A random field model and fracture research method of granite based on nanoindentation

Abstract

The invention relates to the technical field of rock and soil analysis, and in particular to a random field model of granite based on nanoindentation and a fracture research method, comprising the following steps: S1: obtaining the material elastic modulus and related mechanical parameters of a granite sample through a nanoindentation test; S2: establishing an elastic modulus Gaussian random field based on the elastic modulus, indentation depth and load-related mechanical parameters of the nanoindentation test; S3: discretizing the elastic modulus Gaussian random field of granite by a moving average method, and establishing a finite discrete element random field model of granite; S4: obtaining test results through a semicircular bending and pulling test of granite; S5: establishing a finite discrete random field model of a semicircular granite fracture simulation experiment; S6: comparing the simulation with the test results, and verifying the accuracy of the random field model in simulating the granite fracture; the invention has high reliability, and the random field model is used to study the influence of different mechanical parameters on the fracture behavior of granite and the representation of these influences in indoor experiments or engineering practice.

Description

Technical Field

[0001] The invention relates to the technical field of rock and soil analysis, and in particular to a granite random field model and fracture research method based on nanoindentation. Background Art

[0002] Rock is a widely distributed natural heterogeneous material. The mechanical properties of rock have an important impact on a series of rock engineering projects such as mining, oil and gas, tunnels, subways, and water conservancy. The mechanical properties of rock are complex and are affected by many factors such as mineral composition, crack pore structure, geological activity history, and surrounding conditions, showing heterogeneous characteristics. From a microscopic perspective, rock is composed of different mineral particles in different forms, and the mineral particles show different spatial distribution characteristics, the crystal structure within the mineral particles is different, and there are intercrystalline and intracrystalline cracks of different shapes and sizes. Traditional rock mechanics analysis is mostly based on the assumption of homogeneity, treating rock materials as homogeneous materials and using unified mechanical parameters for mechanical analysis of rock engineering. This is inconsistent with the actual situation of rock heterogeneity. When faced with rock, a heterogeneous material with many internal defects, there are a lot of problems that need to be solved.

[0003] Rock fracture behavior is one of the important research objects of rock mechanics, and fracture phenomena can be seen everywhere in production activities. On the one hand, when conducting excavation and blasting operations, we hope that the rock is easy to fracture and damage; on the other hand, when facing disasters such as collapse and rock burst, we hope that the rock can bear more loads without being damaged. However, the rock itself is heterogeneous, and has obvious brittle or quasi-brittle fracture characteristics. Since it contains a large number of joints and fissures, the rock may still have the ability to continue to bear after fracture. However, the existing fracture mechanics is difficult to explain the accumulation of tiny crack damage before the macroscopic fracture of the rock. For the study of the mechanical properties of rock materials themselves, numerical simulation has become a better research method.

[0004] In the prior art, methods such as CT scanning and digital image identification of minerals are often used to perform three-dimensional modeling of real rocks. Although this type of method can explain the heterogeneous characteristics of rocks during the stress process, there are two problems: first, the accuracy of the scanning method is limited, and second, the model is only for a specific specimen, and it is difficult to represent a certain type of rock as a whole for statistical analysis; the method of simulating mineral particles by simplifying the geometric structure and randomly generating geometric bodies to simulate the heterogeneous structure of granite is simple and efficient, but it also means that a large number of mineral particles will lose their distribution characteristics and geometric information; another type of heterogeneity research is through the microscopic joints and pore structures inside the rock. This method can meet the large number of modeling requirements required for statistical analysis and is a better means of studying the spatial heterogeneity of joints. However, when the joint scale is further reduced, this method also faces the problem of grid size. For granite, the aperture of the microscopic cracks before the macroscopic fracture of the rock is at the micron level. The characteristics of these cracks can be observed by mesoscopic means, but it is difficult to directly reflect them in the numerical model. Summary of the invention

[0005] The purpose of the present invention is to provide a granite random field model and fracture research method based on nanoindentation to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A random field model and fracture research method of granite based on nanoindentation, comprising the following steps:

[0008] S1: The material elastic modulus and related mechanical parameters of granite samples were obtained by nanoindentation test;

[0009] S2: Based on the elastic modulus, indentation depth, and load-related mechanical parameters of the nanoindentation test, the elastic modulus Gaussian random field is established;

[0010] S3: The Gaussian random field of elastic modulus of granite is discretized by moving average method, and a finite discrete element random field model of granite is established;

[0011] S4: Test results obtained from the granite semicircular bending tensile test;

[0012] S5: Based on the parameters and spatial distribution characteristics of the random field model obtained in S2, a finite discrete random field model is obtained according to S3 and a calculation model of a semicircular granite specimen is generated, and a finite element analysis of the fracture performance is performed;

[0013] S6: Compare the simulation results with the experimental results to verify the accuracy of the random field model in simulating granite fracture.

[0014] Preferably, the S1 comprises the following specific steps:

[0015] S11: Prepare the granite specimens required for the nanoindentation test and arrange the nanoindentation points;

[0016] S12: Encode each indentation point of the granite sample in turn, and correspond the load and indentation depth data of each indentation point obtained to the code;

[0017] S13: determining the penetration depth interval, and calculating and analyzing the data in the interval using the quartile method;

[0018] S14: Determine whether there is an abnormal value in the pressing depth interval. If there is an abnormal value, enter S15; if there is no abnormal value, jump directly to S18;

[0019] S15: Eliminate abnormal values ​​and obtain the corresponding codes of the abnormal values;

[0020] S16: observe the indentation test sample under an electron microscope and capture the sample image; extract the indentation point image corresponding to the number of the abnormal value, identify the effective boundary of the indentation point image, and identify the indentation area according to the pixels within the effective boundary;

[0021] S17: Calculate the elastic modulus according to the obtained indentation area and make it correspond to the code corresponding to the abnormal value and fill it to the corresponding position;

[0022] S18: Calculate each indentation depth data and the corresponding elastic modulus;

[0023] S19: extract and summarize all elastic modulus parameters.

