Sandstone dynamic damage and energy evolution mechanism research method under water immersion effect

Abstract

The invention relates to a research method for sandstone dynamic damage and an energy evolution mechanism under the action of water immersion, and belongs to the technical field of rock mass mechanics research methods. According to the technical scheme, the method comprises the following steps: preparing and pretreating a rock sample; the SHPB impact device and the dynamic monitoring system are used for carrying out dynamic impact tests on sandstone samples under different conditions; further analyzing the energy evolution law of the sandstone in the damage process under the dynamic impact action by calculating the input energy, the dissipation energy and the elastic energy of the sandstone sample per unit volume in the natural state; and establishing a corrected dynamic damage constitutive model, and carrying out damage characteristic analysis on the saturated sandstone under the impact load. The method has the beneficial effects that theoretical analysis is provided for the failure instability mechanism of the sandstone containing the initial damage after disturbance in the mining of the large water mine, and the safe mining of the large water mine is guided.

Description

Technical Field

[0001] The present invention relates to a research method for the dynamic damage and energy evolution mechanism of sandstone under immersion, belonging to the technical field of rock mechanics research methods. Background Art

[0002] As a heterogeneous multi-phase complex structural material, rock naturally has various defects. When it comes into contact with moisture in nature, the deterioration trend of these original damage defects is significantly enhanced, and in severe cases, it will lead to the failure and instability of the rock mass. Therefore, studying the dynamic response characteristics and damage constitutive relationship of saturated damaged sandstone under impact loads is of great significance for guiding the formation mechanism of sandstone dynamic disasters and guiding the safe mining of mines.

[0003] Currently, in the field of damage constitutive model technology, scholars at home and abroad have carried out a large number of experimental studies based on the Split Hopkinson Pressure Bar (SHPB) device. Duan Jichao et al. constructed a macro-meso scale composite damage constitutive model of limestone under the coupling action of dry and wet dynamic loads based on the Lemaitre strain equivalence principle, and analyzed the stress-strain problem under the action of dry-wet cycles. Wang Dengke et al. established a strength-type statistical damage constitutive model of coal and rock under different conditions based on the D-P criterion and statistical damage theory, which can effectively describe the dynamic characteristics of coal and rock. Sun Qingpei et al. established a simple damage constitutive model considering the rock mass structure effect and load effect. Cui Huidong established a statistical damage constitutive model of frozen sandstone under dynamic load with initial damage, describing the damage evolution process of low-temperature sandstone with different water contents. Yang et al. studied the dynamic viscoelastic damage characteristics of soft rock from macroscopic and microscopic perspectives, and believed that the strength of micro-elements and damage variables obey the Weibull distribution. Long Yu established a damage constitutive model of sandstone based on the Weibull distribution to describe the damage evolution process of sandstone under different strain rates. Fu Jingjing et al. accurately characterized the stress-strain curve shape and mechanical characteristics of 3D printed layered rock-like materials based on the Zhu-Wang-Tang constitutive model. Ji Dongliang et al. constructed a constitutive model of macro-meso scale damage of composite rock mass based on the dynamic load response characteristics of rock mass, reproducing the internal damage process of composite rock mass C-R.

[0004] Regarding the mechanical mechanism of rock mass, previous studies have carried out static and dynamic experiments. Feng Guorui et al. studied the influence of early loading on the later mechanical properties of gangue-cemented filling bodies, and established a damage model and constitutive equation for gangue-cemented filling columns with different cross-sectional side lengths. Ma Binwen et al. studied the phenomenon of surrounding rock impact instability induced by dynamic disturbance, revealing the relationship between dynamic load disturbance and surrounding rock impact failure. Zhou Changtai et al. constructed a strain energy release dispersion continuity function for rock materials, which is effectively applicable to the yield and failure of rock under dynamic disturbance. Hou et al. studied the evolution and energy dissipation law of cemented filling bodies under dynamic impact tests, and established a damage growth model. Liang et al. studied the influence of chemical corrosion on sandstone from the mesoscopic perspective and established a damage evolution model.

