Included body total stress-strain constitutive equation construction method based on volumetric quadratic moment

Abstract

The invention discloses a volume quadratic moment-based inclusion total stress-strain constitutive equation construction method, which comprises the following steps of: manufacturing a spatial variability artificial sample comprising an inclusion and a matrix material, and maintaining the spatial variability artificial sample for preset days; carrying out a compression test on the spatial variability artificial sample, and recording a whole-process stress curve, characteristic stress and strain data; based on the parameters of the spatial variability artificial sample, calculating the volume quadratic moment of the inclusion; fitting a function relation between the volumetric quadratic moment and the characteristic stress and strain data based on the characteristic stress and strain data and the volumetric quadratic moment of the inclusion; fitting a total stress curve according to the function relation; the method designed by the invention breaks through the limitation of traditional homogenization hypothesis, directly predicts the total stress curve of a new sample by using the model, reduces repeated experiment requirements, is used for simulating rocks with spatial variability in nature, and has a wide application prospect in the field of rock mass research.

Description

Technical Field

[0001] The present invention relates to the field of rock mass structure and parameter prediction, and in particular to a method for constructing a total stress-strain constitutive equation of an inclusion based on the second moment of volume. Background Art

[0002] Spatial variability in rock masses is a common phenomenon in nature. Due to the influence of natural factors such as diagenesis, sedimentation, and weathering, rock masses may exhibit non-uniform characteristics such as cavities, stratification, and stress concentration. The structure and mechanical parameters of rock masses often vary at different spatial locations. Traditional models often use a homogenization assumption for rock mass structure, treating the rock mass as a continuous medium and assuming that its mechanical properties are the same in all directions in space, ignoring discontinuities in internal structures such as joints and cracks. Constitutive equations are established using elasticity or elastoplastic theory. When rock masses are located in areas with complex geological structures or in nonlinear deformation stages, the mechanical properties of the rock mass cannot be accurately predicted using homogenization models, which will lead to distortions in engineering stability assessments based on the mechanical properties of the rock mass. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for constructing the full stress-strain constitutive equation of inclusions based on the second moment of volume, establish a mathematical correlation model between it and the stress-strain response, and construct a nonlinear mapping of "spatial distribution characteristics to mechanical behavior" through statistical regression methods to reduce the need for repeated experiments.

[0004] To achieve the above functions, the present invention designs a method for constructing the total stress and strain constitutive equation of inclusions based on the volume second moment, and performs the following steps S1 to S5 to complete the total stress and strain prediction of spatially variable inclusions:

[0005] Step S1: preparing a spatially variable artificial sample, the spatially variable artificial sample comprising a brittle matrix material and a plurality of plastic inclusions periodically and evenly distributed in the matrix material; placing the spatially variable artificial sample in a curing box and curing it to a preset age;

[0006] Step S2: placing the spatial variability artificial specimen on a testing machine for a uniaxial compression test, recording the stress curve of the spatial variability artificial specimen from the beginning to failure, and photographing the process before and after the failure of the spatial variability artificial specimen, and recording the characteristic stress and strain data of the spatial variability artificial specimen during the test;

[0007] Step S3: Calculating the volume second moment of the inclusion based on the side length of the spatial variability artificial sample and the number of inclusions on each side of the spatial variability artificial sample;

[0008] Step S4: Based on the characteristic stress and strain data of the artificial specimen with spatial variability during the test and the volume second moment of the inclusion, a functional relationship between the volume second moment and the characteristic stress and strain data is fitted;

[0009] Step S5: According to the functional relationship between the volume second moment and the characteristic stress and strain data, a total stress curve is fitted, and based on the total stress curve, the total stress and strain prediction of the spatially variable inclusion is completed.