[0024] Preferably, S3 includes the following specific steps:

[0025] S31: Submit the granite elastic modulus calculation file and related calculation parameters from MATLAB to ABAQUS;

[0026] S32: Meshing for FDEM calculations in ABAQUS;

[0027] S33: Based on the given mechanical parameters, the centroid of the triangular finite element unit is calculated to obtain the position coordinates of each unit node;

[0028] S34: determining the neighboring random field grid nodes in the regular random field grid, and obtaining the distances between them;

[0029] S35: Mapping the obtained grid node coordinates and mutual distances to the triangular grid calculated by FDEM;

[0030] S36: Insert Cohesive unit parameters;

[0031] S37: Generate a finite discrete random field model of granite in ABAQUS.

[0032] Preferably, the S4 comprises the following specific steps:

[0033] S41: Prepare several prefabricated crack specimens with different horizontal angles in the semicircular bending tensile test;

[0034] S42: Conduct fracture simulation tests on semicircular prefabricated crack specimens with different horizontal angles;

[0035] S43: Obtain fracture crack path diagrams of tests at different horizontal angles and maximum load values ​​corresponding to fracture of prefabricated crack specimens at different angles, and generate a horizontal angle-maximum load numerical test curve.

[0036] Preferably, S5 includes the following specific steps:

[0037] S51: Brazilian splitting and triaxial tests were performed on the same granite specimens from the nanoindentation test to obtain the mechanical parameters of the simulation test;

[0038] S52: Obtain the parameters and spatial distribution characteristics of the random field model through S2, and generate a random field with the same characteristics as in S3; the parameters of the random field model include the mean and the coefficient of variation, and the spatial distribution characteristics include the correlation distance;

[0039] S53: Random fracture simulation calculations were performed in ABAQUS at horizontal angles of 15°, 30°, 45°, 60°, 75°, and 90°;

[0040] S54: Map the random results that meet the requirements to the grid divided by the finite element software to generate a random field calculation model of the semicircle;

[0041] S55: obtaining the crack simulation paths of fractures at different angles and the maximum load values ​​corresponding to the fractures of prefabricated fracture specimens at different angles, and generating a numerical simulation curve corresponding to the horizontal angle-maximum load and a summary diagram of the crack simulation paths of fractures at different angles.

[0042] Preferably, the accuracy of the random field model in simulating granite fracture is verified by two aspects: first, the comparison between the fracture path diagram of the fracture under different horizontal angle tests and the fracture simulation path; second, the comparison between the horizontal angle-maximum load numerical test curve and the horizontal angle-maximum load corresponding numerical simulation curve;

[0043] Preferably, the fissure path diagrams of the test fractures at different horizontal angles are compared with the fracture simulation paths of the fractures, including determining whether the test fracture fissures are within the range of the simulation path. If the test fracture fissures are within the range of the simulation path, it is proved that the random field model has good accuracy in simulating granite fractures; if the test fracture fissures are not within the range of the simulation path, then return to step S52.

[0044] Preferably, the horizontal angle-maximum load numerical test curve is compared with the horizontal angle-maximum load corresponding numerical simulation curve, including determining whether the test result is within the range of three times the standard deviation of the simulation result; if the maximum load value of the test is within the range of three times the standard deviation of the maximum load value of the simulation result, it is proved that the random field model has good accuracy in simulating granite fracture; if the maximum load value of the test is outside the range of three times the standard deviation of the maximum load value of the simulation result, then return to step S52.

[0045] Preferably, the establishment of the elastic modulus Gaussian random field includes: establishing models of several granite specimens, assigning several elastic modulus parameters obtained from a preset database to several granite specimen models respectively, outputting data models of several granite specimen elastic modulus parameters, and using MATLAB software to simulate the spatial random fields of the elastic modulus parameters of several granite specimens respectively, and obtaining simulation results.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The invention provides a method for constructing a random field model of granite and studying fracture properties based on nanoindentation. The method first studies the elastic modulus and spatial distribution of granite at a microscopic scale through a nanoindentation test, and generates a Gaussian random field, which reflects that the spatial distribution correlation of the elastic modulus of granite is extremely strong. Since the random field acquisition method skips the cause of the heterogeneity of granite and directly takes mechanical parameters as the research object instead of mineral particles or fine joints as the research object, the heterogeneity of the rock can be described by the intuitive parameter spatial correlation, bypassing the complex composition and structure of the rock itself, avoiding the inability to establish a mathematical model through non-mineral particles or fine joints, so that the mechanical properties of rocks such as granite can be statistically analyzed as a whole, and the analysis reliability is good.

[0048] A discrete Gaussian random field is generated by the moving average method, and a discrete grid of the random field is generated using MATLAB, and the random field grid is mapped to the computational grid of ABAQUS. The fracture of granite is simulated and calculated using the FDEM method, and the reliability of the model in fracture calculation is verified by comparing semicircular bending tests at different angles with random field simulation tests. The grid dependence of the random field model and the number of samples when the mean is stable are verified for reliability and compared with the test results. The reliability of the random field model is excellent, and it is consistent with the test results in terms of specimen strength and failure mode. The overall random field is constructed by assuming that the relevant fracture parameters are linearly related to the elastic modulus. This method has good performance in terms of random field generation speed, clarity and accuracy of random field information, which is convenient for subsequent research on the influence of different mechanical parameters on the fracture behavior of granite and the characterization of these influences in indoor experiments or engineering practice through the random field model.

