A calculation method for dynamic fracture toughness of filling body

Abstract

The present invention relates to a method for calculating the dynamic fracture toughness of a filling body, and belongs to the technical field of mining engineering. The present invention prepares a filling body specimen; uses a split-type Hopkinson pressure bar (SHPB) testing system to perform a uniaxial impact test on the filling body specimen, and records the experimental data during the uniaxial impact test; performs a dynamic stress balance test on the experimental data of each uniaxial impact test, and screens the stress and strain test data of the filling body specimen under dynamic stress balance; calculates the absorption energy W of the filling body under the impact load. S (t) and plotting the stress-strain curve of the filling specimen. The Young's modulus is taken as the slope of the tangent to the loading curve at 0.5 times the uniaxial strength. The dynamic fracture toughness of the filling is calculated based on the absorbed energy and Young's modulus. This method calculates the dynamic fracture toughness of the filling from an energy consumption perspective. The calculation process does not involve specimen size parameters, resulting in accurate results and effectively avoiding specimen size effects.

Description

Technical Field

[0001] The invention relates to a calculation method for dynamic fracture toughness of a filling body, and belongs to the technical field of mining engineering. Background Art

[0002] In recent years, backfill mining has become a common trend in the mining industry due to its advantages in controlling ground pressure, preventing rockbursts, and maximizing mineral resource recovery. During mining operations, backfills are subjected not only to slowly changing quasi-static loads but also to rapidly changing dynamic loads such as seismic and blasting loads. The long-term interaction between the surrounding rock and backfill leads to a decrease in backfill strength, causing the evolution, expansion, and interconnection of existing joints and fissures, which in turn can lead to geological hazards such as roof falls, rock spalling, and goaf collapse. Therefore, exploring the fracture characteristics of backfills is of great practical significance for preventing underground backfill geological hazards.

[0003] Currently, relatively little research has been conducted on the fracture toughness of backfills, with studies still in the exploratory development stage. However, as a concrete-like material, backfills can draw upon certain research findings and methods from the concrete field for analogical analysis. Numerous researchers have used the three-point bending beam method and the wedge splitting method to study the fracture energy of concrete. However, the fracture energy measured under laboratory conditions exhibits a significant size effect, as small-scale concrete specimens do not meet the linear elastic fracture conditions. This size effect is unavoidable as the specimen size increases, gradually satisfying the linear elastic fracture conditions. However, casting and testing large-scale concrete specimens under laboratory conditions present significant challenges. Backfills, as typical multiphase composite materials, are artificially made by mixing tailings, cementitious materials, and water in a specific ratio. They inevitably contain numerous micropores, microcracks, and air bubbles within them, resulting in significant damage characteristics and a strength far lower than that of concrete. Summary of the Invention

[0004] In response to the shortcomings of fracture toughness measurement methods, the present invention proposes a method for calculating the dynamic fracture toughness of a filling body. The present invention calculates the dynamic fracture toughness of a filling body from the perspective of energy consumption. The calculation process does not involve specimen size parameters, the calculation results are accurate, and the specimen size effect is effectively avoided.

[0005] A method for calculating the dynamic fracture toughness of a filling body, the specific steps are as follows:

[0006] (1) Preparation of filling specimens;

[0007] The tailings from the dressing plant, cementitious materials and water were weighed in a predetermined ratio and then placed in a mixing barrel for thorough mixing. The prepared slurry was poured into a cylindrical mold of Φ50×25mm. After 24 hours, the mold was removed and the filling specimen was cured in a constant temperature and humidity curing box (temperature (20±1)°C, humidity 90%) to obtain a filling specimen.

[0008] (2) A split-Hopkinson pressure bar (SHPB) testing system was used to conduct uniaxial impact tests on the filling specimens, and the experimental data during the uniaxial impact tests were recorded. The experimental data included the incident wave, reflected wave, transmitted wave, stress and strain of the filling specimens, sampling time, and voltage signals.