[0005] In summary, the existing technical methods mainly focus on the dynamic mechanical properties of rock masses and the damage laws of rocks in different states. However, the research methods for the dynamic damage and energy evolution mechanism of sandstone under the coupled action of water saturation and initial damage still need to be supplemented. It is urgent to propose a research method for the dynamic damage and energy evolution mechanism of sandstone under the action of immersion, explore the influence of initial damage and water saturation degree on the dynamic damage and energy evolution law of sandstone, and the research results can provide theoretical analysis for the failure and instability mechanism of sandstone with initial damage after being disturbed in the mining of large-water mines, guiding the safe mining of large-water mines. Summary of the Invention

[0006] The purpose of the present invention is to provide a research method for the dynamic damage and energy evolution mechanism of sandstone under the action of immersion. By using the SHPB impact device and the dynamic monitoring system to conduct dynamic impact tests on sandstone with different damage and water saturation degrees, the energy evolution during the dynamic failure process is obtained based on the energy balance theory, and a damage constitutive model considering initial damage and water saturation degree is established in combination with the dynamic stress-strain curve, providing theoretical analysis for the failure and instability mechanism of sandstone with initial damage after being disturbed in the mining of large-water mines, guiding the safe mining of large-water mines, and effectively solving the above problems existing in the background technology.

[0007] The technical solution of the present invention is: a research method for the dynamic damage and energy evolution mechanism of sandstone under the action of immersion, comprising the following steps:

[0008] The first step is to prepare and preprocess the rock samples;

[0009] The second step is to use the SHPB impact device and the dynamic monitoring system to conduct dynamic impact tests on sandstone specimens under different conditions;

[0010] The third step is the analysis of the dynamic failure energy evolution process. By calculating the input energy, dissipated energy and elastic energy of the sandstone specimen per unit volume in the natural state, the energy evolution law during the dynamic impact failure process of the sandstone is further analyzed;

[0011] The fourth step is to establish a modified dynamic damage constitutive model, conduct damage variable analysis of the sandstone and micro-element strength analysis of the sandstone, construct a modified damage constitutive model, determine the fitting parameters of the damage constitutive model, and verify the accuracy of the damage constitutive model;

[0012] The fifth step is to analyze the damage characteristics of water-saturated sandstone under impact load.

[0013] In the first step, the rock samples are divided into three groups: undamaged, low-damage and medium-damage, and each group of rock samples is divided into natural, water-saturated and dry states.

[0014] In the second step, the impact air pressure is set to 0.45 MPa.

[0015] In the fourth step, the specific steps are as follows:

[0016] (1) Analysis of the damage variable of sandstone. It is assumed that the sandstone specimen is an aggregate of micro-elements composed of many micro-elements. Let the strength of the micro-elements conform to the Weibull distribution, and the probability density is:

[0017]

[0018] In the formula: F represents the strength of the micro-element, and m and F0 are the Weibull distribution parameters;

[0019] Sandstones with different damages and water saturations are impacted. Let the number of damaged micro-elements after being subjected to the impact load be N a , and the total number of micro-elements is set to N. Then the damage variable D under the impact of sandstones with different damages and water saturations can be defined as:

[0020]

[0021] (2) Analysis of the micro-element strength of sandstone. It can be seen from Equation (2) that there is a certain relationship between the damage variable D of the rock and the strength F of the micro-element. The D-P criterion can more intuitively reflect the relationship between the micro-element strength and the mechanical properties of the material, and can more accurately reflect the true situation of the rock than other criteria. Using the D-P criterion to define the micro-element strength of sandstone, we have:

[0022]

[0023]

[0024] In the formula: α is the strength parameter; c is the internal friction angle; I1 and J2 are the first invariant of the stress tensor and the second invariant of the stress deviator; σ1, σ2, and σ3 are the nominal stresses in the triaxial test; E is the elastic modulus; μ is the Poisson's ratio; ε1 is the axial strain;

[0025] In the uniaxial test, σ1 = σ2 = 0, ε1 = ε. By combining Equation (3) and Equation (4), we can obtain:

[0026]

[0027] (3) Construct a modified damage constitutive model

[0028] Based on the strain equivalence hypothesis proposed by Lemaitre, combined with Equation (2), the damage constitutive model of sandstone under uniaxial dynamic load can be obtained

[0029]

[0030] The parameters m and F0 in the damage constitutive model can be obtained through the peak point coordinates (ε in the dynamic stress-strain curvea , σ a ) It is obtained that the derivative of the known peak point is 0 and it is located in the damage constitutive model of the rock, which is the critical failure point of the rock. Substituting it in, we can obtain:

[0031]

[0032]

[0033] Substituting Equation (7), Equation (8) and Equation (5) into Equation (6), the modified damage constitutive equation of different damage-saturation sandstones can be obtained as:

[0034]