[0010] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0011] 1. Construct spatially variable artificial specimens combining brittle matrix materials and plastic inclusions to accurately simulate the rock mass structural characteristics in areas with complex geological structures, breaking through the limitations of traditional homogenization assumptions;

[0012] 2. Conduct uniaxial compression tests on artificial specimens with spatial variability to reflect the compressive properties of each specimen and accurately simulate the nonlinear deformation stage of the rock mass structure, such as the stress-strain characteristics of the rock mass nearing failure;

[0013] 3. Based on the existing spatially variable artificial specimen data (spatial distribution characteristics such as the geometric size and position of inclusions), a mathematical correlation model between it and the stress-strain response is established. A nonlinear mapping of "spatial distribution characteristics to mechanical behavior" is constructed through statistical regression methods. The model is used to directly predict the full stress curve of the new specimen (including peak strength, elastic modulus in the linear elastic stage, residual stage, etc.), simplifying the prediction model and reducing the need for repeated experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a schematic diagram of an artificial sample of spatial variability provided by an embodiment of the present invention;

[0015] Figure 2 1. are cross-sectional views and stereoscopic views of a spatially variable artificial sample B16 provided in an embodiment of the present invention;

[0016] Figure 3 1. are cross-sectional views and stereoscopic views of a spatially variable artificial sample B15 provided in an embodiment of the present invention;

[0017] Figure 4 are a cross-sectional view and a stereoscopic view of a spatially variable artificial sample B14 provided in an embodiment of the present invention;

[0018] Figure 5 1. are cross-sectional views and stereoscopic views of a spatially variable artificial sample B13 provided in an embodiment of the present invention;

[0019] Figure 6are a cross-sectional view and a stereoscopic view of a spatially variable artificial sample B24 provided in an embodiment of the present invention;

[0020] Figure 7 are a cross-sectional view and a stereoscopic view of a spatially variable artificial sample B23 provided in an embodiment of the present invention;

[0021] Figure 8 are a cross-sectional view and a stereoscopic view of a spatially variable artificial sample B22 provided in an embodiment of the present invention;

[0022] Figure 9 are a cross-sectional view and a stereoscopic view of a spatially variable artificial sample B33 provided in an embodiment of the present invention;

[0023] Figure 10 are a cross-sectional view and a stereoscopic view of a spatially variable artificial sample B32 provided in an embodiment of the present invention;

[0024] Figure 11 is a comparison chart of the compressive strength of different groups of spatially variable artificial specimens provided by an embodiment of the present invention;

[0025] Figure 12 is a diagram of a volume second moment calculation model provided according to an embodiment of the present invention;

[0026] Figure 13 is a total stress curve of a spatially variable artificial specimen provided by an embodiment of the present invention;

[0027] Figure 14 is a fitting curve diagram of volume second moment, characteristic stress and strain provided according to an embodiment of the present invention;

[0028] Figure 15 3 is a fitted full stress curve diagram provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0030] The method for constructing the total stress and strain constitutive equation of inclusions based on the volume second moment provided in an embodiment of the present invention performs the following steps S1 to S5 to complete the total stress and strain prediction of spatially variable inclusions:

[0031] Step S1: preparing a spatially variable artificial sample, the spatially variable artificial sample comprising a brittle matrix material and a plurality of plastic inclusions periodically and evenly distributed in the matrix material; placing the spatially variable artificial sample in a curing box and curing it to a preset age;

[0032] The specific steps of step S1 are as follows:

[0033] Step S1.1: Apply vaseline evenly to the side walls and bottom of a 150 mm cube test mold.

[0034] Step S1.2: Mixing the matrix material according to a predetermined ratio;

[0035] The inclusion is made of a filler material with a ring-to-cement ratio of 1:1.2, a water-to-cement ratio of 0.24, 30% kaolin to cement, 0.25% silane to water-based epoxy resin, and a ring-to-solid ratio of 1:1.5. The mass per unit volume of each component in the inclusion is shown in Table 1:

[0036] Table 1. Ratio of inclusion filling materials

[0037]

[0038] The matrix material is made by mixing ultrafine cement, standard sand and water in a water-cement ratio of 0.34 and a cement-sand ratio of 1:2. The unit volume mass of each component in the matrix material is shown in Table 2:

[0039] Table 2. Matrix material ratio

[0040]

[0041] Step S1.3: Add matrix material to the test mold. When the height of the first layer of matrix material reaches the expected height, press each inclusion of the first layer into the matrix material one by one, so that the top surface of all inclusions in the first layer is at the same level as the top surface of the first layer of matrix material.