[0009] Before the test, check whether all equipment components are connected properly. Then, inspect the SHPB test system. Adjust the rod base to align the axis of the bullet head, incident rod, transmission rod and absorption rod. Do not add test pieces during the operation. After the end faces of the rods are tightly fitted, perform multiple air impact tests to observe whether the waveform meets the test standards. The original waveform under air impact loading is as follows: Figure 1 As shown by Figure 1 It can be seen that most of the incident waves are transmitted, and the amplitudes of the incident and transmitted waves are similar, with the error within the test allowable range. This indicates that the SHPB test system operates normally and can be used for uniaxial impact testing. At the same time, before loading the filling body specimen, it is necessary to ensure that the bullet head and the pressure rod are coaxial. The end surface of the filling body specimen is finely ground and polished to ensure that the end surface is flat, so that it can be placed tightly between the incident rod and the transmission rod, and the axes of the specimen and the pressure rod should be on the same line.

[0010] (3) Perform dynamic stress equilibrium test on the experimental data of each uniaxial impact test and screen the stress and strain test data of the filling specimen under dynamic stress equilibrium;

[0011] (4) Calculate the absorption energy W of the filling body under impact load S (t), and the stress-strain curve of the filling specimen was drawn. The slope of the tangent of the loading curve at 0.5 times the uniaxial strength was taken as the Young's elastic modulus. The dynamic fracture toughness of the filling was calculated based on the absorbed energy of the filling and the Young's elastic modulus.

[0012] The method for dynamic stress balance test in step (3) is as follows:

[0013] 1) Draw the curve of the incident wave voltage, reflected wave voltage, transmitted wave voltage, and the sum of the incident wave voltage and reflected wave voltage over time for each uniaxial impact test;

[0014] 2) The stress balance factor η is used to characterize the degree of balance of the specimen under impact load. When the stress difference at both ends of the specimen is less than 5% of the average stress inside the specimen, it indicates that the stress balance state has been reached. That is, when the stress balance factor is -0.05≤η≤0.05, the time-varying curve of the sum of the incident wave voltage and the reflected wave voltage tends to overlap with the time-varying curve of the transmitted wave voltage, and the filling body specimen is judged to be in a dynamic stress balance state under the impact condition. The calculation method of the stress balance factor η is:

[0015]

[0016] Where U I is the incident wave voltage, U R is the reflected wave voltage, U T Transmitted wave voltage.

[0017] Step (4) The absorption energy W of the filling body S (t) is calculated as

[0018] According to the one-dimensional stress wave theory and stress equilibrium hypothesis, the average strain rate of the filling specimen is obtained Stress σ S and strain ε S The relationship over time is as follows

[0019] ε T (t) = ε I (t)+ε R (t)

[0020]

[0021]

[0022]

[0023] ε calculated according to the SHPB test principle R (t) is the reflected strain, ε T (t) is the transmission strain and ε I (t) is the incident strain. Based on the stress wave theory and the law of conservation of energy, the incident energy W of the filling specimen under the dynamic load test is I (t), reflected energy W R (t), transmission energy W T (t) and absorbed energy W S (t) satisfies the following calculation formula

[0024] W S (t) = W I (t)-W R (t)-W T (t)

[0025]

[0026]

[0027]

[0028] Where W S (t) is the absorbed energy, W I (t) is the incident energy, W R (t) is the reflected energy, W T (t) is the transmitted energy, A is the cross-sectional area of ​​the incident rod, and A S is the cross-sectional area of ​​the specimen, E is the elastic modulus of the rod, l S is the thickness of the specimen, C0 is the velocity of the elastic stress wave, σ S (t) is the dynamic stress of the specimen, ε S (t) is the strain of the specimen, is the strain rate of the specimen, ε R (t) is the reflected strain, ε T (t) is the transmission strain, ε I (t) is the incident strain.

[0029] The calculation method of the dynamic fracture toughness of the filling body in step (4) is:

[0030] The absorbed energy mainly acts on the deformation and destruction of the filling specimen. In order to better study its energy dissipation law, the following hypothesis is proposed:

[0031] ① No heat energy is dissipated during the deformation and destruction of the filling body;

[0032] ② All the absorbed energy is used to expand the crack of the specimen;

[0033] ③The fracture process of the material is quasi-static, that is, the absorbed energy is equal to the fracture energy;

[0034] Under this assumption, the fracture energy G F (which characterizes the energy required to produce a crack per unit area) is equal to the absorbed energy W S , which is also equal to the critical strain energy release rate G IC (which characterizes the energy consumed per unit area at the crack tip when the crack expands), that is,