[0049] The present invention provides a method for constructing a random field model of granite and studying its fracture based on nanoindentation. The elastic modulus is calculated based on the indentation depth and other related parameters obtained from the nanoindentation test. In order to avoid the loss of the measured indentation depth value due to repeated tests of the indenter, which affects the accuracy of the test result, the four-section method is used to verify the numerical range of the indentation depth. If there are abnormal values ​​in the values, an electron microscope is used to obtain the indentation image corresponding to the abnormal value on the specimen, and the indentation area is extracted to obtain a convenient way to obtain the indentation area, thereby calculating the indentation depth to replace the abnormal value. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a schematic diagram of a process for constructing a random field model of granite and a fracture research method based on nanoindentation according to an embodiment of the present invention;

[0051] Figure 2 Schematic diagram of the process of Example S1 of the present invention;

[0052] Figure 3 Schematic diagram of the process of Example S3 of the present invention;

[0053] Figure 4 Schematic diagram of the process of S4, S5 and S6 of the embodiments of the present invention;

[0054] Figure 5 A schematic diagram of a random field mapping parameter assignment method according to an embodiment of the present invention;

[0055] Figure 6 It is a summary line graph of horizontal angle-maximum load of an embodiment of the present invention;

[0056] Figure 7 This is a comparison diagram of the granite specimen test with semicircular prefabricated cracks of different horizontal angles and the simulated cracks according to the embodiment of the present invention;

[0057] Figure 8 It is a schematic diagram of a load-COD curve and a fitted uniform curve of a granite specimen test with a horizontal angle of 15° simulated by a random field according to an embodiment of the present invention;

[0058] Fig. 9 It is a schematic diagram of a load-COD curve and a fitted uniform curve of a random field simulation test of a granite specimen with a horizontal angle of 30° in an embodiment of the present invention;

[0059] Fig.10 It is a schematic diagram of a load-COD curve and a fitted uniform curve of a random field simulation test of a granite specimen with a horizontal angle of 45° in an embodiment of the present invention;

[0060] Fig.11 It is a schematic diagram of a load-COD curve and a fitted uniform curve of a random field simulation test of a granite specimen with a horizontal angle of 60° in an embodiment of the present invention;

[0061] Fig.12 It is a schematic diagram of a load-COD curve and a fitted uniform curve of a random field simulation test of a granite specimen with a horizontal angle of 75° in an embodiment of the present invention;

[0062] Fig.13 It is a schematic diagram of a load-COD curve and a fitted uniform curve of a random field simulation test of a granite specimen with a horizontal angle of 90° in an embodiment of the present invention;

[0063] Fig.14 This is a schematic diagram of the failure morphology at the peak load quartile of each sample and the corresponding random field after the random field simulation test of the granite specimen with a horizontal angle of 15° in an embodiment of the present invention;

[0064] Fig.15 This is a schematic diagram of the failure morphology at the peak load quartile of each sample and the corresponding random field after the random field simulation of the granite specimen with a horizontal angle of 30° in the embodiment of the present invention;

[0065] Fig.16 It is a schematic diagram of the failure morphology at the peak load quartile of each sample and the corresponding random field after the random field simulation test of the granite specimen with a horizontal angle of 45° in the embodiment of the present invention;

[0066] Fig.17 It is a schematic diagram of the failure morphology at the peak load quartile of each sample and the corresponding random field after the random field simulation test of the granite specimen with a horizontal angle of 60° in the embodiment of the present invention;

[0067] Fig.18 It is a schematic diagram of the failure morphology at the peak load quartile of each sample and the corresponding random field after the random field simulation test of the granite specimen with a horizontal angle of 75° in an embodiment of the present invention;

[0068] Fig.19It is a schematic diagram of the failure morphology at the peak load quartile of each sample and the corresponding random field after the random field simulation test of the granite specimen with a horizontal angle of 90° in an embodiment of the present invention;

[0069] Fig. 20 Schematic diagram of coding of some nanoindentation points in the nanoindentation test according to an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0071] In the following description of the invention, it should be noted that the terms "upper", "lower", "left", "right", "inner", "outer", etc., indicating directions or positional relationships, are based on directions or positional relationships shown in the drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific direction or be constructed and operated in a specific direction. The term "connection" only indicates the connection between devices and has no special meaning.

[0072] In addition, the technical fields and installation methods involved in the embodiments of the present invention described below can be combined with each other as long as there is no conflict between them.

[0073] Specific implementation: Please refer to Figure 1-Figure 4 A method for constructing a random field model of granite and studying its fracture based on nanoindentation includes the following steps:

[0074] S1: The material elastic modulus and related mechanical parameters of granite samples were obtained by nanoindentation test;

[0075] Nanoindentation test is a test method for obtaining the micromechanical parameters of materials. It uses the Hertz contact principle and a nanoindentation test system to obtain the elastic modulus of materials at the nanoscale.

[0076] The nanoindentation test system includes an indenter, a loading and displacement sensor, a stage, and a microscopic observation system. The indenter is a Bosch indenter. The loading system is usually loaded by electromagnetic loading, electrostatic loading, and piezoelectric loading, and the displacement is monitored by a capacitive sensor, a transformer sensor, or a laser interferometer.

[0077] Specifically, the geometric parameters of the Bosch indenter include: the angle α between the center line and the surface is 65.3°, the side length to depth ratio l / h is 7.5315, and the projected area Ap(h) is 24.56h2 , the volume-depth relationship V(h) is 8.8173h 3 , the volume and area relationship V(A) is 0.067A 3 / 2 , the ratio of projected area to surface area A p / A f is 0.908, and the equivalent cone angle ψ is 70.32°;

[0078] The specific steps of obtaining the material elastic modulus and related mechanical parameters of granite samples through nanoindentation test include:

[0079] S11: Prepare the granite specimens required for the nanoindentation test and arrange the nanoindentation points;

[0080] The granite specimens were cube specimens with a side length of 10 mm, and the test surface was polished;

[0081] A rectangular dot matrix position is taken for testing to obtain the elastic modulus at different positions. In this embodiment, 100 indentation points are taken as an example. The dot matrix has 10 rows and 10 columns. The horizontal and vertical distances between adjacent points are both 300 μm, and the overall side length of the dot matrix is ​​2.7 mm.