[0035] (4) Determine the fitting parameters of the damage constitutive model

[0036] Define the initial damage as d and the saturation as W s , After the sandstone specimen is damaged, the wave velocity changes, and after saturation, the mass changes. The functional relationships between the dynamic elastic modulus E, the peak stress σ a and the peak strain ε a and the wave velocity w and the mass difference rate m can be established. To express their functional relationships, a response surface diagram with the wave velocity and the mass difference rate as the abscissa and the dynamic elastic modulus, the peak stress and the peak strain as the ordinate is designed through response surface design; combining with the surface diagram, E, σ a and ε a The relationships with w and m are as shown in the following equations (10 - 12). Substitute the parameters of the wave velocity w, where w > 0, and the mass difference rate m, where m > -0.032, into the model (10 - 12) to obtain the damage constitutive curves of sandstones under different initial damages and saturations

[0037] E = -5627.712 + 3.428×10 5 m + 5.322w - 55.56mw - 6.54×10 6 m 2 -3.16×10 -4 w 2 (10)

[0038] σ a = 343.18 - 796.01m + 0.196w + 0.081mw + 8266.46m 2 + 3.3×10 -5 w 2 (11)

[0039] ε a= -77.024 - 1042.16m + 0.0562w + 0.3095mw + 2674.597m 2 -9.25×10 -6 w 2 (12)

[0040] (5) Verification of the accuracy of the damage constitutive model

[0041] Draw a comparison chart of the dynamic stress-strain curves of sandstone measured in the indoor impact test under different states and the fitted damage constitutive curves to verify the accuracy of the damage constitutive model.

[0042] In the fifth step, the initial damage variable of sandstone can be defined by the wave velocity before and after damage, and the saturated water damage can be defined by the porosity before and after saturation, that is

[0043]

[0044] D 初-饱 = D 初 + D 饱 (15)

[0045] In the formula: W represents the longitudinal wave velocity of sandstone, and T represents the total area of the T2 spectral peaks of saturated sandstone;

[0046] Calculate the damage value existing in the sandstone after initial damage through formula (13), calculate the damage caused by saturation to the sandstone through formula (14), and calculate the damage value existing in the sandstone before dynamic load through formula (15);

[0047] It can be seen from formulas (6) and (9) that the expression of the damage variable of sandstone under dynamic load is:

[0048]

[0049] Combining formulas (15) and (16), the damage expression in the state of saturated water with initial damage can be obtained as: D 总 = D 初-饱 + D 荷 - D 初-饱 D 荷 (17)

[0050] The damage value of sandstone changes with the change of strain. In order to analyze the influence of initial damage and saturation degree on the whole process of damage, combine the dynamic stress-strain curve to analyze the damage evolution characteristics of sandstone under dynamic load; draw the whole process damage curves of sandstone in different states and analyze them; the whole process damage curves include the dynamic stress-strain curves measured in the indoor impact test and the strain-damage value curves drawn according to formula (17).

[0051] The beneficial effects of the present invention are as follows: By using the SHPB impact device and the dynamic monitoring system to conduct dynamic impact tests on sandstones with different damage and water saturation degrees, the energy evolution during the dynamic failure process is obtained based on the energy balance theory, and a damage constitutive model considering the initial damage and water saturation degree is established in combination with the dynamic stress-strain curve, providing a theoretical analysis for the failure and instability mechanism of sandstones with initial damage after being disturbed during the mining of large-water mines and guiding the safe mining of large-water mines. Brief Description of the Drawings

[0052] Figure 1 is a schematic flow chart of the method of the present invention;

[0053] Figure 2 is a diagram of the dynamic energy evolution process of sandstones with natural-undamaged damage degree in an embodiment of the present invention;

[0054] Figure 3 is a diagram of the dynamic energy evolution process of sandstones with natural-low damage degree in an embodiment of the present invention;

[0055] Figure 4 is a diagram of the dynamic energy evolution process of sandstones with natural-medium damage degree in an embodiment of the present invention;

[0056] Figure 5 is a response surface diagram of the dynamic elastic modulus in an embodiment of the present invention;

[0057] Figure 6 is a response surface diagram of the peak stress in an embodiment of the present invention;

[0058] Figure 7 is a response surface diagram of the peak strain in an embodiment of the present invention;

[0059] Figure 8 is a comparison diagram of the dynamic stress-strain curves between the natural state test and the theoretical (model) in an embodiment of the present invention;

[0060] Figure 9 is a comparison diagram of the dynamic stress-strain curves between the water-saturated state test and the theoretical (model) in an embodiment of the present invention;

[0061] Figure 10 is a comparison diagram of the dynamic stress-strain curves between the dry state test and the theoretical (model) in an embodiment of the present invention;

[0062] Figure 11 is a damage evolution curve diagram of sandstones in the natural state in an embodiment of the present invention;

[0063] Figure 12 is a damage evolution curve diagram of sandstones in the water-saturated state in an embodiment of the present invention. Detailed Embodiments

[0064] In order to make the objectives, technical solutions, and advantages of the invention implementation cases clearer, the following will, in combination with the attached drawings in the implementation cases, clearly and completely describe the technical solutions in the implementation cases of the present invention. Obviously, the described implementation cases are a small part of the implementation cases of the present invention, rather than all of them. Based on the implementation cases in the present invention, all other implementation cases obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present invention.