[0035] W S =G F =G IC

[0036] Because the three-point bending beam method and wedge splitting method for measuring the fracture energy of materials are inevitably affected by the size effect, when the crack of the material propagates, its G ICSatisfies the following relationship

[0037] G F ≥G IC

[0038]

[0039] Since the filling body is a mixture of tailings, cement and water, the research method of the fracture energy of concrete can be referred to. The fracture toughness is used to characterize the ability of the material to prevent crack propagation, that is, the ability of the material to resist brittle fracture. Therefore, the expansion law of the fracture toughness of the filling body specimen is as follows:

[0040]

[0041] Therefore

[0042]

[0043] When the material fracture process is quasi-static or the specimen size is large enough, G F =G IC , that is, the fracture toughness calculation formula of the filling body under this condition is

[0044]

[0045] Where: W S is the absorbed energy, J; E is the Young's elastic modulus, MPa; G F is the fracture energy, J; G IC is the critical strain energy release rate, J; K IC is the fracture toughness, kPa·m 0.5 .

[0046] The beneficial effects of the present invention are:

[0047] (1) The traditional three-point bending beam method is used to measure fracture toughness. However, the span-to-height ratio often limits the size of the specimen, making casting and transportation difficult. In addition, the weight of the specimen has a significant impact on the measured fracture parameters. The wedge splitting method is used to measure fracture toughness. The test device is complex and requires the test personnel to have professional operating skills. At the same time, wedge splitting specimens of different heights and sizes need to correspond to loading slots of corresponding proportions. Otherwise, the vertical component of the force acting on the specimen by the fixture, the weight of the specimen, and the support force of the support will not be collinear, resulting in additional bending moment at the crack tip, which will increase the error of the fracture toughness measured by the test. The present invention uses the SHPB test technology to study the fracture toughness of the filling body, derives the calculation formula of the fracture toughness from the perspective of energy consumption, and avoids the influence of the specimen size effect.

[0048] (2) The method of calculating the dynamic fracture toughness of the filling body from the perspective of energy consumption of the present invention has the advantages of simple test operation, few parameters to be determined, easy casting and transportation of specimens, and reliable results, which will provide more accurate results for the calculation of the dynamic fracture toughness of the filling body. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is the original waveform of SHPB under empty charge loading in Example 1;

[0050] Figure 2 This is a dynamic stress balance test diagram of the test data of Example 1;

[0051] Figure 3 This is a schematic diagram of Young's modulus of elasticity of Example 1;

[0052] Figure 4 This is the original waveform of SHPB under empty impulse loading in Example 2;

[0053] Figure 5 This is a dynamic stress balance test diagram of the test data of Example 2;

[0054] Figure 6 Schematic diagram of Young's modulus of Example 2. DETAILED DESCRIPTION

[0055] The present invention will be further described in detail below in conjunction with specific embodiments, but the protection scope of the present invention is not limited to the contents described above.

[0056] This paper aims to measure the dynamic fracture toughness of filling materials. From an energy consumption perspective, it proposes a fracture toughness calculation formula that effectively avoids specimen size effects, simplifies the test operation, and produces accurate results. This test involves uniaxial impact testing of the filling specimen using a Split Hopkinson Pressure Bar (SHPB) testing system. The absorbed energy and Young's modulus during the filling's deformation and failure processes are then substituted into the formula to calculate the dynamic fracture toughness. The new test method for determining the fracture toughness of filling materials using this invention primarily involves three steps: specimen preparation, SHPB uniaxial impact testing, and data processing and analysis.

[0057] A method for calculating the dynamic fracture toughness of a filling body, the specific steps are as follows:

[0058] (1) Preparation of filling specimens;

[0059] The tailings from the dressing plant, cementitious materials and water were weighed in a predetermined ratio and then placed in a mixing barrel for thorough mixing. The prepared slurry was poured into a cylindrical mold of Φ50×25mm. After 24 hours, the mold was removed and the filling specimen was cured in a constant temperature and humidity curing box (temperature (20±1)°C, humidity 90%) to obtain a filling specimen.

[0060] (2) A split-Hopkinson pressure bar (SHPB) testing system was used to conduct uniaxial impact tests on the filling specimens, and the experimental data during the uniaxial impact tests were recorded. The experimental data included the incident wave, reflected wave, transmitted wave, stress and strain of the filling specimens, sampling time, and voltage signals.