[0082] The tester model used in the nanoindentation test is Anton Paar HNT3. The sample surface can be tracked during the test. There is no need to wait for thermal stabilization during the test, and the dot matrix can be quickly measured. The test uses a Bosch indenter. The maximum load set during the test is 50.00mN, the loading speed is 100mN / min, and the linear loading is performed. After reaching the peak load, it pauses for 15s and then unloads. The unloading speed is the same as the loading speed.

[0083] S12: Encode each indentation point of the granite sample in turn, and correspond the load and indentation depth data of each indentation point obtained to the code;

[0084] The data of the granite sample test process is transmitted to the processor, which includes a coding module and a storage module. The coding module encodes each indentation point in turn, such as Fig.10 As shown, and corresponding to the test data of each indentation point such as load, loading speed, unloading speed, etc., the coded data and the corresponding test data are saved in the storage module;

[0085] After the granite sample was subjected to the nanoindentation test, the corresponding indentation depths of multiple 100 indentation points under different load pressures were obtained, and the different loads and corresponding indentation depth data were aggregated into a load-indentation depth curve;

[0086] S13: determining the penetration depth interval, and calculating and analyzing the data in the interval using the quartile method;

[0087] Arrange the indentation depth data obtained in S12 in sequence to determine the indentation depth interval;

[0088] Specifically, this embodiment uses the quartile method to eliminate outliers, where an outlier is defined as a value less than QL-1.5IQR or greater than QU+1.5IQR;

[0089] Among them, QL is the lower quartile, QU is the upper quartile, and IQR is the difference between the upper quartile QU and the lower quartile QL. According to the penetration depth data obtained after the test, the lower quartile QL and the upper quartile QU in the penetration depth data, as well as the difference IQR between the upper quartile QU and the lower quartile QL are obtained;

[0090] S14: Determine whether there is an abnormal value in the pressing depth interval. If there is an abnormal value, enter S15; if there is no abnormal value, jump directly to S18;

[0091] When the value of the indentation depth is greater than QU+k (QU-QL) or less than QL-k (QU-QL), it is an abnormal value; among them, if k=1.5, it is moderately abnormal, and if k=3, it is extremely abnormal;

[0092] S15: Eliminate abnormal values ​​and obtain the corresponding codes of the abnormal values;

[0093] If the values ​​of the indentation depths are all abnormal values, the indentation depths are discarded, and the codes corresponding to the abnormal values ​​are obtained, and the process proceeds to S16;

[0094] S16: observe the indentation test sample under an electron microscope and capture the sample image; extract the indentation point image corresponding to the number of the abnormal value, identify the effective boundary of the indentation point image, and identify the indentation area according to the pixels within the effective boundary;

[0095] The processor also includes an image processing module. After the granite sample experiment, the surface image data of the sample after the experiment is intercepted by a scanning electron microscope and transmitted to the image processing module. The image processing module extracts the indentation points in the acquired image in sequence and stores them in the storage module in a one-to-one correspondence with the codes in the coding module.

[0096] The image processing module first converts the image format into the HSV format, then performs image threshold processing, uses a rectangular frame to extract the effective area of ​​the indentation point from the image after threshold processing, and stores it in the storage module after matching it with the code;

[0097] If an abnormal value appears, extract the indentation image of the corresponding coding unit; use the Open-CV tool to extract the effective boundary of the indentation image, generate an area measurement unit based on the effective boundary, and use the pixel size of the area measurement unit to identify the indentation area;

[0098] S17: Calculate the elastic modulus according to the obtained indentation area and make it correspond to the code corresponding to the abnormal value and fill it to the corresponding position;

[0099] Specifically, if an abnormal value appears, the indentation area obtained in S15 is substituted into the relevant formula, and the corresponding indentation depth is calculated, and the calculated indentation depth is used to replace the eliminated abnormal value; the calculation formula is:

[0100]

[0101] Among them, P max is the maximum load, h max is the maximum penetration depth, h f is the residual depth of the indenter after complete unloading. S is the contact stiffness, h c is the contact depth between the indenter and the sample;

[0102] Specifically, the calculation formula for measuring the elastic modulus and hardness of the corresponding mechanical parameters obtained by the nanoindentation method is:

[0103]

[0104] Where H represents the hardness of the material being tested (unit: GPa); P max Represents the load when the indenter reaches the maximum penetration depth; A(h c ) represents the corresponding contact area. E r represents the reduced modulus, that is, the elastic modulus of the joint deformation of the indenter and the sample to be tested; β is a constant, which is determined by the shape of the indenter and is 1.034 for the Bosch indenter; S represents the contact stiffness; A represents the contact area;

[0105]

[0106] Where, E and ν represent the elastic modulus and Poisson’s ratio of the sample to be tested respectively; E i , ν i represent the elastic modulus and Poisson’s ratio of the indenter, respectively;

[0107] S18: Calculate each indentation depth data and the corresponding elastic modulus;

[0108] S19: extracting and summarizing all elastic modulus parameters and saving them to a preset database;

[0109] Specifically, the elastic modulus and parameters such as indentation depth and load obtained from several nanoindentation points were used as data samples to generate a preset database to provide relevant data for subsequent modeling. A total of 100 sets of load-displacement curves were obtained in the experiment, and the corresponding elastic modulus was obtained. The average elastic modulus of the 100 measuring points was 65.6368 Gpa.