[0065] A research method for the dynamic damage and energy evolution mechanism of sandstone under immersion includes the following steps:

[0066] The first step is to prepare and preprocess the rock samples;

[0067] The second step is to use the SHPB impact device and the dynamic monitoring system to conduct dynamic impact tests on sandstone specimens under different conditions;

[0068] The third step is the analysis of the dynamic failure energy evolution process. By calculating the input energy, dissipated energy, and elastic energy of the sandstone specimen per unit volume in the natural state, further analyze the energy evolution law during the failure process of the sandstone under dynamic impact;

[0069] The fourth step is to establish a modified dynamic damage constitutive model, conduct damage variable analysis of the sandstone and microelement strength analysis of the sandstone, construct a modified damage constitutive model, determine the fitting parameters of the damage constitutive model, and verify the accuracy of the damage constitutive model;

[0070] The fifth step is to analyze the damage characteristics of saturated sandstone under impact load.

[0071] In the first step, the rock samples are divided into three groups: undamaged, low-damage, and medium-damage, and each group of rock samples is divided into natural, saturated, and dry states.

[0072] In the second step, the impact air pressure is set to 0.45 MPa.

[0073] In the fourth step, the specific steps are as follows:

[0074] (1) Damage variable analysis of the sandstone. Assume that the sandstone specimen is an aggregate of microelements composed of many microelements, and assume that the strength of the microelements conforms to the Weibull distribution, and the probability density is:

[0075]

[0076] In the formula: F represents the strength of the microelement, and m and F0 are Weibull distribution parameters;

[0077] Impact different damaged and saturated sandstones, and assume that the number of damaged microelements after being subjected to the impact load is N a, if the total number of micro-elements is set to N, then the damage variable D under the impact of sandstone with different damage and water saturation can be defined as:

[0078]

[0079] (2) Analysis of the strength of micro-elements of sandstone. It can be seen from Equation (2) that there is a certain relationship between the damage variable D of the rock and the strength F of the micro-element. The D-P criterion can more intuitively reflect the relationship between the strength of the micro-element and the mechanical properties of the material, and can reflect the true situation of the rock more accurately than other criteria. Using the D-P criterion to define the strength of the micro-element of sandstone, we have:

[0080]

[0081] Where: α is the strength parameter; c is the internal friction angle; I1 and J2 are the first invariant of the stress tensor and the second invariant of the stress deviator; σ1, σ2, and σ3 are the nominal stresses in the pseudo-triaxial test; E is the elastic modulus; μ is the Poisson's ratio; ε1 is the axial strain;

[0082] In the uniaxial test, σ1 = σ2 = 0, ε1 = ε. By combining Equation (3) and Equation (4), we can obtain:

[0083]

[0084] (3) Construct a modified damage constitutive model

[0085] Based on the strain equivalence hypothesis proposed by Lemaitre, combined with Equation (2), the damage constitutive model of sandstone under uniaxial dynamic load can be obtained

[0086]

[0087] The parameters m and F0 in the damage constitutive model can be obtained through the peak point coordinates (ε a , σ a ) of the dynamic stress-strain curve. It is known that the derivative of the peak point is 0 and it is located in the damage constitutive model of the rock, which is the critical failure point of the rock. Substituting it in, we can obtain:

[0088]

[0089] Substituting Equation (7), Equation (8), and Equation (5) into Equation (6), the modified damage constitutive equation of sandstone with different damage-water saturation degrees can be obtained as:

[0090]

[0091] (4) Determine the fitting parameters of the damage constitutive model

[0092] Define the initial damage as d and the water saturation as W s, after the sandstone specimen is damaged, the wave velocity changes, and after saturation with water, the mass changes. The dynamic elastic modulus E, peak stress σ a and peak strain ε a The functional relationships with wave velocity w and mass difference rate m are established. To express these functional relationships, response surface design is used to create a response surface plot with wave velocity and mass difference rate as the abscissa and dynamic elastic modulus, peak stress, and peak strain as the ordinate; combined with the surface plot, E, σ a and ε a The relationships with w and m are as shown in the following equations (10 - 12). Substitute the parameters of wave velocity w, where w > 0, and mass difference rate m, where m > -0.032, into model (10 - 12) to obtain the damage constitutive curves of sandstone under different initial damages and degrees of water saturation

