Method for obtaining elastic modulus and hardness of a pancake core in a high stress area

Abstract

The present application relates to the technical field of deep rock mechanics parameter acquisition, and provides a method for acquiring the elastic modulus and hardness of a pie-shaped core in a high ground stress area, wherein a drill is sleeved in the center area of the pie-shaped core and line cutting is performed to obtain a rock sample in a region with less unloading damage influence; according to the different rock density and particle size sorting, a φ2.5mm or φ5mm Brinell spherical indenter is reasonably selected to perform millimeter indentation testing on the rock sample, a cyclic loading and unloading mode is adopted for single testing point, and the elastic modulus and hardness of the rock sample are calculated according to the displacement-load curve. The present application provides a method for testing the elastic modulus and hardness of a pie-shaped core, and can more accurately acquire the mechanical parameters of deep rock. The mechanical parameters obtained by the present application can be applied to deep rock engineering such as ground stress inversion, rock burst prediction, drilling well wall stability analysis, unconventional oil and gas reservoir brittleness evaluation, and has high application value.

Description

Technical Field

[0001] This invention relates to the field of obtaining mechanical parameters of deep rocks, and is particularly applicable to obtaining the elastic modulus and hardness parameters of rocks. Background Technology

[0002] The prerequisite for the scientific development of deep rock engineering is the accurate acquisition of the mechanical parameters of deep rocks, among which the elastic modulus and hardness of rocks are of considerable importance. Problems such as geological advance prediction, in-situ stress inversion, evaluation of rock brittleness and compressibility, and drilling design are all closely related to the elastic modulus of rocks, while the hardness of rocks also plays a very important role in assessing rock brittleness, compressive strength, and drillability.

[0003] Currently, the main method for obtaining deep rock mechanical parameters is through drilling and coring, followed by the preparation of standard samples for laboratory testing, including uniaxial, triaxial, and ultrasonic wave velocity measurements. However, in areas with high geostress, drilling and coring often results in the core fragmentation into disc-shaped or fragmented pieces of varying thicknesses, ranging from a few millimeters to tens of millimeters, due to the large principal stress difference and high-rate unloading. This disc-shaped, fragmented core cannot be used to prepare standard samples for laboratory rock mechanics experiments. Even when thicker cores are selected for standard sample preparation, the damage caused by drilling and unloading often leads to lower experimental results, resulting in an underestimation of the mechanical parameters of deep rocks.

[0004] In summary, core sampling of deep rocks in high-stress areas is difficult, and the cores are severely distorted, making it hard to accurately obtain the mechanical parameters of deep rocks through conventional mechanical experiments. There is an urgent need for a new method to test distorted cores to provide support for deep resource development and underground engineering construction. Summary of the Invention

[0005] This invention primarily addresses the shortcomings of existing technologies by providing a method for obtaining the elastic modulus and hardness of core samples from high-stress zones. The method involves drilling into the central region of the core sample and performing wire cutting to obtain a rock sample from an area less affected by unloading damage. Depending on the rock's density and grain size sorting, a φ2.5mm or φ5mm Brinell spherical indenter is appropriately selected to perform millimeter indentation tests on the rock sample. A cyclic loading and unloading method is used for each test point, and the elastic modulus and hardness of the rock sample are calculated based on the displacement-load curve.

[0006] The present invention provides a method for obtaining the elastic modulus and hardness of a core sample from a high-stress zone, comprising the following steps: S1. Preparation of rock samples for millimeter indentation testing: The central area of ​​the disc-shaped rock core is drilled, and two parallel end faces are cut out by wire cutting. The two end faces of the rock sample are then ground and polished. S2. Perform millimeter indentation tests on the rock samples prepared in step S1: Select multiple test points on the rock samples. For rock samples with a maximum mineral particle size < 0.5 mm, use a φ2.5 mm or φ5 mm Brinell spherical indenter. For rock samples with a maximum mineral particle size ≥ 0.5 mm, use a φ5 mm Brinell spherical indenter. Use a cyclic loading and unloading method to obtain multiple test parameters for each test point, thereby obtaining the displacement-load curve. S3. Calculate the elastic modulus and hardness of the rock sample based on the displacement-load curve.