[0110] S2: Based on the elastic modulus, indentation depth, and load-related mechanical parameters of the nanoindentation test, the elastic modulus Gaussian random field is established;

[0111] Specifically, several granite specimen models are established, several elastic modulus parameters obtained from a preset database are assigned to several granite specimen models, several data models of elastic modulus parameters of granite specimens are output, and MATLAB software is used to simulate the spatial random fields of elastic modulus parameters of several granite specimens, and simulation results are obtained;

[0112] Specifically, after setting appropriate range of random field generation, random field correlation distance and grid size in MATLAB, and the grid size is between 1 / 4 and 1 / 2 of the correlation distance, the obtained elastic modulus is discretized into Gaussian random field using moving average method; in this embodiment, the range of random field generation is 100 mm in x direction and 100 mm in y direction, the established random field correlation distance is 0.57 mm, and when generating the grid, the grid size is designed to be 0.25 mm, which meets the grid size requirement; the mean of the random field generated in this embodiment is 65.6368, and the coefficient of variation is 0.18373.

[0113] S3: The moving average method is used to discretize the Gaussian random field of the elastic modulus of granite, and a finite discrete element random field model of granite is established. The random field always changes continuously in space, but in the actual study of granite fracture properties, it is impossible to discuss the problem using a random field with continuous infinite divisions. Therefore, when using the random field, the established Gaussian random field needs to be discretized, which includes the following steps:

[0114] S31: Submit the granite elastic modulus calculation file and related calculation parameters from MATLAB to ABAQUS;

[0115] Specifically, one of the above-mentioned random field simulation results of elastic modulus of several granite specimens is randomly selected, and the random field model is discretized in MATLAB by moving average method, and the discretized random field data file is exported to inp format, and the finite element software (ABAQUS) is used to read and import the data file in inp format, ABAQUS obtains the granite indentation model, sets relevant properties and creates the indentation boundary of the granite specimen, divides the grid size for FEDM calculation, and then performs finite-discrete element simulation in ABAQUS; after finite element calculation simulation, the corresponding data file is stored to provide original parameters for subsequent modification of single random field unit node information, and the changed parameters include grid size, node coordinates and other parameters;

[0116] Specifically, the inp format file usually includes the model's geometric information, material properties, boundary conditions, and node parameters.

[0117] The moving average method used in this embodiment is one of the most common methods for discretizing Gaussian fields in the prior art, and will not be described in detail here.

[0118] S32: Meshing for FDEM calculations in ABAQUS;

[0119] Among them, when performing finite-discrete element simulation, there are meshes for the elastic modulus random field and meshes for FEDM calculation. During finite element calculation, the mesh size used for FEDM calculation is often inconsistent with the random field mesh due to computational efficiency or convergence; the random field mesh is a regular rectangular mesh. In this embodiment, the mesh unit used for FEDM calculation is a triangular unit. Therefore, it is necessary to map the mesh to transmit the random field mesh information to the finite element mesh, such as Figure 5 As shown;

[0120] S33: Based on the given mechanical parameters, the centroid of the triangular finite element unit is calculated to obtain the position coordinates of each unit node;

[0121] Specifically, ABAQUS reads the inp file and obtains the position coordinates of the nodes of each random field unit. When mapping the elastic modulus in the random field, it is first necessary to calculate the center of mass of the finite element unit. The calculation formula is:

[0122]

[0123] Among them, Figure 5 As shown, x 0 ,y 0 is the coordinate of the unit centroid, x 1 With y 1 、x 2 With y 2 、x 3 With y 3 are the coordinates of the three nodes respectively.

[0124] S34: determining the neighboring random field grid nodes in the regular random field grid, and obtaining the distances between them;

[0125] Specifically, after the position coordinates of the computational grid nodes are established, the adjacent random field grid nodes in the regular random field grid can be determined, and the distances between them can be obtained. The elastic modulus of the computational grid nodes is designed to be E 0 , the elastic moduli of adjacent random field grid nodes are E 1 、E 2 、E 3 、E 4 , and their distances are l 1 , l 2 , l 3 , l4 ,but:

[0126]

[0127] S35: Mapping the obtained grid node coordinates and mutual distances to the triangular grid calculated by FDEM;

[0128] S36: Insert Cohesive unit parameters;

[0129] Specifically, in the FDEM method, in addition to the elastic modulus, the strength σ 0 and fracture energy G, while strength σ 0 and fracture energy G are difficult to obtain through nanoindentation tests. Although nanoindentation tests can obtain the fracture toughness of materials, this requires measuring the crack size around the residual indentation. It is extremely difficult and costly to measure the crack size one by one in a large range of lattices. At the same time, there may be no cracks around some indentations, which also affects the acquisition of data. In practice, cohesive units gradually replaced the original virtual cracks. Cohesive units are a special unit used to describe possible fracture interfaces and their mechanical behaviors. They are usually thickness-free. When inserting cohesive units, it is necessary to renumber the nodes for existing solid units. The insertion of cohesive units can be achieved by modifying the inp file in ABAQUS. During the calculation process, the displacements at various locations in the cohesive unit are still interpolated through shape functions. When the stress at the node reaches the tensile strength (or shear strength), the cohesive unit begins to have a large displacement until it reaches the maximum opening. The cohesive unit then fails, and the two adjacent units enter a discrete state. The two begin to have a contact relationship and start contact calculation when they approach each other.

[0130] The mapping method of cohesive unit parameters is the same as that of solid units, and is still determined by the center of mass position; the shape of the cohesive unit is a line segment, and its center of mass is the midpoint of the line segment; when mapping, the elastic modulus is used as the mapping value to convert into strength and fracture energy:

[0131]

[0132] Among them, E 0 is the random field mapping value of the cohesive unit, σ 0 is the strength of the cohesive unit, G 0 is the fracture energy of the cohesive unit, E m is the average value of the elastic modulus random field, σ m is the average intensity, G m is the average fracture energy; σ mWith G m It can be approximately obtained through indoor tests, namely the tensile strength and fracture energy of rock.

