System and method for calculating NSCB sample shale I-type fracture toughness size effect
By using NSCB samples and three-point bending loading methods in shale, combined with dimensionless energy release rate and linear regression analysis, a shale type I fracture toughness dimensional effect calculation model was established, which solved the accuracy and reliability of shale fracture behavior prediction in the existing technology, achieved more accurate fracture toughness prediction, and provided more reliable theoretical support for hydraulic fracturing design.
Patent Information
- Application Number
- CN202510189638.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-20
- Publication Date
- 2025-05-23
AI Technical Summary
The prior art has problems of accuracy and reliability in predicting fracture behavior of shale in different sizes and directions, and cannot adequately capture the heterogeneity and anisotropic characteristics of shale.
The fracture toughness value was measured experimentally by using NSCB samples combined with three-point bending loading method, and the fracture toughness size effect calculation model was established using dimensionless energy release rate and linear regression analysis.
This model can accurately predict the fracture toughness of shale samples of different sizes, reveal the dimensional effect law of shale fracture toughness, and provide more reliable theoretical support for hydraulic fracturing design optimization.
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Figure CN120030786A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of shale gas exploitation, and in particular to a system and method for calculating the size effect of type I fracture toughness of NSCB sample shale. Background Art
[0002] As an important unconventional natural gas resource, the efficient exploitation of shale gas is of great significance to the global energy supply. As a key means of shale gas exploitation, hydraulic fracturing technology is based on the formation of a fracture network in the shale layer through high-pressure water flow, thereby increasing the permeability of shale gas and improving the extraction efficiency. Commonly used fracturing technologies include multi-stage fracturing, clean water fracturing, hydraulic jet fracturing, repeated fracturing and synchronous fracturing technology. In this process, the fracture toughness of shale becomes the core parameter for controlling the initiation and expansion of cracks. Fracture toughness refers to the ability of a material to resist crack propagation. For shale, its fracture toughness is not only affected by factors such as mineral composition and microstructure, but also significantly affected by the size of the sample, that is, there is an obvious size effect.
[0003] Type I fracture, also known as opening fracture, is a basic fracture mode in fracture mechanics. In type I fracture, the crack is subjected to normal stress perpendicular to the crack surface, causing the crack to open along its length. For shale, type I fracture is one of the most common fracture modes during hydraulic fracturing. Therefore, in-depth research on the fracture toughness and size effect of shale in type I fracture mode is of great significance for understanding the fracture behavior of shale and optimizing hydraulic fracturing design.
[0004] The size effect refers to the difference in the mechanical properties of a material as the size of the sample changes. In the fracture toughness test of shale, samples of different sizes may show completely different fracture behaviors and fracture toughness values. This is mainly due to the presence of a large number of defects such as microcracks, pores and bedding in the shale. The distribution and density of these defects may vary greatly in samples of different sizes, which affects the reliability and accuracy of the test results. Therefore, in-depth research on the size effect of shale fracture toughness and the establishment of an accurate size effect model are of great significance for optimizing hydraulic fracturing design and improving shale gas extraction efficiency.
[0005] In the prior art, there have been a number of achievements in the study of size effect models.
[0006] Bazant fracture toughness size effect model: Based on the energy release theory, this model introduces the size effect factor and establishes the mathematical relationship between fracture toughness and specimen size, which can effectively predict the fracture toughness of quasi-brittle materials, especially for heterogeneous and anisotropic rock materials such as shale.
[0007] Fracture size effect model based on MMTS criterion: By introducing high-order stress terms and considering the length of the fracture process zone, the Williams stress expansion series is corrected, which significantly improves the accuracy of predicting material fracture behavior. It is particularly suitable for complex fracture problems, but the model is relatively complex and needs to be adaptively adjusted for different materials.
[0008] Bazant shear size effect model: Using fracture mechanics and statistical size effect theory, the shear failure formula derived by Bazant is used to simulate and analyze the nominal shear strength in shear failure, which is suitable for the study of rock shear failure process.
[0009] Plastic shear strain gradient model of rock specimen size effect: Considering the stable shear band formed under uniaxial compression and its size effect, the nominal shear strength of samples of different sizes in shear failure can be predicted more accurately. However, under extreme load conditions or complex stress states, the prediction results have certain deviations.