[0007] The preferred technical solution is that, in step S1, the vertical distance between the two parallel end faces cut by wire cutting is not less than 5mm; the two end faces of the rock sample are ground and polished so that the parallelism between the two ends of the rock sample is not greater than 0.005mm.

[0008] A further preferred technical solution is that, in step S1, the method for grinding and polishing the two end faces of the rock sample includes: Place the rock sample in a mold, mix the acrylic resin powder and hardener at a mass ratio of 10:8, stir evenly, pour the mixture into the mold, and ensure that the liquid just submerges the rock sample. After the sample has cured, remove it from the mold and use a special fixture to grind and polish the rock sample fixed with acrylic resin on a metallographic polishing machine, so that both ends of the rock sample are exposed on the surface of acrylic resin. The polishing grit increases sequentially from 120, 240, 400, and 800 grit.

[0009] A further preferred technical solution is that, in step S2, when selecting multiple test points on the rock sample, the distance between each experimental test point on the rock sample should be greater than 3 mm.

[0010] A further preferred technical solution is that step S2 further includes: before testing, the diameter of the Brinell indenter needs to be checked, and the error should be less than ±0.003mm.

[0011] A further preferred technical solution is that, in step S2, multiple test parameters are obtained at each test point using a cyclic loading and unloading method with a Brinell spherical indenter. The specific method for obtaining the displacement-load curve based on the cyclic loading and unloading includes: S2.1. Set the loading rate to 0.05 mm / min and the unloading rate to 0.01 mm / min. When using a φ2.5 mm Brinell spherical indenter, the maximum load is 125 N. When using a φ5 mm Brinell spherical indenter, the maximum load is 500 N. S2.2. Load sequentially along the test points. For a single test point, use a cyclic loading and unloading method. After each loading to the maximum load, maintain the maximum load for 20 seconds before unloading. In a single cycle, unload to 1N before starting the next round of loading until the experiment ends. Save the displacement-load data obtained from the experiment. S2.3. If a significant increase in maximum displacement is observed during cyclic loading, and a large area of ​​hysteresis loop appears on the experimental curve, the experiment should be stopped immediately, the test point changed, the maximum load reduced, and the experiment repeated.

[0012] A further preferred technical solution is that, in step S2.2, the number of cycles for loading and unloading a single test point is 5 to 30.

[0013] A further preferred technical solution is that, in step S2, the method for selecting multiple test points on the rock sample includes: making a grid plate with a spacing of 3mm, covering the rock sample with the grid plate, and printing the experimental test points on the rock sample with spray paint.

[0014] A further preferred technical solution is that, in step S3, the method for calculating the elastic modulus and hardness of the rock sample based on the displacement-load curve includes: S3.1. Preprocess the displacement-load data obtained in step S2: S3.1.1. Take the first 30 data points and perform linear fitting. The fitting relationship is as follows: -----(1) In the formula: p is the load (N), h is the displacement (mm), and a and b are the fitting coefficients; Let p=0, then h0=-(b / a). Subtract h0 from all displacement data to complete the correction of the loading start point. S3.1.2. Identify the experimental data of a single unloading in the cyclic loading and unloading, and extract the experimental data corresponding to the maximum load of 80% to the load of 2N for each single unloading curve; S3.2. Calculate the elastic modulus and hardness of the rock sample based on the preprocessing curve obtained in S3.1.