[0093] E = -5627.712 + 3.428×10 5 m + 5.322w - 55.56mw - 6.54×10 6 m 2 -3.16×10 -4 w 2 (10)

[0094] σ a = 343.18 - 796.01m + 0.196w + 0.081mw + 8266.46m 2 + 3.3×10 -5 w 2 (11)

[0095] ε a = -77.024 - 1042.16m + 0.0562w + 0.3095mw + 2674.597m 2 - 9.25×10 -6 w 2 (12)

[0096] (5) Verification of the accuracy of the damage constitutive model

[0097] Plot the comparison diagram of the dynamic stress - strain curves of sandstone measured in the indoor impact test under different states and the fitted damage constitutive curves to verify the accuracy of the damage constitutive model

[0098] In the fifth step described above, the initial damage variable of the sandstone can be defined by the wave velocity before and after damage, and the water - saturated damage can be defined by the porosity before and after water saturation, that is

[0099]

[0100] D 初-饱 = D 初+D 饱 (15)

[0101] Where: W represents the longitudinal wave velocity of sandstone, and T represents the total area of the T2 spectral peaks of water-saturated sandstone;

[0102] The damage value existing in the sandstone after initial damage is calculated by Equation (13), the damage caused by water saturation to the sandstone is calculated by Equation (14), and the damage value existing in the sandstone before dynamic loading is calculated by Equation (15);

[0103] It can be seen from Equations (6) and (9) that the damage variable expression of sandstone under dynamic loading is:

[0104]

[0105] Combining Equations (15) and (16), the damage expression in the water-saturated state with initial damage can be obtained as: D 总 = D 初-饱 + D 荷 - D 初-饱 D 荷 (17)

[0106] The damage value of sandstone changes with the change of strain. In order to analyze the influence of initial damage and water saturation on the whole damage process, the damage evolution characteristics of sandstone under dynamic loading are analyzed by combining the dynamic stress-strain curve; the whole-process damage curves of sandstone in different states are plotted and analyzed; the whole-process damage curves include the dynamic stress-strain curve measured by the indoor impact test and the strain-damage value curve plotted according to Equation (17).

[0107] Example:

[0108] (1) Rock sample preparation and pretreatment. The sandstone is taken from a mine in Hebei. The sandstone is made into a round cake specimen with a size of 50mm×25mm according to relevant test standards, and the end face is flat. The rock samples are pretreated, and two damage states are created for the sandstone specimens by selecting impact air pressures of 0.3MPa and 0.35MPa; the water saturation and drying test procedures follow the International Society for Rock Mechanics. Finally, the rock samples are divided into three groups: undamaged, low-damage, and medium-damage, with 6 samples in each group, and each group of rock samples is divided into natural, water-saturated, and dry states. The following Table 1 shows the physical and mechanical parameters of the sandstone.

[0109] Table 1 Physical parameters of sandstone specimens

[0110]

[0111] (2) Using the SHPB impact device and dynamic monitoring system, dynamic impact tests are carried out on sandstone specimens under different conditions, and the impact air pressure is set to 0.45MPa.

[0112] (3) Analysis of the dynamic failure energy evolution process. By calculating the input energy, dissipated energy, and elastic energy of the sandstone specimen per unit volume in the natural state, the energy evolution law during the dynamic impact failure process of the sandstone is further analyzed. Figure 2-4 Figure 2 shows the evolution process of the input energy, dissipated energy, and elastic energy of sandstone specimens with different damage degrees per unit volume with strain. As can be seen from the figure, under dynamic loading, the dynamic failure process of sandstone can be divided into four stages by combining the energy evolution curve and the stress-strain curve of sandstone. The OA segment is linear elastic: as the strain increases, the stress shows a rapid linear increase trend, the original cracks inside the specimen expand, new cracks begin to generate, and the input energy of the specimen is mainly converted into elastic strain energy. The AB segment is the non-linear yield stage: the plastic deformation increases, and as the strain grows, the stress reaches the peak limit, and the increase in damage of the sandstone specimen causes energy dissipation. The BC segment is the stage of elastic energy accumulation after the peak: after the sandstone specimen reaches the compressive strength, the stress begins to decrease, and the rapid growth of dissipated energy leads to internal damage of the specimen. The CD segment is the stage of elastic energy release after the peak: point D is the stress residual point of the stress-strain curve, the elastic energy reaches the energy storage limit at point C, and the elastic energy is released as the kinetic energy of the broken rock blocks.