[0042] Reference Figure 1 The spatial variability artificial specimen is a 15cm cube, composed of a cement mortar matrix and inclusions made of GW9 material. There are three types of inclusions: 1cm cubes, 2cm cubes, and 3cm cubes. The inclusions are evenly distributed throughout the spatial variability artificial specimen, with several inclusions per side. Therefore, the size and spacing of the inclusions vary between different types of spatial variability artificial specimens.

[0043] The following is an example of an inclusion distribution scheme:

[0044] 1. The side length of the inclusions in the spatial variability artificial sample B16 is 1 cm. Six inclusions are evenly distributed on each side of the spatial variability artificial sample. The interval between two inclusions is 1.5 cm. Therefore, a total of 216 (6×6×6) inclusions are evenly distributed in the spatial variability artificial sample B16. The cross-sectional view and stereoscopic view are shown in Figure 1. Figure 2 As shown;

[0045] 2. The side length of the inclusions in the spatial variability artificial sample B15 is 1 cm. In the spatial variability artificial sample, 5 inclusions are evenly arranged on each side. The interval between two inclusions is 2 cm. Therefore, a total of 125 (5×5×5) inclusions are evenly arranged in the spatial variability artificial sample B15. The cross-sectional view and stereoscopic view are as follows: Figure 3 As shown;

[0046] 3. The inclusions in the spatial variability artificial sample B14 have a side length of 1 cm. Four inclusions are evenly distributed on each side of the spatial variability artificial sample, and the interval between two inclusions is 2.75 cm. Therefore, a total of 64 (4×4×4) inclusions are evenly distributed in the spatial variability artificial sample B14; the cross-sectional view and stereoscopic view are shown in Figure 2. Figure 4 As shown;

[0047] 4. The inclusions in the spatial variability artificial sample B13 have a side length of 1 cm. Three inclusions are evenly distributed on each side of the spatial variability artificial sample. The interval between two inclusions is 4 cm. Therefore, a total of 27 (3×3×3) inclusions are evenly distributed in the spatial variability artificial sample B13. The cross-sectional view and stereoscopic view are as follows: Figure 5 As shown;

[0048] 5. The side length of the inclusions in the spatial variability artificial sample B24 is 2 cm. There are 4 inclusions evenly distributed on each side of the spatial variability artificial sample, and the interval between two inclusions is 1.75 cm. Therefore, a total of 64 (4×4×4) inclusions are evenly distributed in the spatial variability artificial sample B24; the cross-sectional view and stereoscopic view are as follows: Figure 6 As shown;

[0049] 6. The side length of the inclusions in the spatial variability artificial sample B23 is 2 cm. Three inclusions are evenly distributed on each side of the spatial variability artificial sample. The interval between two inclusions is 3 cm. Therefore, a total of 27 (3×3×3) inclusions are evenly distributed in the spatial variability artificial sample B23. The cross-sectional view and stereoscopic view are as follows: Figure 7 As shown;

[0050] 7. The side length of the inclusions in the spatial variability artificial sample B22 is 2 cm. Two inclusions are evenly distributed on each side of the spatial variability artificial sample. The interval between two inclusions is 5.5 cm. Therefore, a total of 8 (2×2×2) inclusions are evenly distributed in the spatial variability artificial sample B22. The cross-sectional view and stereoscopic view are as follows: Figure 8 As shown;

[0051] 8. The side length of the inclusions in the spatial variability artificial sample B33 is 3 cm. Three inclusions are evenly distributed on each side of the spatial variability artificial sample. The interval between two inclusions is 2 cm. Therefore, a total of 27 (3×3×3) inclusions are evenly distributed in the spatial variability artificial sample B33. The cross-sectional view and stereoscopic view are as follows: Figure 9 As shown;