[0133] S37: Generate a finite discrete random field model of granite in ABAQUS;

[0134] The generated random field discrete model skips the causes of granite heterogeneity and directly takes mechanical parameters as the research object rather than mineral particles or fine joints. It can describe the heterogeneity of rock through intuitive parameter spatial correlation, bypassing the complex composition and structure of the rock itself, and avoids the inability to establish a mathematical model through non-mineral particles or fine joints. In the subsequent fracture performance research, it is possible to conduct a statistical analysis of the mechanical properties of rocks such as granite as a whole.

[0135] S4: Test results obtained from the granite semicircular bending tensile test;

[0136] S41: Prepare several prefabricated crack specimens with different horizontal angles in the semicircular bending tensile test;

[0137] The semicircular granite specimen is made of the same rock sample as that used in the nanoindentation test. The size and prefabricated crack conditions of the semicircular granite specimen are the same as those of the granite fracture simulation test model.

[0138] S42: Conduct fracture simulation tests on semicircular prefabricated crack specimens with different horizontal angles;

[0139] In this embodiment, the test loading device can be a TFD-20D rock fracture toughness tester; the test conditions of the granite semicircular bending tensile test are the same as the test conditions of the granite fracture simulation test;

[0140] S43: obtaining fracture crack path diagrams of tests with different horizontal angles and maximum load values ​​corresponding to fracture of prefabricated crack specimens with different angles, and generating a horizontal angle-maximum load numerical test curve;

[0141] Among them, the crack path on the specimen surface after the test can be recorded by digital image correlation (DIC) to obtain the fracture crack paths of the prefabricated crack specimens with horizontal angles of 15°, 30°, 45°, 60°, 75° and 90°, respectively, as shown in Figure 2. Figure 7 As shown in the test results;

[0142] Specifically, the maximum loads of the semicircular prefabricated crack specimens with different horizontal angles are obtained, and the maximum load-horizontal angle line graph is generated (such as Figure 6 shown).

[0143] S5: Based on the parameters and spatial distribution characteristics of the random field model obtained in S2, a finite discrete random field model is obtained according to S3 and a calculation model of a semicircular granite specimen is generated, and a finite element analysis of the fracture performance is performed. The specific steps include:

[0144] When simulating fracture problems, the FDEM method only needs to adjust the relevant parameters determined by the experiment to change the results of the finite element simulation.

[0145] S51: Brazilian splitting and triaxial tests were performed on the same granite specimens from the nanoindentation test to obtain the mechanical parameters of the simulation test;

[0146] Specifically, granite specimens under the same rock block as the nanoindentation test were subjected to Brazilian splitting and triaxial tests to determine relevant test parameters, see Table 1, so as to obtain simulation parameters, see Table 2;

[0147] Table 1 Test parameters

[0148]

[0149] Table 2 Simulation parameters

[0150]

[0151] The elastic modulus, tensile strength, shear strength, mode I fracture energy, and mode II fracture energy in the above table specifically refer to the mean values ​​of the random field, while Poisson's ratio, mode I initial stiffness, and mode II initial stiffness are definite values.

[0152] S52: Obtain the parameters and spatial distribution characteristics of the random field model through S2, and generate a random field with the same characteristics as in S3; the parameters of the random field model include the mean and the coefficient of variation, and the spatial distribution characteristics include the correlation distance;

[0153] Based on the simulation parameters in Table 2 above, one or more mechanical parameters in the random field model are changed, and a random field model with the same parameters (mean and coefficient of variation) and spatial distribution characteristics (correlation distance) as the above random field model is randomly selected from the generated random field models and imported into ABAQUS.

[0154] S53: Random fracture simulation calculations were performed in ABAQUS at horizontal angles of 15°, 30°, 45°, 60°, 75°, and 90°;

[0155] S54: Map the random results that meet the requirements to the grid divided by the finite element software to generate a random field calculation model of the semicircle;

[0156] Obtain several random fracture simulation results (one random field model corresponds to multiple calculation models), and randomly extract the random results of multiple random field models and map them to the grid divided by the finite element software;

[0157] Among them, the mesh size range of the finite element software can be determined according to the relevant distance, and the mesh size range has little effect on the generation of random results;

[0158] Specifically, in this embodiment, the semicircular granite specimen model can be a plurality of semicircular granite specimen models with a radius of 25.00 mm, a thickness of 12.5 mm, a prefabricated crack width of 0.3 mm, a length of 10.0 mm, and a prefabricated crack angle of 15°, 30°, 45°, 60°, 75°, and 90° to the horizontal;

[0159] Vertical constraints were applied 5 mm away from the edges of both ends of the specimen, a vertical position was applied to the top, and under the simulated test conditions with a loading speed of 0.0005 mm / s, different pressures were applied to the semicircular granite specimens with prefabricated cracks at different horizontal angles to obtain the maximum load value after fracture.

[0160] S55: obtaining the fracture simulation paths of fractures at different angles and the maximum load values ​​corresponding to the fractures of prefabricated fracture specimens at different angles, and generating a numerical simulation curve corresponding to the horizontal angle-maximum load and a summary diagram of the fracture simulation paths of fractures at different angles;

[0161] Specifically, the fracture simulation paths of fractures with different angles include the summary of fracture paths obtained after multiple simulated fracture tests of semicircular granite specimens with prefabricated fractures at horizontal angles of 15°, 30°, 45°, 60°, 75° and 90°, as shown in Figure 2. Figure 7 As shown in the simulation results;

[0162] Specifically, the semicircular granite specimens with prefabricated cracks at the same horizontal angle were simulated and calculated multiple times to obtain the load and prefabricated crack length change curves of multiple fracture simulation tests. When conducting statistical analysis, a set of reliable and representative statistics is needed to characterize the overall characteristics of granite. Therefore, the maximum load value adopts the sample mean of the minimum number of samples when the mean of the random field model is stable.

