with the elastic modulus damage evolution model curve and the porosity damage evolution model curve to verify the effectiveness of the rock damage evolution fractal model.

8. The rock damage assessment method according to claim 1, characterized in that: The evaluation of the damage degree of the rock to be tested based on the rock damage evolution fractal model is specifically as follows: parameters such as the loading time, loading method, and loading rate of the rock to be tested are input into the rock damage evolution fractal model, and the damage degree of the rock to be tested under corresponding conditions is output.

9. A rock damage assessment device, characterized in that: The device is used to implement the method according to any one of claims 1 to 8, comprising: Mechanical testing module, used to perform compression tests on rock samples; A multi-scale detection module, including a CT scanner, a SEM microscope, and a liquid nitrogen adsorption instrument, is used to process the damaged rock samples to obtain the multi-scale damage fractal dimension of the damaged rock samples; A data processing module is used to calculate the weight coefficient of each scale fractal dimension on the damage of the rock sample through the hierarchical analysis method based on the multi-scale damage fractal dimension; A model building module for building a multi-scale rock damage evolution fractal model based on the weight coefficients The evaluation output module is used to evaluate the damage degree of the rock to be tested based on the rock damage evolution fractal model and output the damage evaluation result.

10. The rock damage assessment device according to claim 9, characterized in that: The device further includes a model verification module, wherein the model verification module is configured to: Receive prediction data from fractal models and benchmark data from traditional damage models; Comparison of damage evolution curves of fractal model and traditional damage model; Output verification results, which include curve fitting index and error analysis data.

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