[0010] Statistical constitutive model of rock damage considering size effect: Based on the strain strength theory of rock, it adopts the damage mechanics theory and includes the damage evolution equation. It can describe the whole process of rock from loading to final failure, but the parameters need to be fitted by experimental data, which may bring uncertainty.
[0011] Secant modulus size effect model for rocks with rough joints: The influence of joint size and inclination on the mechanical properties of rocks is studied through numerical simulation, which improves the accuracy of strength prediction of rocks with different joints. However, it is not applicable to rocks with larger joints or joints containing fillings.
[0012] Based on the PFC2D rock particle crushing strength and energy fractal model: using the fractal dimension D to represent the energy and strength of rock particle crushing can more accurately predict the fracture behavior caused by microcracks or defects inside the material, and is suitable for the study of rock particle crushing strength and energy.
[0013] Concrete equivalent crack fracture model based on size effect: Using a virtual crack model to describe the distribution law of crack closure force can more accurately predict the fracture behavior caused by microcracks or defects inside the material, and is suitable for fracture research of materials such as concrete.
[0014] The above model has the following disadvantages.
[0015] Limitations of specimen configuration: Existing fracture toughness test methods, such as SR, CB, CCNBD and NSCB specimens, may not be able to fully simulate the complex stress state of shale during actual hydraulic fracturing. These specimen configurations may not fully capture the heterogeneity and anisotropy of shale, resulting in differences between test results and practical applications.
[0016] Applicability of size effect models: Existing size effect models, especially the Bazant model, although theoretically widely applicable, may need to be adjusted and validated when applied to heterogeneous and anisotropic materials such as shales. These models may not accurately predict the fracture behavior of shales at different sizes and directions.
[0017] Accuracy and reliability of test results: Due to the heterogeneity of shale, the fracture toughness test results between different samples may vary greatly, which affects the accuracy and reliability of the test results. In addition, errors in sample preparation and test operation may also affect the test results.
[0018] The influence of internal structure and defects of shale: The structure and defects of shale, such as microcracks, pores and bedding, have a significant impact on its fracture toughness. Existing technologies may not be able to accurately simulate the influence of these internal features on the fracture process.
[0019] Universality of models: The universality of existing models may be affected by the properties of the shale itself (such as mineral composition, pore structure, etc.) and experimental conditions (such as loading rate, ambient temperature, etc.). Models may need to be adjusted and verified for different shale types and experimental conditions. Summary of the invention
[0020] The technical problem to be solved by the present invention is to provide a system and method for calculating the size effect of type I fracture toughness of NSCB sample shale, which can solve the shortcomings of the existing technology, more accurately predict the fracture toughness of shale at different sizes, and provide more reliable theoretical support for the optimization of hydraulic fracturing design.
[0021] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows.
[0022] A method for calculating the size effect of type I fracture toughness of NSCB specimen shale includes the following steps:
[0023] A. Prepare NSCB specimens, use the NSCB specimens to carry out load loading tests, and measure the mode I fracture toughness values of the NSCB specimens;
[0024] B. Obtain the dimensionless energy release rate g(α 0 ) calculation formula;
[0025] C. Calculate the corrected peak load, set the definition of coordinate points and perform linear regression analysis;
[0026] D. Calculate the fracture energy and obtain the length r of the fracture process zone of the infinite sample c∞ and the fracture toughness value when the size of NSCB specimens tends to infinity The calculation formula of
[0027] E. Use the radius of the NSCB specimen, the thickness of the NSCB specimen, and the peak load to calculate the ordinate value of the linear regression. Perform linear regression with the radius R of the NSCB specimen as the abscissa to obtain the linear regression equation. Substitute the slope A and intercept C of the linear regression equation into r c∞ and The calculation formula for r c∞ and Substitute the calculated value of The calculation formula of the size effect of mode I fracture toughness of the current NSCB specimen is obtained, where g′(α 0 ) is g(α 0 )About α 0 The derivative of .
[0028] Preferably, in step A, the method for preparing the NSCB sample is:
[0029] The large rock sample was processed into a cylinder by a coring machine, and then cut into a disc by a cutting machine and the two end faces were polished. The whole disc was then cut into two symmetrical half discs. The initial crack was opened in the center of the cutting plane of the half disc using a hydraulic knife cutting process to obtain the NSCB specimen.