[0061] (3) Perform dynamic stress equilibrium test on the experimental data of each uniaxial impact test and screen the stress and strain test data of the filling specimen under dynamic stress equilibrium;

[0062] The method for dynamic stress equilibrium test is

[0063] 1) Draw the curve of the incident wave voltage, reflected wave voltage, transmitted wave voltage, and the sum of the incident wave voltage and reflected wave voltage over time for each uniaxial impact test;

[0064] 2) The stress balance factor η is used to characterize the degree of balance of the specimen under impact load. When the stress difference at both ends of the specimen is less than 5% of the average stress inside the specimen, it indicates that the stress balance state has been reached. That is, when the stress balance factor is -0.05≤η≤0.05, the time-varying curve of the sum of the incident wave voltage and the reflected wave voltage tends to overlap with the time-varying curve of the transmitted wave voltage, and the filling body specimen is judged to be in a dynamic stress balance state under the impact condition. The calculation method of the stress balance factor η is:

[0065]

[0066] Where U I is the incident wave voltage, U R is the reflected wave voltage, U T Transmitted wave voltage.

[0067] (4) Calculate the absorption energy W of the filling body under impact load S (t), and draw the stress-strain curve of the filling specimen. The slope of the tangent of the loading curve at 0.5 times the uniaxial strength is the Young's elastic modulus. The dynamic fracture toughness of the filling is calculated based on the absorbed energy of the filling and the Young's elastic modulus.

[0068] The absorption energy of the filling body is W S (t) is calculated as

[0069] According to the one-dimensional stress wave theory and stress equilibrium hypothesis, the average strain rate of the filling specimen is obtained Stress σ S and strain ε S The relationship over time is as follows

[0070] ε T (t) = ε I(t)+ε R (t)

[0071]

[0072]

[0073]

[0074] ε calculated according to the SHPB test principle R (t) is the reflected strain, ε T (t) is the transmission strain and ε I (t) is the incident strain. Based on the stress wave theory and the law of conservation of energy, the incident energy W of the filling specimen under the dynamic load test is I (t), reflected energy W R (t), transmission energy W T (t) and absorbed energy W S (t) satisfies the following calculation formula

[0075] W S (t) = W I (t)-W R (t)-W T (t)

[0076]

[0077]

[0078]

[0079] Where W S (t) is the absorbed energy, W I (t) is the incident energy, W R (t) is the reflected energy, W T (t) is the transmitted energy, A is the cross-sectional area of ​​the incident rod, and A S is the cross-sectional area of ​​the specimen, E is the elastic modulus of the rod, l S is the thickness of the specimen, C0 is the velocity of the elastic stress wave, σ S (t) is the dynamic stress of the specimen, ε S (t) is the strain of the specimen, is the strain rate of the specimen, ε R (t) is the reflected strain, ε T (t) is the transmission strain, ε I (t) is the incident strain;

[0080] The calculation method of the dynamic fracture toughness of the filling body is

[0081] The absorbed energy mainly acts on the deformation and destruction of the filling specimen. In order to better study its energy dissipation law, the following hypothesis is proposed:

[0082] ① No heat energy is dissipated during the deformation and destruction of the filling body;

[0083] ② All the absorbed energy is used to expand the crack of the specimen;

[0084] ③The fracture process of the material is quasi-static, that is, the absorbed energy is equal to the fracture energy;

[0085] Under this assumption, the fracture energy G F (which characterizes the energy required to produce a crack per unit area) is equal to the absorbed energy W S , which is also equal to the critical strain energy release rate G IC (which characterizes the energy consumed per unit area at the crack tip when the crack expands), that is,

[0086] W S =G F =G IC

[0087] Because the three-point bending beam method and wedge splitting method for measuring the fracture energy of materials are inevitably affected by the size effect, when the crack of the material propagates, its G IC Satisfies the following relationship

[0088] G F ≥G IC

[0089]

[0090] Since the filling body is a mixture of tailings, cement and water, the research method of the fracture energy of concrete can be referred to. The fracture toughness is used to characterize the ability of the material to prevent crack propagation, that is, the ability of the material to resist brittle fracture. Therefore, the expansion law of the fracture toughness of the filling body specimen is as follows:

[0091]

[0092] Therefore

[0093]

[0094] When the material fracture process is quasi-static or the specimen size is large enough, G F =G IC , that is, the fracture toughness calculation formula of the filling body under this condition is

[0095]

[0096] Where: W S is the absorbed energy, J; E is the Young's elastic modulus, MPa; GF is the fracture energy, J; G IC is the critical strain energy release rate, J; K IC is the fracture toughness, kPa·m 0.5 .