[0163] Each horizontal angle has its corresponding maximum load value. Multiple horizontal angles and their corresponding maximum load values ​​are summarized to generate a maximum load-horizontal angle line graph (such as Figure 6 shown).

[0164] S6: Compare the simulation results with the test results to verify the accuracy of the random field model in simulating granite fracture;

[0165] The accuracy of the random field model in simulating granite fracture is verified in two aspects: first, the comparison between the fracture path diagrams of the fracture under different horizontal angle tests and the fracture simulation paths; second, the comparison between the horizontal angle-maximum load numerical test curve and the horizontal angle-maximum load corresponding numerical simulation curve;

[0166] First, determine whether the test fracture crack is within the simulation path range; second, determine whether the test result is within the three standard deviation range of the simulation result; if the test fracture crack is within the simulation path range, and the maximum load value of the test is within the three standard deviation range of the maximum load value of the simulation result, it is proved that the random field model has good accuracy in simulating granite fracture; if the test fracture crack is not within the simulation path range, or the maximum load value of the test is outside the three standard deviation range of the maximum load value of the simulation result, then return to step S52;

[0167] Specifically, Figure 6 As shown in the figure, according to the central limit law, the maximum load of the semicircular bending test should conform to the normal distribution, and the rationality of the result is tested within the range of three times the standard deviation (3σ test); the maximum load obtained from the test of the specimens at each horizontal angle is within the 3σ range of the simulation result, which means that the numerical simulation parameters can better reflect the test results;

[0168] like Figure 7 As shown in the figure, the black curve in the simulation results is the experimental crack path extracted by DIC, and the gray curve is the summary of the fracture crack path simulated by the random field model. If the black curve is within the range of the gray curve, it means that the random field model has simulated the possible crack distribution range well.

[0169] In this embodiment, the fracture behavior of granite is studied based on the finite discrete random field model of granite established in step S3. Thirty random field model load-COD curves are plotted, and uniform curves of the thirty groups of curves are fitted. The uniform curve represents the average level of the random field model, such as Figure 8 As shown in the figure, the random field causes the curve to fluctuate up and down. In the early stage of loading, the curve is relatively consistent. At this time, the load is small, and no damage or cracks have occurred. The modulus of the specimen as a whole in the elastic stage is relatively consistent, and the heterogeneity has not yet had a huge impact on the deformation. When the load increases, the specimen enters the nonlinear deformation stage, and the heterogeneity begins to appear, indicating that the local material characteristics of the specimen begin to become obvious at this time. The load-COD curve of the specimen changes, and the loads at which each specimen begins to fail are different. In the post-peak section, the differences in the crack extension paths and the material parameters in the paths lead to greater differences between the curves. Taking the quartile of the peak load of the sample as an example, the final failure morphology of each sample is consistent with the corresponding random field as shown in the figure. Fig. 9 As shown in the figure, COD is the abbreviation of the opening displacement of the original crack site when the elastoplastic body is subjected to type I (opening type) load.

[0170] Thus, the development path characteristics of cracks under random fields are obtained: (1) Cracks always tend to pass through the part with smaller parameters in the random field, which represents the weak area of ​​granite, such as the area around fine cracks and fragile minerals; (2) Cracks always avoid passing through the part with larger parameters in the random field, which represents the complete high-strength mineral particles in granite; (3) Cracks do not always penetrate directly during the development process. In some local areas, independent cracks will be generated in the weak areas around existing cracks. These independent cracks will interconnect with the main cracks as loading occurs to form the final failure form.

[0171] The present invention provides a random field model of granite based on nanoindentation and a fracture research method. The elastic modulus and its spatial distribution of granite at a microscopic scale are first studied by nanoindentation test, and a Gaussian random field is generated, reflecting that the spatial distribution correlation of the elastic modulus of granite is extremely strong. Since the random field acquisition method skips the cause of the heterogeneity of granite, and directly takes mechanical parameters as the research object instead of mineral particles or fine joints as the research object, the heterogeneity of the rock can be described by the intuitive parameter spatial correlation, bypassing the complex composition and structure of the rock itself, avoiding the inability to establish a mathematical model through non-mineral particles or fine joints, so that the mechanical properties of rocks such as granite can be statistically analyzed as a whole, and the analysis reliability is good.

[0172] A discrete Gaussian random field is generated by the moving average method, and a discrete grid of the random field is generated using MATLAB, and the random field grid is mapped to the computational grid of ABAQUS. The fracture of granite is simulated and calculated using the FDEM method, and the reliability of the model in fracture calculation is verified by comparing semicircular bending tests at different angles with random field simulation tests. The grid dependence of the random field model and the number of samples when the mean is stable are verified for reliability and compared with the test results. The reliability of the random field model is excellent, and it is consistent with the test results in terms of specimen strength and failure mode. The overall random field is constructed by assuming that the relevant fracture parameters are linearly related to the elastic modulus. This method has good performance in terms of random field generation speed, clarity and accuracy of random field information, which is convenient for subsequent research on the influence of different mechanical parameters on the fracture behavior of granite and the characterization of these influences in indoor experiments or engineering practice through the random field model.

[0173] The present invention provides a random field model of granite based on nanoindentation and a fracture research method. The elastic modulus is calculated based on the indentation depth and other related parameters obtained from the nanoindentation test. In order to avoid the loss of the measured indentation depth value due to repeated tests of the indenter, which affects the accuracy of the test result, the four-section method is used to verify the numerical range of the indentation depth. If there are abnormal values ​​in the values, an electron microscope is used to obtain the indentation image corresponding to the abnormal value on the specimen, and the indentation area is extracted to obtain a convenient way to obtain the indentation area, thereby calculating the indentation depth to replace the abnormal value.