[0030] Preferably, in step A, the test process of the load loading test is:
[0031] A force column is set at the center of the semicircular top surface of the NSCB specimen, and two supporting columns are symmetrically set on the bottom surface on the side of the semicircular top surface. Then, a load force is applied to the force column. The load force is gradually increased, and the mode I fracture toughness value of the NSCB specimen is measured.
[0032] As a preferred embodiment, in step B,
[0033] Nominal strength of NSCB specimen σ n The calculation formula is Where F is the maximum load, C n is the inherent coefficient of the NSCB specimen, b is the thickness of the NSCB specimen, d is the characteristic size of the NSCB specimen, and the characteristic size is the radius of the NSCB specimen; σ n / 2E′ represents the strain energy density, then the strain energy U is Where V represents the volume of the NSCB sample, that is, V = bd 2 ; f(α 0 ) is a function related to the crack length of the NSCB specimen; α 0 =a 0 / d represents the dimensionless crack length, a 0 represents the crack length of the NSCB specimen; under plane stress state, E′=E; under plane strain state, E′=E / (1-v2 ); E represents Young's modulus, v is Poisson's ratio; the energy release rate G is Right now in g(α 0 ) represents the geometric shape function of the NSCB specimen, i.e., the dimensionless energy release rate, k(α 0 ) is a function related to the specimen configuration and loading method;
[0034] The stress intensity factor K of NSCB specimen under linear elastic conditions Ic The relationship between the energy release rate G satisfies the formula Right now R is the radius of the NSCB specimen, B is the thickness of the NSCB specimen, and Y represents the dimensionless stress intensity factor. The calculation formula for Y of the NSCB specimen structure is:
[0035]
[0036] The expression of dimensionless energy release rate of NSCB specimen is:
[0037] Preferably, in step C,
[0038] The calculation formula for the modified peak load is: Where E j is the deadweight of the NSCB specimen, and n is the total number of specimens of the same material;
[0039] The analysis process of linear regression is to first calculate the coordinate point (X j , Y j ), and set the definition of the coordinate point for this, where X j =R j , R j is the radius of sample j, Y j =(B j R j / F j ) 2 , B j is the thickness of sample j, F j is the peak load of sample j, and the regression line equation is Y=AX+C, In the formula,
[0040] Preferably, in step D,
[0041] The calculation process of fracture energy is as follows: the nominal strength σ n The calculation formula is transformed into Substituting into the static size effect formula In, get When F→peak load F max When , the above formula can be transformed into Get fracture energy
[0042] Combining the above formula, we get
[0043] Under linear elastic conditions, the stress intensity factor of the NSCB specimen satisfies the following relationship with the energy release rate G: IC 2 =GE'; where E' is the plane strain state, E' = E / (1-υ 2 ), υ is Poisson’s ratio. When the sample is infinite, i.e. R→∞, G→G f , under plane strain state In the formula, E' is the plane stress state, E' = E, under the plane stress state
[0044] A NSCB sample shale type I fracture toughness size effect calculation system, used for the above-mentioned NSCB sample shale type I fracture toughness size effect calculation method, comprising:
[0045] Load loading test module, used to carry out load loading test on NSCB specimens and measure the mode I fracture toughness value of NSCB specimens;
[0046] Dimensionless energy release rate g(α 0 ) calculation module, used to calculate the dimensionless energy release rate g(α 0 );
[0047] Linear regression analysis module, used to perform linear regression analysis to obtain the modified peak load and regression line equation;
[0048] The length of the fracture process zone of the infinite sample r c∞ And the fracture toughness value when the NSCB specimen size tends to infinity Calculation module, used to calculate r c∞ and
[0049] The module for generating the calculation formula for the size effect of type I fracture toughness is used to generate the calculation formula for the size effect of type I fracture toughness.
[0050] The beneficial effect brought about by adopting the above technical solution is that the shale type I fracture toughness size effect model constructed by the present invention can accurately predict the fracture toughness of shale samples of different sizes by combining experimental data and theoretical analysis. The model can reveal the size effect law of shale fracture toughness and provide an important theoretical basis for the optimization of hydraulic fracturing design. This not only improves the understanding of the mechanical properties of shale, but also can effectively guide the efficient exploitation of shale gas, improve fracturing efficiency and safety, reduce construction costs, and provide a scientific basis for selecting appropriate fracture toughness parameters according to specific stress states in actual engineering.