[0097] Example 1: A method for calculating the dynamic fracture toughness of a filling body, the specific steps are as follows:

[0098] (1) Preparation of filling specimens;

[0099] Tailings from a certain mine were selected as filling aggregate, the cementitious material was ordinary slag silicate cement, and the test water was ordinary tap water. The tailings needed to be dried before the test to prepare a filling specimen with a mass concentration of 66% and a ash-sand ratio of 1:4. An electronic scale with an accuracy of 0.01g was used to weigh the corresponding mass of tailings and cement. A measuring cylinder was used to weigh the corresponding mass of water and then put it into a mixing bucket for thorough stirring to ensure that the slurry was evenly mixed. The prepared slurry was poured into a Φ50×25mm cylindrical mold, demoulded after 24 hours, and placed in a constant temperature and humidity curing box (temperature of (20±1)℃, humidity of 90%) for curing for 28 days to obtain a filling specimen.

[0100] (2) A split-Hopkinson pressure bar (SHPB) testing system was used to conduct uniaxial impact tests on the filling specimens, and the experimental data during the uniaxial impact tests were recorded. The experimental data included the incident wave, reflected wave, transmitted wave, stress and strain of the filling specimens, sampling time, and voltage signals.

[0101] Before the test, check whether all equipment components are connected properly. Then, inspect the SHPB test system. Adjust the rod base to align the axis of the bullet head, incident rod, transmission rod and absorption rod. Do not add test pieces during the operation. After the end faces of the rods are tightly fitted, perform multiple air impact tests to observe whether the waveform meets the test standards. The original waveform under air impact loading is as follows: Figure 1 As shown by Figure 1 It can be seen that most of the incident waves are transmitted, and the amplitudes of the incident and transmitted waves are similar, with the error within the test allowable range. This indicates that the SHPB test system operates normally and can be used for uniaxial impact testing. At the same time, before loading the filling body specimen, it is necessary to ensure that the bullet head and the pressure rod are coaxial. The end surface of the filling body specimen is finely ground and polished to ensure that the end surface is flat, so that it can be placed tightly between the incident rod and the transmission rod, and the axes of the specimen and the pressure rod should be on the same line.

[0102] The rods of this embodiment are made of high-strength carbon steel with a density of 7650 kg / m 3The elastic modulus is 210 GPa, the longitudinal wave velocity is 5100 m / s, the incident and transmission rods are 2.5 m long, the rod diameter is 50 mm, and the impact rod (bullet-shaped) is 0.4 m long and conical in shape. Before loading, the cross section of the filling specimen must be polished with sandpaper to ensure a smooth cross section. In addition, a coupling agent is applied to the cross section of the filling and rod to ensure a complete fit between the filling specimen and the rod.

[0103] According to the dynamic strength value of the filling body, different impact air pressures (0.20, 0.22, 0.23, and 0.25 MPa) were set to carry out impact tests on the filling body specimens under different conditions.

[0104] (3) Perform dynamic stress equilibrium test on the experimental data of each uniaxial impact test and screen the stress and strain test data of the filling specimen under dynamic stress equilibrium;

[0105] The method for dynamic stress equilibrium test is

[0106] 1) Draw the curve of the incident wave voltage, reflected wave voltage, transmitted wave voltage, and the sum of the incident wave voltage and reflected wave voltage over time for each uniaxial impact test;

[0107] 2) The stress balance factor η is used to characterize the degree of balance of the specimen under the impact load. When the stress difference at both ends of the specimen is less than 5% of the average stress inside the specimen, it means that the stress balance state has been reached. That is, when the stress balance factor is -0.05≤η≤0.05, the curve of the sum of the incident wave voltage and the reflected wave voltage over time tends to overlap with the curve of the voltage of the transmitted wave over time (see Figure 2 ), it is determined that the filling specimen is in a dynamic stress equilibrium state under the impact condition, and the calculation method of the stress equilibrium factor η is:

[0108]

[0109] Where U I is the incident wave voltage, U R is the reflected wave voltage, U T Transmitted wave voltage.