[0015] A more preferred technical solution is that, in step S3.2, the method for calculating the elastic modulus and hardness of the tested rock sample based on the preprocessing curve obtained in S3.1 includes: S3.2.1. Perform nonlinear fitting on each group of experimental data, with the fitting function in the form of: -----(2) Where: c, d, h fi All are fitting coefficients, where h fiRepresents the residual displacement at the i-th unloading; S3.2.2. Differentiate equation (2) and substitute the maximum displacement h before each unloading. maxi Calculate the contact stiffness S during each unloading. i The calculation formula is: -----(3) In the formula: S i h represents the contact stiffness during each i-th unloading operation. maxi The maximum displacement before the i-th unloading; S3.2.3. Calculate the contact depth h based on the contact stiffness. ci The calculation formula is: -----(4) Where: h ci p is the contact depth calculated based on the data from the i-th unloading. max For maximum load, For a Brinell spherical indenter, the coefficient is related to the geometry of the indenter. It is 0.75; S3.2.4. Calculate the contact area after a single unloading based on the contact depth. For a Brinell spherical indenter, the formula for calculating the contact area is: -----(5) In the formula: A ci The contact area is the area corresponding to the maximum load during the i-th loading, and D is the diameter of the indenter. S3.2.5. Calculate the equivalent modulus for a single loading and unloading operation based on the contact area. The calculation formula is as follows: -----(6) In the formula: E ri The reduced modulus is calculated based on the i-th unloading curve, and β is the indenter correction coefficient. For a Brinell spherical indenter, β is 1.0. S3.2.6. Calculate the measured rock sample based on the reduced modulus. The calculation formula is as follows: -----(7) In the formula: μ0 and E0 are Poisson's ratio and elastic modulus of the Brinell spherical indenter, respectively, with values ​​of 0.24 and 700 GPa; μ i and E i The Poisson's ratio and elastic modulus of the rock are calculated for the i-th loading and unloading operation, respectively. For rocks with an unknown Poisson's ratio, μ i Take 0.25.

[0016] S3.2.7. Calculate the hardness of the rock obtained from a single loading and unloading operation. The calculation formula is as follows: -----(8) Where: H i The hardness is calculated based on the loading and unloading data of the i-th loading and unloading operation.

[0017] The beneficial effects of this invention are as follows: 1. This invention provides a method for testing the elastic modulus and hardness of disc-shaped rock cores, which can obtain the mechanical parameters of deep rocks more accurately than conventional mechanical experiments used in the prior art. It solves the problem in the prior art that disc-shaped, fractured rock cores cannot be made into standard samples for indoor rock mechanics experiments. Even when thicker rock cores are selected to make standard samples, damage caused by drilling and unloading often leads to lower experimental results, resulting in an underestimation of the mechanical parameters of deep rocks.

[0018] 2. According to the relevant definition of the international standard ISO 14577-1 for instrumented indentation, the millimeter indentation proposed in this patent belongs to the macroscopic indentation method. The difference between it and the traditional nano / micro indentation is: (1) Nano / micro indentation requires hundreds or thousands of indentation test results to obtain the statistical distribution law of elastic modulus and hardness of different minerals, while the millimeter indentation method proposed in this patent only requires a small number of experiments to obtain relatively ideal results; (2) Due to the small indentation depth and indentation load, nano / micro indentation can often only obtain the elastic modulus and hardness of a single mineral in the rock. Then, the macroscopic elastic modulus of the rock is finally obtained through homogenization theory or numerical simulation method. The calculation process is relatively complicated. However, the millimeter indentation method proposed in this patent can directly measure the macroscopic elastic modulus of the rock due to the large indentation depth.

[0019] 3. The mechanical parameters obtained by this invention can be applied to deep rock engineering such as stress inversion in high-stress areas, rockburst prediction, wellbore stability analysis, and brittleness evaluation of unconventional oil and gas reservoirs, and have high application value. Attached Figure Description

[0020] Figure 1 This is a flowchart of the testing process used in the embodiments of the present invention.

[0021] Figure 2 This is a schematic diagram of a method for preparing rock samples for millimeter indentation testing in an embodiment of the present invention.