[0051] During the model construction process, the NSCB specimen is first combined with the three-point bending loading method. This specimen configuration can more effectively simulate the complex stress state of shale during the actual hydraulic fracturing process, and can more accurately capture the heterogeneity and anisotropy of shale compared to the traditional specimen structure. Compared with the existing size effect model, the constructed model has stronger applicability and accuracy, and can provide a more reliable theoretical basis for hydraulic fracturing design optimization. In addition, the present invention also conducts in-depth research on the fracture toughness under two different states of plane stress and plane strain, and provides more comprehensive theoretical calculation values and prediction formulas, further enriching the application scope of the model and its engineering guidance significance. These innovations make the application of the present invention in the field of shale gas extraction have significant technical advantages and practical value. BRIEF DESCRIPTION OF THE DRAWINGS
[0052] Figure 1 It is a schematic diagram of the NSCB sample loading configuration in a specific embodiment of the present invention.
[0053] Figure 2 This is a photograph of a NSCB sample in a specific embodiment of the present invention.
[0054] Figure 3 It is a system principle diagram of a specific implementation mode of the present invention.
[0055] Figure 4 It is a regression line coordinate diagram of a specific embodiment of the present invention. DETAILED DESCRIPTION
[0056] Test measurement
[0057] The NSCB (Notched Semi-Circular Bend) specimen was used to conduct the test by three-point bending loading to simulate the fracture behavior of shale in the actual stress process. In the NSCB structure, the specimen is usually processed into a semicircle and a straight groove is opened in the center. This groove can be regarded as a prefabricated crack, and the crack initiation and expansion process in the rock is simulated by applying a load to the vertex.
[0058] The schematic diagram of the loading configuration of the NSCB specimen in this test is as follows: Figure 1 The direction of the deadweight and the load of the specimen are both vertically downward, the specimen is subjected to a concentrated load F, the radius of the disk is R, the thickness of the disk is greater than 0.8R or 30mm, and the ratio of the crack length to the radius is a 0 / R ranges from 0.4 to 0.6. In this study, the disk thickness is B = D / 2, and the initial length of the crack is set to a 0 / R=0.3, the distance between the two support points is S, and the distance between the left and right support points satisfies S / 2R=0.8.
[0059] The test samples come from Sichuan Longmaxi shale, which is processed into NSCB specimens of different diameters (25mm, 50mm, 75mm, 100mm). Before processing the samples, the core is a large rock sample, which is processed into a cylinder by a professional coring machine, and then cut into a disc by a cutting machine and polished on both ends. Then the entire disc is cut into two symmetrical semicircles. For the cutting of the initial cracks, hydraulic knife cutting technology is used to ensure the accuracy of NSCB sample processing. In order to study the effect of sample size on rock fracture toughness, a total of four NSCB specimens with diameters of 25mm, 50mm, 75mm, and 100mm were made, as shown in the table below.
[0060] Table 1 Specimen preparation dimensions details
[0061]
[0062] The experimental system of this study consists of a load loading system, a DIC image acquisition system and the latest version of the DS5 acoustic emission data acquisition system. In this experiment, all NSCB specimens were placed on a three-point loading base and loaded by a pressure head in displacement control mode. Four acoustic emission probes were placed on the front and back sides of the specimen to monitor the acoustic emission signal in real time. At the same time, a high-speed camera was used to capture images of the deformation and fracture process of the NSCB specimen during the load loading process.
[0063] Before the test, the surface of the shale sample was first polished with sandpaper, and then the surface of the sample was evenly sprayed with white matte paint to provide a high-contrast background, which is crucial for edge recognition and displacement measurement of images in DIC technology. After the white paint dried, black matte paint was sprayed on the top of the sample, so that the black paint particles were evenly scattered on the surface of the sample to form speckles. By analyzing the changes in the position of these speckles before and after loading, we can accurately calculate the deformation of the sample surface and obtain the data required for the test.