[0052] 9. The inclusions in the spatial variability artificial sample B32 have a side length of 3 cm. Two inclusions are evenly distributed on each side of the spatial variability artificial sample. The interval between two inclusions is 4.5 cm. Therefore, a total of 8 (2×2×2) inclusions are evenly distributed in the spatial variability artificial sample B32. The cross-sectional view and stereogram are as follows: Figure 10 As shown;

[0053] Step S1.4: Continue adding matrix material to the test mold. When the height of the second layer of matrix material reaches the expected height, press each inclusion of the second layer into the matrix material one by one, so that the top surface of all inclusions in the second layer is on the same level as the top surface of the second layer of matrix material.

[0054] Step S1.5: Repeat steps S1.3 to S1.4, adding matrix material and inclusions layer by layer until the number of layers is preset, and pouring to obtain an artificial sample with spatial variability; the estimated pouring height of each layer of matrix material is shown in Table 3:

[0055] Table 3. Estimated pouring height of each layer of matrix material

[0056]

[0057] Step S1.6: Place the cast spatial variability artificial specimen in a constant temperature and humidity curing chamber for 24 hours, and demould it after curing.

[0058] Step S1.7: Place the spatially variable artificial specimen in a curing chamber and maintain it in a constant temperature and humidity environment at 95% humidity and 22°C until it reaches a predetermined age. The curing period can be 3 days, 7 days, or 28 days. In one embodiment, the spatially variable artificial specimen is placed in the curing chamber and maintained for 28 days.

[0059] Step S2: placing the spatial variability artificial specimen on a testing machine for a uniaxial compression test, gradually increasing the load until the spatial variability artificial specimen fails, recording the stress curve of the spatial variability artificial specimen from the beginning to failure, and photographing the process before and after the failure of the spatial variability artificial specimen. The characteristic stress and strain data of the spatial variability artificial specimen during the test are recorded;

[0060] The recorded characteristic stresses include transition stress, peak stress, and residual stress; the recorded strains include transition strain, peak strain, and residual strain.

[0061] Different artificial specimens with different spatial variability exhibit different compressive properties, and these differ significantly from one another. The compressive strengths of the specimens with different inclusions at different ages are summarized in Table 4. The compressive properties of the specimens at the same age are ranked by compressive strength. Finally, the rankings for the three ages are summed to obtain the summed value. The compressive properties of the specimens with inclusions are analyzed based on this summed value.

[0062] Table 4. Compressive strength of samples with different inclusions and their performance ranking

[0063]

[0064] Based on the summed values of the compressive performance rankings of the samples in Table 4, the nine inclusion samples (B13 to B33) can be divided into four tiers: the first tier comprises B14 and B13; the second tier comprises B22, B23, and B24; the third tier comprises B15 and B16; and the fourth tier comprises B32 and B33. The average summed values of the rankings for the four tiers are 5, 15, 17, and 23, respectively. Compared to the inclusion samples in the first and second tiers, the inclusion samples in the first and second tiers exhibit essentially the same number of inclusions within the same volume (except for sample B22), but differ in size. The inclusion samples with smaller inclusions exhibited better compressive performance. This conclusion can also be drawn from a comparison of the samples in the second and fourth tiers. A comparison of the first and third tiers reveals that, within the same volume, the inclusions are of the same size but differ in number, with the inclusion samples with fewer inclusions exhibiting better compressive performance.