[0022] Figure 3 The test curve and unloading fitting curve are for a φ2.5mm Brinell spherical indenter.

[0023] Figure 4 The test curve and unloading fitting curve are for a φ5mm Brinell spherical indenter.

[0024] Figure 5 This refers to situations that require immediate cessation of the experiment during cyclic loading.

[0025] Figure 6 This is a histogram of the elastic modulus.

[0026] Figure 7 This is a hardness histogram.

[0027] Figure 8 This is a schematic diagram of the structure of a pancake-shaped rock core.

[0028] Figure 9 Rock samples with test points marked after being fixed with acrylic resin and polished.

[0029] Figure 10 Experimental data were extracted for single unloading curves corresponding to 80% of the maximum load to a load of 2N when using a φ2.5mm Brinell spherical indenter.

[0030] Figure 11 Experimental data were extracted to obtain the single unloading curve corresponding to 80% of the maximum load to a load of 2N when using a φ5mm Brinell spherical indenter.

[0031] Among them, 1-disc core, 2-the working area of ​​the water drill with a diameter of 25mm, 3-the small core with a diameter of φ25mm obtained by drilling, 4-the first position of wire cutting, and 5-the second position of wire cutting. Detailed Implementation

[0032] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, provides a detailed description of the specific implementation method and working principle of a method for obtaining the elastic modulus and hardness of pancake cores in high geostress zones according to the present invention.

[0033] like Figure 1 As shown, the method for obtaining the elastic modulus and hardness of a disc-shaped rock core from a high-stress zone, as used in this embodiment, mainly includes: preparing a rock sample for millimeter indentation testing: drilling the central area of ​​the disc-shaped rock core, cutting out two parallel end faces using wire cutting, and polishing the two end faces of the rock sample; performing millimeter indentation testing on the prepared rock sample: selecting multiple test points on the rock sample, and using a φ2.5mm or φ5mm Brinell spherical indenter to obtain multiple test parameters at each test point through cyclic loading and unloading, thereby obtaining a displacement-load curve; and calculating the elastic modulus and hardness of the rock sample based on the displacement-load curve. The specific operation methods for each step are as follows: 1. Collect such as Figure 8 The disc-shaped core 1 shown is as follows: Figure 2As shown, a φ25mm diamond water drill was used to drill from the axis 2 of the cake core 1 to obtain a small core 3 of φ25mm; a wire cutting machine was used to drill... Figure 2 Wire cutting is performed at the first wire cutting position 4 and the second wire cutting position 5 on the small core 3 shown to obtain two parallel end faces. The vertical distance between the two end faces should be greater than 5mm.

[0034] 2. Place the rock sample prepared according to step 1 in a φ40... In a 25mm silicone mold, acrylic resin powder and hardener are mixed at a mass ratio of 10:8. After thorough mixing, the mixture is poured into the mold, ensuring the liquid just covers the rock sample. Once the sample has cured, it is demolded and polished using a metallographic polishing machine with a specialized fixture, ensuring both ends of the sample are exposed above the acrylic resin surface. The polishing grit increases sequentially from 120, 240, 400, and 800 grit. After polishing, the parallelism of the sample is checked using a micrometer; the parallelism between the two ends should not exceed 0.005mm. A 3mm spacing stainless steel mesh is then placed over the rock sample, and test points are printed on the sample using black spray paint. The completed sample preparation is shown below. Figure 9 As shown.

[0035] 3. Since the maximum mineral grain size of the Jinping marble used in this case is less than 0.5mm, both φ2.5mm and φ5mm Brinell indenters can be used. Here, millimeter indentation tests are performed using both types of indenters to compare the experimental results. Referring to the Brinell hardness test standard for metals, in order to make the hardness tests of Brinell indenters of different diameters comparable, the maximum load is 125N when using a φ2.5mm Brinell indenter and 500N when using a φ5mm Brinell indenter. Before testing, the diameter of the Brinell indenter must be checked, and the error should be less than ±0.003mm.