[0064] By conducting type I fracture toughness tests on shale NSCB specimens of different diameters, the influence of specimen size on shale fracture toughness was deeply analyzed. The study found that with the increase of specimen size, the load-displacement curve of shale specimens showed obvious stage changes. Small-sized specimens mainly showed two-stage characteristics from linear elasticity to failure, while large-sized specimens included three-stage characteristics of compaction, linear elasticity and failure. This experiment innovatively divided the load-displacement curve of the specimen into three stages: I-fracture compaction stage, II-linear elastic stage and III-post-peak failure stage. In addition, the peak load increased significantly with the increase of specimen diameter. From 25mm to 100mm specimens, the average peak load increased from 0.57kN to 5.86kN, indicating that large-sized specimens have greater bearing capacity and deformation before failure. In terms of fracture toughness, with the increase of specimen diameter, the fracture toughness generally showed a trend of slow increase. When the sample diameter increases from 25mm to 100mm, the average value of NSCB shale fracture toughness increases from 0.96MPa.m1 / 2 to 1.22MPa.m1 / 2, with an increase of 10.1%, 8.19% and 6.82% respectively. This discovery reveals the significant size effect of shale fracture toughness, that is, larger samples have higher fracture toughness values due to more uniform stress distribution, while smaller samples have lower fracture toughness test values due to stress concentration at the edges or corners. These research results not only deepen the understanding of shale mechanical properties, but also provide an important theoretical basis for the optimization of hydraulic fracturing design, especially in predicting and controlling the path and range of crack extension.
[0065] In order to analyze the evolution characteristics of the displacement field and strain field of the specimen during the loading and rupture process, this experiment selected four key points (A, B, C, and D) in three stages, and analyzed the distribution and change characteristics of the horizontal and vertical displacement fields and the horizontal strain field through digital image correlation technology (DIC). Point A is the starting point of the formal loading of the test, at which time the speckle image of the specimen begins to be collected. Point B corresponds to the compaction stage, and the specimen undergoes significant compaction deformation. Point C is in the linear elastic stage, and the specimen exhibits elastic deformation characteristics. Point D is the peak load point, at which time the macro crack has formed and completed the destruction process.
[0066] The displacement field and strain field of shale samples during loading were analyzed in detail using digital image correlation (DIC) technology. The study found that in the initial loading stage, the displacement field and strain field distribution of the sample had no obvious regularity, and the displacement contours were randomly distributed. As the loading progressed, the sample entered the compaction stage. At this time, the horizontal displacement field showed that the right end of the sample deformed to the right as a whole, and the left end deformed to the left as a whole, while the vertical displacement field was symmetrically distributed, and the sample deformed downward as a whole. After entering the linear elastic stage, the contour lines of the displacement field and strain field began to be "layered", with a clear displacement direction and symmetry about the extension line of the prefabricated crack. When the peak load was reached, the crack propagation was completed rapidly, the displacement field variation range was significantly expanded, the strain field was significantly localized, and the crack propagated along the path with the most concentrated strain. These studies not only revealed the evolution characteristics of the displacement field and strain field of shale at different loading stages, but also provided an important theoretical basis for understanding the failure mechanism of shale and optimizing hydraulic fracturing design.
[0067] This experiment deeply analyzed the changing characteristics of the two parameters of acoustic emission cumulative ring count and cumulative impact number during the shale loading process and their influence on the shale failure mechanism. By monitoring the acoustic emission of shale samples of four different sizes, the study revealed the changing rules of cumulative impact number and cumulative ring count in different loading stages, and compared them with the load-displacement curve.
[0068] The internal damage and fracture process of shale samples at different loading stages were deeply analyzed through acoustic emission tests. The study found that the activity of acoustic emission signals increased significantly with the increase of sample size. In the compaction stage, the sample almost did not generate acoustic emission signals because the internal microcracks gradually closed under the load. After entering the linear elastic stage, the acoustic emission signal gradually increased, and the cumulative ringing count and the cumulative number of impacts began to rise. When the load on the sample approached the peak, both parameters showed a significant surge, indicating that the crack propagation accelerated. In addition, larger-sized samples produced stronger acoustic emission signals due to the accumulation of more internal microcracks and damage. However, as the sample size increased, the cumulative number of impacts showed a downward trend, which may be due to the attenuation effect of the acoustic emission signal during the propagation process inside the larger sample. These studies not only reveal the acoustic emission characteristics of shale at different loading stages, but also provide an important theoretical basis for understanding the failure mechanism of shale and optimizing hydraulic fracturing design.