[0065] In order to more intuitively reflect the compressive properties of each inclusion sample, the compressive strength of each inclusion sample at different ages is drawn as a bar graph, such as Figure 11 As shown in the figure. The compressive strength of most inclusion specimens increases with the increase of curing age. However, the compressive strength of the B13 inclusion specimen cured for 7 days decreased by about 6.5% compared with that of the 3-day curing, and the compressive strength of the B24 inclusion specimen cured for 28 days decreased by about 11.5% compared with that of the 7-day curing. The blue horizontal line in the figure represents the compressive strength of the matrix made of mortar after curing for 28 days. The specimens of the same age that exceed this strength are the B13, B14 and B22 inclusion specimens. These three inclusion specimens show that adding certain inclusions to the mortar is helpful in enhancing the compressive strength of the mortar, similar to concrete (adding pebbles or stones to the mortar). Inclusions can hinder the destruction of the inclusion specimens during their destruction, thereby improving the compressive performance of the inclusion specimens. The volume proportion of inclusions in other inclusion samples (such as B15, B16, B23, etc.) is greater than that in B13, B14, and B22 inclusion samples. At the same time, the compressive strength values are lower than the blue baseline, indicating that adding excessive inclusions to the matrix not only fails to improve the compressive properties of the sample, but instead leads to a decrease in its compressive strength.

[0066] Step S3: Calculating the volume second moment of the inclusion based on the side length of the spatial variability artificial sample and the number of inclusions on each side of the spatial variability artificial sample;

[0067] Reference Figure 12 In step S3, a spatial coordinate system is established for the spatial variability artificial sample, the coordinate origin o is taken as the geometric space center of the spatial variability artificial sample, and the directions of the three coordinate axes are taken as the directions of the three sides of the spatial variability artificial sample;

[0068] The second moment of volume of inclusions is calculated as follows:

[0069]

[0070] Where, I v represents the volume second moment of the inclusion, v represents the volume of the inclusion, X represents the distance between the projection point of the center point of the inclusion on the xOy plane and the y-axis, Y represents the distance between the projection point of the center point of the inclusion on the xOy plane and the x-axis, and Z represents the distance between the center point of the inclusion and the xOy plane.

[0071] When the number of inclusions n on each side of the spatial variability artificial specimen is an even number, the volume quadratic moment of each inclusion in the specimen with respect to the coordinate origin o is taken, and the following formula can be obtained:

[0072]

[0073] When the number of inclusions n on each side of the spatial variability artificial sample is an odd number, the derivation method is the same as that for an even number. When the number of inclusions n on each side of the spatial variability artificial sample is 5, the volume second moment of each inclusion in the sample with respect to the coordinate origin o is taken, and the following formula can be obtained:

[0074]

[0075] When the number of inclusions n on each side of the spatial variability artificial sample is 3, the volume second moment of each inclusion in the sample with respect to the coordinate origin o is taken, and the following formula can be obtained:

[0076]

[0077] The calculation results of the volume second moment of inclusions in each sample about the coordinate origin are shown in Table 5. When the size b of the inclusions in the sample and the number n of inclusions arranged on each side are small, the volume second moment of the inclusions in the sample is small, and vice versa.

[0078] Table 5. Volume percentage and volume second moment of inclusions in different samples

[0079]

[0080] Step S4: Based on the characteristic stress and strain data of the artificial specimen with spatial variability during the test and the volume second moment of the inclusion, a functional relationship between the volume second moment and the characteristic stress and strain data is fitted;

[0081] The functional relationship between the fitted volume second moment and the characteristic stress and strain data in step S4 is as follows:

[0082] y=ax 2 +bx+c

[0083] Among them, a, b, and c are unknown parameters, x is the volume second moment of the spatially variable artificial specimen, and y is the characteristic stress and strain data.

[0084] Reference Figure 13 There are three key points in the full stress curve: turning point A, peak point B, and residual point C. Turning point A refers to the turning point where the sample turns from the compaction stage to the linear elastic stage. Before and after this point, the elastic modulus of the sample changes greatly, showing different elastic stiffness. Peak point B refers to the point where the sample reaches the ultimate compressive strength, and the strain corresponding to this point is called the peak strain. The residual strength corresponding to the residual point C means that the sample is obviously damaged and ruptured after experiencing the peak stress, but there is still friction and bite between the broken aggregate and the cement matrix, so that the sample can still withstand a certain load.