[0113] (4) Establish a modified dynamic damage constitutive model.

[0114] 1) Analysis of the damage variable. Assume that the sandstone specimen is a micro-element aggregate composed of many micro-elements, and the strength of the micro-element conforms to the Weibull distribution, and the probability density is:

[0115]

[0116] where: F represents the strength of the micro-element, and m and F0 are the Weibull distribution parameters.

[0117] Impact different damaged and water-saturated sandstones, and assume that the number of damaged micro-elements after being subjected to the impact load is N a , and the total number of micro-elements is set to N. Then the damage variable D under the impact of different damaged and water-saturated sandstones can be defined as:

[0118]

[0119] 2) Analysis of the micro-element strength of sandstone. It can be seen from Equation (2) that there is a certain relationship between the damage variable D of the rock and the strength F of the micro-element. The D-P criterion can more intuitively reflect the relationship between the micro-element strength and the mechanical properties of the material, and can more accurately reflect the true situation of the rock than other criteria. Define the micro-element strength of sandstone with the D-P criterion, and there is:

[0120]

[0121] In the formula: α is the strength parameter; c is the internal friction angle; I1 and J2 are the first invariant of the stress tensor and the second invariant of the stress deviator respectively; σ1, σ2, and σ3 are the nominal stresses in the pseudo-triaxial test; E is the elastic modulus; μ is the Poisson's ratio; ε1 is the axial strain.

[0122] In the uniaxial test, σ1 = σ2 = 0, ε1 = ε. By combining Equation (3) and Equation (4), we can obtain:

[0123]

[0124] 3) Construct the modified damage constitutive model.

[0125] Based on the strain equivalence hypothesis proposed by Lemaitre and combined with Equation (2), the damage constitutive model of sandstone under uniaxial dynamic load can be obtained.

[0126]

[0127] The parameters m and F0 in the damage constitutive model can be obtained through the peak point coordinates (ε a , σ a ) in the dynamic stress-strain curve. Given that the derivative of the peak point is 0 and it is located in the damage constitutive model of the rock, which is the critical failure point of the rock. Substituting it in, we can obtain:

[0128]

[0129] Substitute Equation (7), Equation (8), and Equation (5) into Equation (6), and the modified damage constitutive equation of sandstone with different damage-saturation degrees can be obtained as:

[0130]

[0131] 4) Determine the fitting parameters of the damage constitutive model.

[0132] Define the initial damage as d and the saturation degree as W s . After the sandstone specimen is damaged, the wave velocity changes, and after saturation, the mass changes. The functional relationships between the dynamic elastic modulus E, the peak stress σ a and the peak strain ε a and the wave velocity w and the mass difference rate m can be established. To express their functional relationships, through the response surface design, with the wave velocity and the mass difference rate as the abscissa and the dynamic elastic modulus, the peak stress, and the peak strain as the ordinate, a response surface diagram is plotted, as shown in Figure 5 --7.

[0133] Combined with the surface diagram, through fitting the indoor impact test data, E, σ a , ε aThe relationship with w and m is as shown in the following formula (10 - 12). Substitute the parameters of wave velocity w (w > 0) and mass difference rate m (m > -0.032) into the model (10 - 12) to obtain the damage constitutive curves of sandstone under different initial damages and water saturation degrees. The specific parameters are shown in Table 2.

[0134] E = -5627.712 + 3.428×10 5 m + 5.322w - 55.56mw - 6.54×10 6 m 2 -3.16×10 -4 w 2 (10)

[0135] σ a = 343.18 - 796.01m + 0.196w + 0.081mw + 8266.46m 2 + 3.3×10 -5 w 2 (11)

[0136] ε a = -77.024 - 1042.16m + 0.0562w + 0.3095mw + 2674.597m 2 -9.25×10 -6 w 2 (12)

[0137] Table 2 Fitting parameters of the damage constitutive model for different initial damage - water saturation

[0138]

[0139] 5) Verification of the accuracy of the damage constitutive model.

[0140] Plot the comparison diagram of the dynamic stress - strain curves of sandstone measured in the indoor impact test under different states and the fitted damage constitutive curves, as shown in Figure 8 --Figure 10. It can be seen from the figure that the model fitting curves under different states are basically consistent with the measured curves. Combining the fitting parameters in Table 2, it can be known that the maximum correlation coefficient between the data fitted by the constitutive model established by the present invention and the test data is 0.991, and the minimum is 0.941, and the fitting effect is good. The changing trends of the fitted stress - strain curve and the measured stress - strain curve are the same. Under different states, as the damage degree increases, the dynamic peak stress of sandstone gradually decreases, and the peak strain gradually increases. And after the sandstone is saturated with water, its dynamic peak stress decreases, and after being dried, its dynamic peak stress increases. The model curve can accurately reflect the deformation characteristics and energy evolution mechanism of sandstone under different states.