[0036] 4. Set the loading rate to 0.05 mm / min, the unloading rate to 0.01 mm / min, and the holding time to 20 s. Reload when unloading to 1 N. The number of cycles for cyclic loading and unloading for a single test point is 5 to 30. In this embodiment, the cyclic loading and unloading method is used 5 times. Therefore, after a total of 5 cycles, the load is unloaded to 0 N and the experiment ends. Save the displacement-load data obtained in the experiment.

[0037] Note that, as Figure 5 As shown, if a significant increase in maximum displacement is observed during cyclic loading, and a large area of ​​hysteresis loop appears on the experimental curve, the experiment should be stopped immediately, the test point changed, the maximum load reduced, and the experiment repeated.

[0038] 5. Preprocess the displacement-load data saved in the previous step. The specific steps are as follows: 5.1. To eliminate the error in the starting position of the loading point caused by the inaccuracy of the LVDT displacement sensor, linear fitting was performed on the first 30 data points before loading. The fitting relationship is as follows: -----(1) In the formula: p is the load (N), h is the displacement (mm), and a and b are the fitting coefficients.

[0039] Let p=0, then h0=-(b / a). Subtract h0 from all displacement data to complete the correction of the loading start point. 5.2 The program was written to automatically identify the experimental data of a single unloading in the cyclic loading and unloading. In order to reduce the impact of elbow effect on the test results during unloading, the experimental data corresponding to the maximum load of 80% to the load of 2N for each single unloading curve were extracted. Figure 10 The figure shows experimental data for extracting a single unloading curve corresponding to 80% of the maximum load to a load of 2N when using a φ2.5mm Brinell spherical indenter. Figure 11 The figure shows experimental data extracted from a single unloading curve when using a φ5mm Brinell spherical indenter, corresponding to 80% of the maximum load to a load of 2N.

[0040] 6. Calculate the elastic modulus and hardness of the tested rock sample based on the pretreatment curve. The specific steps are as follows: 6.1. Perform nonlinear fitting on each group of experimental data, with the fitting function in the form of: -----(2) Where: c, d, h fi All are fitting coefficients, where h fi This represents the residual displacement during the i-th unloading.

[0041] 6.2. Differentiate equation (2) and substitute the maximum displacement h before each unloading. maxi Calculate the contact stiffness S during each unloading. i The calculation formula is: -----(3) In the formula: S i h represents the contact stiffness during each i-th unloading operation. maxi This represents the maximum displacement before the i-th unloading. Figure 3 and Figure 4 It includes experimental data and fitting data, wherein the experimental data is obtained by the method provided in this embodiment up to step 4, and the fitting data is obtained by the method provided in this embodiment up to step 6.2.

[0042] 6.3. Calculate the contact depth h based on the contact stiffness. ci The calculation formula is: -----(4) Where: h ci p is the contact depth calculated based on the data from the i-th unloading. max For maximum load, For a Brinell spherical indenter, the coefficient is related to the geometry of the indenter. It is 0.75.

[0043] 6.4. Calculate the contact area after a single unloading based on the contact depth. For a Brinell spherical indenter, the formula for calculating the contact area is: -----(5) In the formula: A ci Let be the contact area corresponding to the i-th loading to the maximum load, and D be the diameter of the indenter.

[0044] 6.5. Calculate the equivalent modulus corresponding to a single loading and unloading operation based on the contact area. The calculation formula is as follows: -----(6) In the formula: E ri β is the reduced modulus calculated based on the i-th unloading curve, and β is the indenter correction coefficient. For a Brinell spherical indenter, β is 1.0.

[0045] 6.6. Calculate the measured rock sample based on the reduced modulus. The calculation formula is as follows: -----(7) In the formula: μ0 and E0 are Poisson's ratio and elastic modulus of the Brinell spherical indenter, respectively, with values ​​of 0.24 and 700 GPa; μ i and E i The Poisson's ratio and elastic modulus of the rock are calculated for the i-th loading and unloading operation, respectively. For rocks with an unknown Poisson's ratio, μ i Take 0.25.