[0085] In the total stress curve, if the six quantities corresponding to the stress and strain at the turning point, the stress and strain at the peak point, and the stress and strain at the residual point are determined, the total stress curve of the specimen can be obtained. In engineering applications, the concrete strength after 28 days of curing is usually used as the standard value of concrete strength. The volume second moment of specimens with different inclusion patterns is different, and specimens with different inclusion patterns exhibit different characteristic stresses (turning stress, peak stress, and residual stress) and strains (turning strain, peak strain, and residual strain). By studying the relationship between the volume second moment of the specimen and the characteristic stress and strain, the total stress curve of the specimen can be inferred based on the spatial distribution of inclusions in the specimen, thereby predicting the total stress curve of more inclusion specimens.

[0086] The characteristic stress and strain values of the samples cured for 28 days refer to Table 6:

[0087] Table 6. Characteristic stress and strain values of samples cured for 28 days

[0088]

[0089] The fitting results of the undetermined parameters in the function of different characteristic stresses and strains and volume second moments in step S4 are shown in Table 7:

[0090] Table 7. Fitting results of quadratic function with undetermined parameters

[0091]

[0092] Step S5: According to the functional relationship between the volume second moment and the characteristic stress and strain data, a total stress curve is fitted, and based on the total stress curve, the total stress and strain prediction of the spatially variable inclusion is completed.

[0093] For general artificial specimens with spatial variability, if the full stress curve is not available, the curves of volume secondary moment, characteristic stress and strain are fitted according to the functional relationship between volume secondary moment and characteristic stress and strain data. The fitting curves of each volume secondary moment, characteristic stress and strain refer to Figure 14 ;in Figure 14 (a) is the turning stress fitting curve, Figure 14 (b) is the turning strain fitting curve, Figure 14 (c) is the peak stress fitting curve, Figure 14 (d) is the peak strain fitting curve, Figure 14 (e) is the residual stress fitting curve, Figure 14 (f) is the residual strain fitting curve; the turning stress is obtained by fitting and turning strain Determine the turning point Get the fitted peak stress and peak strain Thus, the peak point is determined Get the fitted residual stress and residual strain Thus, the residual points Connect the origin, point A, point B and point C in sequence with straight lines, and then the full stress curve of the specimen can be obtained by fitting method, such as Figure 15 shown.

[0094] Based on the existing inclusion sample data (spatial distribution characteristics such as the geometric size and position of the inclusions), a mathematical correlation model between it and the stress-strain response is established. Through the statistical regression method, a nonlinear mapping of "spatial distribution characteristics to mechanical behavior" is constructed, breaking through the limitations of the traditional homogenization assumption. The model is used to directly predict the full stress curve of the new sample (including peak strength, elastic modulus in the linear elastic stage, residual stage, etc.), reducing the need for repeated experiments.

[0095] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A method for constructing the full stress-strain constitutive equation of inclusions based on the second moment of volume, characterized by: Execute the following steps S1 to S5 to complete the full stress and strain prediction of spatially variable inclusions: Step S1: preparing a spatially variable artificial sample, the spatially variable artificial sample comprising a brittle matrix material and a plurality of plastic inclusions periodically and evenly distributed in the matrix material; placing the spatially variable artificial sample in a curing box and curing it to a preset age; Step S2: placing the spatial variability artificial specimen on a testing machine for a uniaxial compression test, recording the stress curve of the spatial variability artificial specimen from the beginning to failure, and photographing the process before and after the failure of the spatial variability artificial specimen, and recording the characteristic stress and strain data of the spatial variability artificial specimen during the test; Step S3: Calculating the volume second moment of the inclusion based on the side length of the spatial variability artificial sample and the number of inclusions on each side of the spatial variability artificial sample; Step S4: Based on the characteristic stress and strain data of the artificial specimen with spatial variability during the test and the volume second moment of the inclusion, a functional relationship between the volume second moment and the characteristic stress and strain data is fitted; Step S5: According to the functional relationship between the volume second moment and the characteristic stress and strain data, a total stress curve is fitted, and based on the total stress curve, the total stress and strain prediction of the spatially variable inclusion is completed.