[0141] (5) Analysis of the damage characteristics of water-saturated sandstone under impact loads.

[0142] The initial damage variable of sandstone can be defined by the wave velocity before and after damage, and the water-saturated damage can be defined by the porosity before and after water saturation, that is

[0143]

[0144]

[0145] D 初-饱 = D 初 + D 饱 (15)

[0146] In the formula: W represents the longitudinal wave velocity of sandstone, and T represents the total area of the T2 spectral peaks of water-saturated sandstone.

[0147] The damage value existing in sandstone after initial damage can be calculated through Equation 13, the damage caused by water saturation to sandstone can be calculated through Equation 14, and the damage value existing in sandstone before dynamic load can be calculated through Equation 15.

[0148] It can be seen from Equations 6 and 9 that the expression of the damage variable of sandstone under dynamic load is:

[0149]

[0150] Combining Equations 15 and 16, the damage expression in the state of water-saturated sandstone with initial damage can be obtained as:

[0151] D 总 = D 初-饱 + D 荷 - D 初-饱 D 荷 (17)

[0152] The damage value of sandstone changes with the change of strain. In order to analyze the influence of initial damage and water saturation degree on the whole damage process, the damage evolution characteristics of sandstone under dynamic load are analyzed by combining the dynamic stress-strain curve. The whole-process damage curves of sandstone in different states are drawn, such as Figure 11As shown in Fig. 12. It can be seen from the figure that the whole process damage curves of sandstone in different states are divided into three stages. The first stage is the slow damage growth stage (elastic stage). As the strain increases, the damage value increases slowly, but the increase is relatively slow. At this time, the internal damage of the sandstone develops stably. The second stage is the linear rapid damage growth stage (nonlinear yield stage). In this stage, the damage value of the sandstone shows an approximately linear growth trend with the increase of strain. When the stress reaches the peak value, the damage of the sandstone is further aggravated, and the internal primary cracks further expand, and pores aggregate and penetrate to generate new fracture surfaces. The third stage is the damage failure stage (failure stage). In this stage, as the strain continues to increase, the damage continues to grow, and the sandstone produces irreversible deformation. Its internal defects continue to expand until complete failure finally occurs.

[0153] The present invention uses the SHPB impact device and the dynamic monitoring system to conduct dynamic impact tests on sandstones with different damage and water saturation degrees, obtains the energy evolution during the dynamic failure process based on the energy balance theory, and establishes a damage constitutive model considering the initial damage and water saturation degree in combination with the dynamic stress-strain curve. This model is simple to calculate. The model fitting curve is basically consistent with the measured curve. The maximum value of the correlation coefficient with the test data is 0.991, and the minimum value is 0.941, showing a good fitting effect. The research results can provide theoretical analysis for the failure instability mechanism of sandstone with initial damage after being disturbed in the mining of large-water mines, and guide the safe mining of large-water mines.

Claims

1. A method for studying the dynamic damage and energy evolution mechanism of sandstone under water immersion, characterized in that The following steps are involved: The first step is to prepare and pretreat the rock sample; In the second step, dynamic impact tests were conducted on sandstone specimens under different conditions using the SHPB impact device and dynamic monitoring system; The third step is to analyze the dynamic failure energy evolution process. By calculating the input energy, dissipated energy and elastic energy of the unit volume of sandstone samples under natural conditions, the energy evolution law of sandstone in the failure process under dynamic impact is further analyzed. The fourth step is to establish a modified dynamic damage constitutive model, conduct damage variable analysis of sandstone and micro-element strength analysis of sandstone, construct a modified damage constitutive model, determine the fitting parameters of the damage constitutive model, and verify the accuracy of the damage constitutive model; The fifth step is to analyze the damage characteristics of saturated sandstone under impact load.

2. The method for studying dynamic damage and energy evolution mechanism of sandstone under water immersion according to claim 1 is characterized by: In the first step, the rock samples are divided into three groups: no damage, low damage and medium damage, and each group of rock samples is divided into natural, saturated and dry states.

3. The method for studying the dynamic damage and energy evolution mechanism of sandstone under water immersion according to claim 1 is characterized by: In the second step, the impact gas pressure is set to 0.45 MPa.