[0046] 6.7. Calculate the hardness of the rock obtained from a single loading and unloading operation. The calculation formula is as follows: -----(8) Where: H i The hardness is calculated based on the loading and unloading data of the i-th loading and unloading operation.

[0047] 7. In this example, three sets of experiments were conducted using φ2.5mm and φ5mm Brinell spherical indenters, respectively. Each set of experiments yielded five sets of elastic modulus and hardness results; the histogram of the elastic modulus test results is shown below. Figure 6 As shown, the histogram of the hardness test results is as follows: Figure 7 As shown in Table 1, the average value of the test results for different pressure heads was taken as the final result.

[0048] Table 1. Millimeter indentation test results of Jinping marble disc cores

[0049] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for obtaining the elastic modulus and hardness of pancake-shaped rock cores from high-stress zones, characterized in that, Includes the following steps: S1. Preparation of rock samples for millimeter indentation testing: The central area of ​​the disc-shaped rock core is drilled, and two parallel end faces are cut out by wire cutting. The two end faces of the rock sample are then ground and polished. S2. Perform millimeter indentation tests on the rock samples prepared in step S1: Select multiple test points on the rock samples. For rock samples with a maximum mineral particle size < 0.5 mm, use a φ2.5 mm or φ5 mm Brinell spherical indenter. For rock samples with a maximum mineral particle size ≥ 0.5 mm, use a φ5 mm Brinell spherical indenter. Use a cyclic loading and unloading method to obtain multiple test parameters for each test point, thereby obtaining the displacement-load curve. S3. Calculate the elastic modulus and hardness of the rock sample based on the displacement-load curve; In step S1, the vertical distance between the two parallel end faces cut by wire cutting is not less than 5 mm; the two end faces of the rock sample are ground and polished so that the parallelism between the two ends of the rock sample is not greater than 0.005 mm. In step S1, the method for grinding and polishing the two end faces of the rock sample includes: Place the rock sample in a mold, mix the acrylic resin powder and hardener at a mass ratio of 10:8, stir evenly, pour the mixture into the mold, and just submerge the rock sample in the liquid. After the sample has cured, remove it from the mold and use a special fixture on a metallographic polishing machine to grind and polish the rock sample fixed with acrylic resin, so that both ends of the rock sample are exposed on the surface of acrylic resin. The polishing grit increases sequentially from 120, 240, 400, and 800 grit. In step S2, multiple test parameters are obtained at each test point using a cyclic loading and unloading method with a Brinell spherical indenter. The specific method for obtaining the displacement-load curve based on the cyclic loading and unloading includes: S2.

1. Set the loading rate to 0.05 mm / min and the unloading rate to 0.01 mm / min. When using a φ2.5 mm Brinell spherical indenter, the maximum load is 125 N. When using a φ5 mm Brinell spherical indenter, the maximum load is 500 N. S2.

2. Load sequentially along the test points. For a single test point, use a cyclic loading and unloading method. After each loading to the maximum load, maintain the maximum load for 20 seconds before unloading. In a single cycle, unload to 1N before starting the next round of loading until the experiment ends. Save the displacement-load data obtained from the experiment. S2.

3. If a significant increase in maximum displacement is observed during cyclic loading, and a large area of ​​hysteresis loop appears on the experimental curve, the experiment should be stopped immediately, the test point changed, the maximum load reduced, and the experiment repeated.

2. The method for obtaining the elastic modulus and hardness of pancake core samples from high-stress zones as described in claim 1, characterized in that, In step S2, when multiple test points are selected on the rock sample, the distance between each experimental test point on the rock sample is greater than 3 mm.