[0069] This test uses the DS5 series dynamic and static full-information acoustic emission all-in-one machine, which is mainly composed of acoustic emission sensors, HV-400V high-voltage power amplifiers, DS5 series acoustic emission instruments and acoustic emission acquisition and analysis systems DS5AE. A total of 4 acoustic emission probes are used on the front and rear ends of the NSCB sample, and they are clamped with a fixing device after coupling with vaseline, which can more accurately receive the acoustic emission signals generated by the shale rock sample under load and fracture.
[0070] In order to make the fracture process of the specimen during loading, the loading data acquisition system and the image acquisition system keep the same time, this test adopts a synchronous triggering method. This test uniaxially compresses four specimens with diameters D of 100, 75, 50, and 25 mm. Six parallel tests are set for each specimen diameter test, totaling 24 specimens. The specific test plan is shown in the table below.
[0071] Table 2 Test plan
[0072]
[0073] Size effect model of type I fracture in shale
[0074] The systems used to build this model include:
[0075] Load loading test module, used to carry out load loading test on NSCB specimens and measure the mode I fracture toughness value of NSCB specimens;
[0076] Dimensionless energy release rate g(α 0 ) calculation module, used to calculate the dimensionless energy release rate g(α 0 );
[0077] Linear regression analysis module, used to perform linear regression analysis to obtain the modified peak load and regression line equation;
[0078] The length of the fracture process zone of the infinite sample r c∞ And the fracture toughness value when the NSCB specimen size tends to infinity Calculation module, used to calculate r c∞ and
[0079] The module for generating the calculation formula for the size effect of type I fracture toughness is used to generate the calculation formula for the size effect of type I fracture toughness.
[0080] The model building process is as follows:
[0081] Firstly, the fracture toughness values of NSCB specimens of different sizes were experimentally measured to obtain basic data.
[0082] Then the dimensionless energy release rate g(α 0 ) is calculated using the formula. The nominal strength of the NSCB specimen is σ n The calculation formula is Where, F is the maximum load, Cn is the inherent coefficient of the NSCB specimen, b is the thickness of the NSCB specimen, d is the characteristic dimension of the NSCB specimen, and the characteristic dimension is the radius of the NSCB specimen; σ n / 2E′ represents the strain energy density, then the strain energy U is Where V represents the volume of the NSCB sample, that is, V = bd2; f(α 0 ) is a function related to the crack length of the NSCB specimen; α 0 =a 0 / d represents the dimensionless crack length, a 0 represents the crack length of the NSCB specimen; under plane stress state, E′=E; under plane strain state, E′=E / (1-v 2 ); E represents Young's modulus, v is Poisson's ratio; the energy release rate G is Right now in g(α 0 ) represents the geometric shape function of the NSCB specimen, i.e., the dimensionless energy release rate, k(α 0 ) is a function related to the specimen configuration and loading method;
[0083] The stress intensity factor K of NSCB specimen under linear elastic conditions Ic The relationship between the energy release rate G satisfies the formula Right now R is the radius of the NSCB specimen, B is the thickness of the NSCB specimen, and Y represents the dimensionless stress intensity factor. The calculation formula for Y of the NSCB specimen structure is:
[0084]
[0085] The expression of dimensionless energy release rate of NSCB specimen is:
[0086] Then calculate the corrected peak load, set the coordinate point definition and perform linear regression analysis. The calculation formula for the corrected peak load is Where W j is the deadweight of the NSCB specimen, and n is the total number of specimens of the same material;
[0087] The analysis process of linear regression is to first calculate the coordinate point (X j , Y j ), and set the definition of the coordinate point for this, where X j =R j , R j is the radius of sample j, Y j =(B j R j / F j ) 2 , B j is the thickness of sample j, F j is the peak load of sample j, and the regression line equation is Y=AX+C, In the formula,
[0088] Then calculate the fracture energy and obtain the length r of the fracture process zone of the infinite sample c∞ and the fracture toughness value when the size of NSCB specimens tends to infinity The calculation process of fracture energy is to convert the nominal strength σ n The calculation formula is transformed into Substituting into the static size effect formula In, get When F→peak load F max When , the above formula can be transformed into Get fracture energy
[0089] Combining the above formula, we get