[0110] (4) Calculate the absorption energy W of the filling body under impact load S (t), and draw the stress-strain curve of the filling specimen (see Figure 3 ), the slope of the tangent line of the loading curve at 0.5 times the uniaxial strength is taken as Young's elastic modulus (specifically 638 MPa), and the dynamic fracture toughness of the filling body is calculated based on the absorbed energy of the filling body and Young's elastic modulus;

[0111] The absorption energy of the filling body is W S (t) is calculated as

[0112] According to the one-dimensional stress wave theory and stress equilibrium hypothesis, the average strain rate of the filling specimen is obtained Stress σ S and strain ε S The relationship over time is as follows

[0113] ε T (t) = ε I (t)+ε R (t) = -6.4 × 10 -6

[0114]

[0115]

[0116]

[0117] ε calculated according to the SHPB test principle R (t) is the reflected strain, ε T (t) is the transmission strain and ε I (t) is the incident strain. Based on the stress wave theory and the law of conservation of energy, the incident energy W of the filling specimen under the dynamic load test is I (t), reflected energy W R (t), transmission energy W T (t) and absorbed energy W S (t) satisfies the following calculation formula

[0118] W S (t) = W I (t)-W R (t)-W T (t) = 1.1469 (J)

[0119]

[0120]

[0121]

[0122] Where W S (t) is the absorbed energy, W I (t) is the incident energy, W R (t) is the reflected energy, W T (t) is the transmitted energy, A is the cross-sectional area of ​​the incident rod, and A S is the cross-sectional area of ​​the specimen, E is the elastic modulus of the rod, l S is the thickness of the specimen, C0 is the velocity of the elastic stress wave, σ S (t) is the dynamic stress of the specimen, ε S(t) is the strain of the specimen, is the strain rate of the specimen, ε R (t) is the reflected strain, ε T (t) is the transmission strain, ε I (t) is the incident strain;

[0123] The calculation method of the dynamic fracture toughness of the filling body is

[0124] The absorbed energy mainly acts on the deformation and destruction of the filling specimen. In order to better study its energy dissipation law, the following hypothesis is proposed:

[0125] ① No heat energy is dissipated during the deformation and destruction of the filling body;

[0126] ② All the absorbed energy is used to expand the crack of the specimen;

[0127] ③The fracture process of the material is quasi-static, that is, the absorbed energy is equal to the fracture energy;

[0128] Under this assumption, the fracture energy G F (which characterizes the energy required to produce a crack per unit area) is equal to the absorbed energy W S , which is also equal to the critical strain energy release rate G IC (which characterizes the energy consumed per unit area at the crack tip when the crack expands), that is,

[0129] W S =G F =G IC

[0130] Because the three-point bending beam method and wedge splitting method for measuring the fracture energy of materials are inevitably affected by the size effect, when the crack of the material propagates, its G IC Satisfies the following relationship

[0131] G F ≥G IC

[0132]

[0133] Since the filling body is a mixture of tailings, cement and water, the research method of the fracture energy of concrete can be referred to. The fracture toughness is used to characterize the ability of the material to prevent crack propagation, that is, the ability of the material to resist brittle fracture. Therefore, the expansion law of the fracture toughness of the filling body specimen is as follows:

[0134]

[0135] Therefore

[0136]

[0137] When the material fracture process is quasi-static or the specimen size is large enough, G F =G IC , that is, the fracture toughness calculation formula of the filling body under this condition is

[0138]

[0139] Where: W S is the absorbed energy, J; E is the Young's elastic modulus, MPa; G F is the fracture energy, J; G IC is the critical strain energy release rate, J; K IC is the fracture toughness, kPa·m 0.5 ;

[0140] The dynamic fracture toughness of the filling specimen in this embodiment is 27.05 kPa·m 0.5 .