4. The method for studying dynamic damage and energy evolution mechanism of sandstone under water immersion according to claim 1 is characterized by: In the fourth step, the specific steps are as follows: (1) Analysis of damage variables of sandstone: Assume that the sandstone sample is a micro-element aggregate composed of many micro-elements. Assume that the micro-element strength conforms to the Weibull distribution, and the probability density is: Where: F represents the strength of the microelement, m and F0 are Weibull distribution parameters; Impact sandstone with different damage and saturation, assuming that the number of micro-elements destroyed after the impact load is N a , the total number of micro-elements is set to N, then the damage variable D of sandstone with different damage and saturation under impact can be defined as: (2) Microelement strength analysis of sandstone. From formula (2), we can see that the damage variable D of rock has a certain relationship with the microelement strength F. The DP criterion can more intuitively reflect the relationship between the microelement strength and the mechanical properties of the material, and more accurately reflect the real condition of the rock than other criteria. The microelement strength of sandstone is defined by the DP criterion: Where: α is the strength parameter; c is the internal friction angle; I1 and J2 are the first invariant of the stress tensor and the second invariant of the stress deviator; σ1, σ2 and σ3 are the nominal stresses in the pseudo triaxial test; E is the elastic modulus; μ is the Poisson's ratio; ε1 is the axial strain; In the uniaxial test, σ1=σ2=0, ε1=ε, and by combining equation (3) and equation (4), we can obtain: (3) Constructing a modified damage constitutive model Based on the strain equivalence hypothesis proposed by Lemaitre, combined with formula (2), the damage constitutive model of sandstone under uniaxial dynamic load can be obtained: The parameters m and F0 in the damage constitutive model can be determined by the peak point coordinates (ε a ,σ a ) is obtained. It is known that the derivative of the peak point is 0 and is located in the damage constitutive model of rock. It is the critical failure point of rock. Substituting it into the peak point, we can get: Substituting equations (7), (8) and (5) into equation (6), the modified damage constitutive equation of sandstone with different damage-saturation can be obtained as follows: (4) Determine the fitting parameters of the damage constitutive model Define the initial damage as d and the saturation as W s The wave velocity of the sandstone sample changes after being damaged, and the mass changes after being saturated with water. The dynamic elastic modulus E and peak stress σ can be established. a and the peak strain ε a In order to express the functional relationship between the wave velocity w and the mass difference rate m, a response surface diagram was designed with the wave velocity and the mass difference rate as the horizontal coordinates and the dynamic elastic modulus, peak stress and peak strain as the vertical coordinates. Combined with the surface diagram, E and σ were obtained by fitting the indoor impact test data. a and ε a The relationship between w and m is as follows (10-12). Substituting the wave velocity w, where w>0, and the mass difference rate m, where m>-0.032, into the model (10-12), the damage constitutive curve of sandstone under different initial damage and saturation is obtained. E=-5627.712+3.428×10 5 m+5.322w-55.56mw-6.54×10 6 m 2 -3.16×10 -4 w 2 (10) s a =343.18-796.01m+0.196w+0.081mw+8266.46m 2 +3.3×10 -5 w 2 (11) e a =-77.024-1042.16m+0.0562w+0.3095mw+2674.597m 2 -9.25×10 -6 w 2 (12) (5) Verification of the accuracy of the damage constitutive model The dynamic stress-strain curves of sandstone under different conditions measured in the indoor impact test were compared with the fitted damage constitutive curves to verify the accuracy of the damage constitutive model.

5. The method for studying dynamic damage and energy evolution mechanism of sandstone under water immersion according to claim 1 is characterized by: In the fifth step, the initial damage variable of sandstone can be defined by the wave velocity before and after damage, and the saturated damage can be defined by the porosity before and after saturation, that is, D 初-饱 =D 初 +D 饱 (15) Where: W represents the longitudinal wave velocity of sandstone, T represents the total area of ​​T2 spectrum peak of saturated sandstone; The damage value of sandstone after initial damage is calculated by formula (13), the damage caused by saturated water to sandstone is calculated by formula (14), and the damage value of sandstone before dynamic load is calculated by formula (15); From equations (6) and (9), it can be seen that the damage variable expression of sandstone under dynamic load is: Combining equations (15) and (16), the damage expression under the saturated state with initial damage is: D 总 =D 初-饱 +D 荷 -D 初-饱 D 荷 (17) The damage value of sandstone changes with the change of strain. In order to analyze the influence of initial damage and saturation on the whole damage process, the damage evolution characteristics of sandstone under dynamic load are analyzed in combination with dynamic stress-strain curve. The full-process damage curves of sandstone under different states are drawn and analyzed; the full-process damage curves include the dynamic stress-strain curve measured by the indoor impact test and the strain-damage value curve drawn according to formula (17).

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