[0090] Under linear elastic conditions, the stress intensity factor of the NSCB specimen satisfies the following relationship with the energy release rate G: KIC 2 =GE'; where E' is the plane strain state, E' = E / (1-υ 2 ), υ is Poisson’s ratio. When the sample is infinite, i.e. R→∞, G→G f , under plane strain state In the formula, ' is the plane stress state, e' = E, under the plane stress state
[0091] Finally, the ordinate value of the linear regression is calculated using the radius of the NSCB specimen, the thickness of the NSCB specimen, and the peak load. The linear regression equation is obtained by taking the radius R of the NSCB specimen as the abscissa. Figure 4 , the slope of the regression line of this experiment is A = 2.86473 and the intercept is C = 0.04371. 0 =0.3, r c∞ =0.004577394727, under plane strain state, In plane stress state Substitute the slope A and intercept C of the linear regression equation into r c∞ and The calculation formula for r c∞ and Substitute the calculated value of The calculation formula of the size effect of mode I fracture toughness of the current NSCB specimen is obtained, where g′(α 0 ) is g(α 0 )About α 0 The derivative of .
[0092] Under plane strain state,
[0093] Under plane stress state,
[0094] This model can accurately predict the fracture toughness of shale samples of different sizes by combining experimental data and theoretical analysis. Specifically, the model first obtains basic data by experimentally measuring the fracture toughness values of NSCB samples of different sizes. Then, through the analysis of energy release rate, the concept of dimensionless energy release rate is introduced, and the size effect formula applicable to plane stress and plane strain states is derived. This model determines the key parameters through linear regression analysis, thereby improving the accuracy of prediction. The model can reveal the size effect law of shale fracture toughness and provide an important theoretical basis for the optimization of hydraulic fracturing design. This not only improves the understanding of the mechanical properties of shale, but also can effectively guide the efficient exploitation of shale gas, improve fracturing efficiency and safety, reduce construction costs, and provide a scientific basis for selecting appropriate fracture toughness parameters according to specific stress states in actual engineering.
[0095] Compared with the existing models, this model can not only describe and explain the variation law of fracture toughness of shale samples of different sizes, but also has a prediction function, which can predict the fracture toughness of shale samples of unknown sizes. Compared with the existing size effect model, this model has stronger applicability and accuracy, and can provide a more reliable theoretical basis for hydraulic fracturing design optimization. In addition, the present invention also conducts in-depth research on the fracture toughness under two different states of plane stress and plane strain, provides more comprehensive theoretical calculation values and prediction formulas, and further enriches the application scope of the model and its engineering guidance significance. These innovations make the application of the present invention in the field of shale gas extraction have significant technical advantages and practical value.
[0096] In the description of the present invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside" and "outside" etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.
[0097] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.
Claims
1. A method for calculating the size effect of type I fracture toughness of NSCB specimen shale, characterized in that The following steps are involved: A. Prepare NSCB specimens, use the NSCB specimens to carry out load loading tests, and measure the mode I fracture toughness values of the NSCB specimens; B. Obtain the calculation formula for the dimensionless energy release rate g(α0); C. Calculate the corrected peak load, set the definition of coordinate points and perform linear regression analysis; D. Calculate the fracture energy and obtain the length r of the fracture process zone of the infinite sample c∞ and the fracture toughness value when the size of NSCB specimens tends to infinity The calculation formula of E. Use the radius of the NSCB specimen, the thickness of the NSCB specimen, and the peak load to calculate the ordinate value of the linear regression. Perform linear regression with the radius R of the NSCB specimen as the abscissa to obtain the linear regression equation. Substitute the slope A and intercept C of the linear regression equation into r c∞ and The calculation formula for T c∞ and Substitute the calculated value of The calculation formula for the size effect of mode I fracture toughness of the current NSCB specimen is obtained, where g′(α0) is the derivative of g(α0) with respect to α0.