3. The method for obtaining the elastic modulus and hardness of pancake cores from high-stress zones as described in claim 2, characterized in that, Step S2 further includes: checking the diameter of the Brinell indenter before testing, and the error should be less than ±0.003mm.

4. The method for obtaining the elastic modulus and hardness of pancake core samples from high-stress zones as described in claim 1, characterized in that, In step S2.2, the number of loops for loading and unloading a single test point is 5 to 30.

5. The method for obtaining the elastic modulus and hardness of pancake cores from high-stress zones as described in claim 2, characterized in that, In step S2, the method for selecting multiple test points on the rock sample includes: making a grid plate with a spacing of 3 mm, covering the rock sample with the grid plate, and printing the test points on the rock sample with spray paint.

6. The method for obtaining the elastic modulus and hardness of pancake core samples from high-stress zones as described in any one of claims 1 to 5, characterized in that, In step S3, the method for calculating the elastic modulus and hardness of the rock sample based on the displacement-load curve includes: S3.

1. Preprocess the displacement-load data obtained in step S2: S3.1.

1. Take the first 30 data points and perform linear fitting. The fitting relationship is as follows: -----(1) In the formula: p is the load in N, h is the displacement in mm, and a and b are the fitting coefficients; Let p=0, then h0=-(b / a). Subtract h0 from all displacement data to complete the correction of the loading start point. S3.1.

2. Identify the experimental data of a single unloading in the cyclic loading and unloading, and extract the experimental data corresponding to the maximum load of 80% to the load of 2N for each single unloading curve; S3.

2. Calculate the elastic modulus and hardness of the rock sample based on the preprocessing curve obtained in S3.

1.

7. The method for obtaining the elastic modulus and hardness of pancake core samples from high-stress zones as described in claim 6, characterized in that, In step S3.2, the method for calculating the elastic modulus and hardness of the tested rock sample based on the preprocessing curve obtained in S3.1 includes: S3.2.

1. Perform nonlinear fitting on each group of experimental data, with the fitting function in the form of: -----(2) Where: c, d, h fi All are fitting coefficients, where h fi This represents the residual displacement at the i-th unloading; S3.2.

2. Differentiate equation (2) and substitute the maximum displacement h before each unloading. maxi Calculate the contact stiffness S during each unloading. i The calculation formula is: -----(3) In the formula: S i h represents the contact stiffness during each i-th unloading operation. maxi The maximum displacement before the i-th unloading; S3.2.

3. Calculate the contact depth h based on the contact stiffness. ci The calculation formula is: -----(4) Where: h ci p is the contact depth calculated based on the data from the i-th unloading. max For maximum load, For a Brinell spherical indenter, the coefficient is related to the geometry of the indenter. It is 0.75; S3.2.

4. Calculate the contact area after a single unloading based on the contact depth. For a Brinell spherical indenter, the formula for calculating the contact area is: -----(5) In the formula: A ci The contact area is the area corresponding to the maximum load during the i-th loading, and D is the diameter of the indenter. S3.2.

5. Calculate the equivalent modulus for a single loading and unloading operation based on the contact area. The calculation formula is as follows: -----(6) In the formula: E ri The reduced modulus is calculated based on the i-th unloading curve, and β is the indenter correction coefficient. For a Brinell spherical indenter, β is 1.

0. S3.2.

6. Calculate the elastic modulus of the tested rock sample based on the reduced modulus. The calculation formula is as follows: -----(7) In the formula: μ0 and E0 are Poisson's ratio and elastic modulus of the Brinell spherical indenter, respectively, with values ​​of 0.24 and 700 GPa; μ i and E i The Poisson's ratio and elastic modulus of the rock are calculated for the i-th loading and unloading operation, respectively. For rocks with an unknown Poisson's ratio, μ i Take 0.25; S3.2.

7. Calculate the hardness of the rock obtained from a single loading and unloading operation. The calculation formula is as follows: -----(8) Where: H i The hardness is calculated based on the loading and unloading data of the i-th loading and unloading operation.

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