2. The method for constructing the total stress-strain constitutive equation of inclusions based on the volume second moment according to claim 1, characterized in that: The specific steps of step S1 are as follows: Step S1.1: Apply vaseline evenly to the side walls and bottom of the cube test mold; Step S1.2: Mixing the matrix material according to a predetermined ratio; Step S1.3: Add matrix material to the test mold. When the height of the first layer of matrix material reaches the expected height, press each inclusion of the first layer into the matrix material one by one, so that the top surface of all inclusions in the first layer is at the same level as the top surface of the first layer of matrix material. Step S1.4: Continue adding matrix material to the test mold. When the height of the second layer of matrix material reaches the expected height, press each inclusion of the second layer into the matrix material one by one, so that the top surface of all inclusions in the second layer is on the same level as the top surface of the second layer of matrix material. Step S1.5: Repeat steps S1.3 to S1.4, adding matrix material and inclusions layer by layer until the number of layers is preset, and casting to obtain an artificial sample with spatial variability; Step S1.6: Place the cast spatial variability artificial specimen in a constant temperature and humidity curing chamber for 24 hours, and demould it after curing. Step S1.7: Place the spatially variable artificial specimen in a curing box and cure it to a preset age.

3. The method for constructing the total stress-strain constitutive equation of inclusions based on the volume second moment according to claim 1, characterized in that: The inclusion is made of a filling material with a ring-to-cement ratio of 1:1.2, a water-to-cement ratio of 0.24, a kaolin content of 30% relative to the mass of cement, a silane content of 0.25% relative to the mass of the waterborne epoxy resin, and a ring-to-solid ratio of 1:1.

5.

4. The method for constructing the total stress-strain constitutive equation of inclusions based on the volume second moment according to claim 1, characterized in that: The matrix material is made by mixing ultrafine cement, standard sand and water in a water-cement ratio of 0.34 and a cement-sand ratio of 1:

2.

5. The method for constructing the total stress-strain constitutive equation of inclusions based on the volume second moment according to claim 1, characterized in that: In step S1, the spatial variability artificial sample is placed in a curing box and cured for 28 days.

6. The method for constructing the total stress-strain constitutive equation of inclusions based on the volume second moment according to claim 1, characterized in that: In step S3, a spatial coordinate system is established for the spatial variability artificial sample, with the coordinate origin o being the geometric center of the spatial variability artificial sample, and the directions of the three coordinate axes being the directions of the three sides of the spatial variability artificial sample; The second moment of volume of inclusions is calculated as follows: Where, I v represents the volume second moment of the inclusion, v represents the volume of the inclusion, X represents the distance between the projection point of the center point of the inclusion on the xOy plane and the y-axis, Y represents the distance between the projection point of the center point of the inclusion on the xOy plane and the x-axis, and Z represents the distance between the center point of the inclusion and the xOy plane.

7. The method for constructing the total stress-strain constitutive equation of inclusions based on the volume second moment according to claim 1, characterized in that: The functional relationship between the fitted volume second moment and the characteristic stress and strain data in step S4 is as follows: y=ax 2 +bx+c Among them, a, b, and c are unknown parameters, x is the volume second moment of the spatially variable artificial specimen, and y is the characteristic stress and strain data.

8. The method for constructing the total stress-strain constitutive equation of inclusions based on the volume second moment according to claim 1, characterized in that: Characteristic stresses include transition stress, peak stress, and residual stress; strains include transition strain, peak strain, and residual strain.

9. The method for constructing the total stress-strain constitutive equation of inclusions based on the volume second moment according to claim 8, characterized in that: The specific steps of step S5 are as follows: Step S5.1: fitting curves of the volume second moment, characteristic stress, and strain respectively according to the functional relationship between the volume second moment and the characteristic stress and strain data; Step S5.2: According to the transition stress obtained by fitting and turning strain Determine the turning point The peak stress obtained by fitting and peak strain Thus, the peak point is determined The residual stress obtained by fitting and residual strain Thus, the residual points Step S5.3: Connect the origin, point A, point B, and point C in sequence with straight lines to obtain a fitted total stress curve.

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