2. The method for calculating the size effect of type I fracture toughness of NSCB specimen shale according to claim 1 is characterized by: In step A, the method for preparing the NSCB sample is as follows: The large rock sample was processed into a cylinder by a coring machine, and then cut into a disc by a cutting machine and the two end faces were polished. The whole disc was then cut into two symmetrical half discs. The initial crack was opened in the center of the cutting plane of the half disc using a hydraulic knife cutting process to obtain the NSCB specimen.
3. The method for calculating the size effect of type I fracture toughness of NSCB specimen shale according to claim 2 is characterized by: In step A, the test process of the load loading test is as follows: A force column is set at the center of the semicircular top surface of the NSCB specimen, and two supporting columns are symmetrically set on the bottom surface on the side of the semicircular top surface. Then, a load force is applied to the force column. The load force is gradually increased, and the mode I fracture toughness value of the NSCB specimen is measured.
4. The method for calculating the size effect of type I fracture toughness of NSCB specimen shale according to claim 3 is characterized by: In step B, Nominal strength of NSCB specimen σ n The calculation formula is Where F is the maximum load, C n is the inherent coefficient of the NSCB specimen, b is the thickness of the NSCB specimen, d is the characteristic size of the NSCB specimen, and the characteristic size is the radius of the NSCB specimen; σ n / 2E′ represents the strain energy density, then the strain energy U is Where V represents the volume of the NSCB sample, that is, V = bd 2 ; f(α0) is a function related to the crack length of the NSCB specimen; α0 = a0 / d represents the dimensionless crack length, a0 represents the crack length of the NSCB specimen; under plane stress state, E′ = E; under plane strain state, E′ = E / (1-v 2 ); E represents Young's modulus, v is Poisson's ratio; the energy release rate G is Right now in g(α0) represents the geometric shape function of the NSCB specimen, i.e., the dimensionless energy release rate, and k(α0) is a function related to the specimen configuration and loading method; The stress intensity factor K of NSCB specimen under linear elastic conditions Ic The relationship between the energy release rate G satisfies the formula Right now R is the radius of the NSCB specimen, B is the thickness of the NSCB specimen, and Y represents the dimensionless stress intensity factor. The calculation formula for Y of the NSCB specimen structure is: The expression of dimensionless energy release rate of NSCB specimen is:
5. The method for calculating the size effect of type I fracture toughness of NSCB specimen shale according to claim 4 is characterized in that: In step C, The calculation formula for the modified peak load is: Where W j is the deadweight of the NSCB specimen, and n is the total number of specimens of the same material; The analysis process of linear regression is to first calculate the coordinate point (X j , Y j ), and set the definition of the coordinate point for this, where X j =R j , R j is the radius of sample j, Y j =(B j R j / F j ) 2 , B j is the thickness of sample j, F j is the peak load of sample j, and the regression line equation is Y=AX+C, In the formula, 6. The method for calculating the size effect of type I fracture toughness of NSCB specimen shale according to claim 5 is characterized by: In step D, The calculation process of fracture energy is as follows: the nominal strength σ n The calculation formula is transformed into Substituting into the static size effect formula In, get When F→peak load F max When , the above formula can be transformed into Get fracture energy Combining the above formula, we get Under linear elastic conditions, the stress intensity factor of the NSCB specimen satisfies the following relationship with the energy release rate G: IC 2 =GE'; where E' is the plane strain state, E' = E / (1-υ 2 ), υ is Poisson’s ratio. When the sample is infinite, i.e. R→∞, G→G f , under plane strain state In the formula, E' is the plane stress state, E' = E, under the plane stress state 7. A NSCB sample shale type I fracture toughness size effect calculation system, used to implement the NSCB sample shale type I fracture toughness size effect calculation method according to any one of claims 1 to 6, characterized in that: include, Load loading test module, used to carry out load loading test on NSCB specimens and measure the mode I fracture toughness value of NSCB specimens; A dimensionless energy release rate g(α0) calculation module, used to calculate the dimensionless energy release rate g(α0); Linear regression analysis module, used to perform linear regression analysis to obtain the modified peak load and regression line equation; The length of the fracture process zone of the infinite sample r c∞ And the fracture toughness value when the NSCB specimen size tends to infinity Calculation module, used to calculate r c∞ and The module for generating the calculation formula for the size effect of type I fracture toughness is used to generate the calculation formula for the size effect of type I fracture toughness.