Claims

1. A random field model of granite and a fracture research method based on nanoindentation, characterized by: The steps include: S1: The material elastic modulus and related mechanical parameters of granite samples were obtained by nanoindentation test; S2: Based on the elastic modulus, indentation depth, and load-related mechanical parameters of the nanoindentation test, the elastic modulus Gaussian random field is established; S3: The Gaussian random field of elastic modulus of granite is discretized by moving average method, and a finite discrete element random field model of granite is established; S4: Test results obtained from the granite semicircular bending tensile test; S5: Based on the parameters and spatial distribution characteristics of the random field model obtained in S2, a finite discrete random field model is obtained according to S3 and a calculation model of a semicircular granite specimen is generated, and a finite element analysis of the fracture performance is performed; S6: Compare the simulation results with the test results to verify the accuracy of the random field model in simulating granite fracture; The S3 includes the following specific steps: S31: Submit the granite elastic modulus calculation file and related calculation parameters from MATLAB to ABAQUS; S32: Meshing for FDEM calculations in ABAQUS; S33: Based on the given mechanical parameters, the centroid of the triangular finite element unit is calculated to obtain the position coordinates of each unit node; S34: determining the neighboring random field grid nodes in the regular random field grid, and obtaining the distances between them; S35: Mapping the obtained grid node coordinates and mutual distances to the triangular grid calculated by FDEM; S36: Insert Cohesive unit parameters; S37: Generate a finite discrete random field model of granite in ABAQUS; The S4 comprises the following specific steps: S41: Prepare several prefabricated crack specimens with different horizontal angles in the semicircular bending tensile test; S42: Conduct fracture simulation tests on semicircular prefabricated crack specimens with different horizontal angles; S43: obtaining fracture crack path diagrams of tests at different horizontal angles and maximum load values ​​corresponding to fracture of prefabricated crack specimens at different angles, and generating a horizontal angle-maximum load numerical test curve; The S5 comprises the following specific steps: S51: Brazilian splitting and triaxial tests were performed on the same granite specimens from the nanoindentation test to obtain the mechanical parameters of the simulation test; S52: Obtain the parameters and spatial distribution characteristics of the random field model through S2, and generate a random field with the same characteristics as in S3; the parameters of the random field model include the mean and the coefficient of variation, and the spatial distribution characteristics include the correlation distance; S53: Random fracture simulation calculations were performed in ABAQUS at horizontal angles of 15°, 30°, 45°, 60°, 75°, and 90°; S54: Map the random results that meet the requirements to the grid divided by the finite element software to generate a random field calculation model of the semicircle; S55: obtaining the crack simulation paths of fractures at different angles and the maximum load values ​​corresponding to the fractures of prefabricated fracture specimens at different angles, and generating a numerical simulation curve corresponding to the horizontal angle-maximum load and a summary diagram of the crack simulation paths of fractures at different angles.

2. The granite random field model and fracture research method based on nanoindentation according to claim 1, characterized in that: The S1 comprises the following specific steps: S11: Prepare the granite specimens required for the nanoindentation test and arrange the nanoindentation points; S12: Encode each indentation point of the granite sample in turn, and correspond the load and indentation depth data of each indentation point obtained to the code; S13: determining the penetration depth interval, and calculating and analyzing the data in the interval using the quartile method; S14: Determine whether there is an abnormal value in the pressing depth interval. If there is an abnormal value, enter S15; if there is no abnormal value, jump directly to S18; S15: Eliminate abnormal values ​​and obtain the corresponding codes of the abnormal values; S16: observe the indentation test sample under an electron microscope and capture the sample image; extract the indentation point image corresponding to the number of the abnormal value, identify the effective boundary of the indentation point image, and identify the indentation area according to the pixels within the effective boundary; S17: Calculate the elastic modulus according to the obtained indentation area and make it correspond to the code corresponding to the abnormal value and fill it to the corresponding position; S18: Calculate each indentation depth data and the corresponding elastic modulus; S19: extract and summarize all elastic modulus parameters.

3. The random field model and fracture research method of granite based on nanoindentation according to claim 1, characterized in that: The accuracy of the random field model in simulating granite fracture is verified by two aspects: first, the comparison between the fracture path diagrams of the fracture tests at different horizontal angles and the fracture simulation paths; second, the comparison between the horizontal angle-maximum load numerical test curve and the horizontal angle-maximum load corresponding numerical simulation curve.

4. The random field model and fracture research method of granite based on nanoindentation according to claim 3, characterized in that: The fissure path diagrams of the test fractures at different horizontal angles are compared with the fissure simulation paths of the fractures, including determining whether the test fracture fissures are within the range of the simulation path. If the test fracture fissures are within the range of the simulation path, it is proved that the random field model has good accuracy in simulating granite fractures; if the test fracture fissures are not within the range of the simulation path, then return to step S52.

5. The random field model and fracture research method of granite based on nanoindentation according to claim 4, characterized in that: The horizontal angle-maximum load numerical test curve is compared with the horizontal angle-maximum load corresponding numerical simulation curve, including determining whether the test result is within the range of three times the standard deviation of the simulation result; if the maximum load value of the test is within the range of three times the standard deviation of the maximum load value of the simulation result, it is proved that the random field model has good accuracy in simulating granite fracture .... If it is out of the range, return to step S52.

6. The random field model and fracture research method of granite based on nanoindentation according to claim 1, characterized in that: The method of establishing the elastic modulus Gaussian random field includes: establishing models of several granite specimens, assigning several elastic modulus parameters obtained from a preset database to the several granite specimen models respectively, outputting data models of the elastic modulus parameters of the several granite specimens, and simulating the elastic modulus parameter space random fields of the several granite specimens respectively by using MATLAB software, and obtaining simulation results.

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