[0141] Example 2: A method for calculating the dynamic fracture toughness of a filling body, the specific steps are as follows:

[0142] (1) Preparation of filling specimens;

[0143] Tailings from a certain mine were selected as filling aggregate, the cementitious material was ordinary slag silicate cement, and the test water was ordinary tap water. The tailings were dried before the test to prepare a filling specimen with a mass concentration of 66% and a ash-sand ratio of 1:4. An electronic scale with an accuracy of 0.01g was used to weigh the corresponding mass of tailings and cement. A measuring cylinder was used to weigh the corresponding mass of water and then put it into a mixing bucket for thorough stirring to ensure that the slurry was evenly mixed. The prepared slurry was poured into a Φ50×25mm cylindrical mold, demoulded after 24 hours, and placed in a constant temperature and humidity curing box (temperature of (20±1)℃, humidity of 90%) for curing for 28 days to obtain a filling specimen.

[0144] (2) A split-Hopkinson pressure bar (SHPB) testing system was used to conduct uniaxial impact tests on the filling specimens, and the experimental data during the uniaxial impact tests were recorded. The experimental data included the incident wave, reflected wave, transmitted wave, stress and strain of the filling specimens, sampling time, and voltage signals.

[0145] Before the test, check whether all equipment components are connected properly. Then, inspect the SHPB test system. Adjust the rod base to align the axis of the bullet head, incident rod, transmission rod and absorption rod. Do not add test pieces during the operation. After the end faces of the rods are tightly fitted, perform multiple air impact tests to observe whether the waveform meets the test standards. The original waveform under air impact loading is as follows: Figure 4 As shown by Figure 4It can be seen that most of the incident waves are transmitted, and the amplitudes of the incident and transmitted waves are similar, with the error within the test allowable range. This indicates that the SHPB test system operates normally and can be used for uniaxial impact testing. At the same time, before loading the filling body specimen, it is necessary to ensure that the bullet head and the pressure rod are coaxial. The end surface of the filling body specimen is finely ground and polished to ensure that the end surface is flat, so that it can be placed tightly between the incident rod and the transmission rod, and the axes of the specimen and the pressure rod should be on the same line.

[0146] The rods of this embodiment are made of high-strength carbon steel with a density of 7650 kg / m 3 The elastic modulus is 210 GPa, the longitudinal wave velocity is 5100 m / s, the incident and transmission rods are 2.5 m long, the rod diameter is 50 mm, and the impact rod (bullet-shaped) is 0.4 m long and conical in shape. Before loading, the cross section of the filling specimen must be polished with sandpaper to ensure a smooth cross section. In addition, a coupling agent is applied to the cross section of the filling and rod to ensure a complete fit between the filling specimen and the rod.

[0147] According to the dynamic strength value of the filling body, different impact air pressures (0.20, 0.22, 0.23, and 0.25 MPa) were set to carry out impact tests on the filling body specimens under different conditions.

[0148] (3) Perform dynamic stress equilibrium test on the experimental data of each uniaxial impact test and screen the stress and strain test data of the filling specimen under dynamic stress equilibrium;

[0149] The method for dynamic stress equilibrium test is

[0150] 1) Draw the curve of the incident wave voltage, reflected wave voltage, transmitted wave voltage, and the sum of the incident wave voltage and reflected wave voltage over time for each uniaxial impact test;

[0151] 2) The stress balance factor η is used to characterize the degree of balance of the specimen under the impact load. When the stress difference at both ends of the specimen is less than 5% of the average stress inside the specimen, it means that the stress balance state has been reached. That is, when the stress balance factor is -0.05≤η≤0.05, the curve of the sum of the incident wave voltage and the reflected wave voltage over time tends to overlap with the curve of the voltage of the transmitted wave over time (see Figure 5 ), it is determined that the filling specimen is in a dynamic stress equilibrium state under the impact condition, and the calculation method of the stress equilibrium factor η is:

[0152]

[0153] Where U I is the incident wave voltage, U R is the reflected wave voltage, U T Transmitted wave voltage.

[0154] (4) Calculate the absorption energy W of the filling body under impact load S (t), and draw the stress-strain curve of the filling specimen (see Figure 6 ), the tangent slope of the loading curve at 0.5 times the uniaxial strength is taken as Young's elastic modulus (specifically 150.58 MPa), and the dynamic fracture toughness of the filling body is calculated based on the absorbed energy and Young's elastic modulus of the filling body;

[0155] The absorption energy of the filling body is W S (t) is calculated as

[0156] According to the one-dimensional stress wave theory and stress equilibrium hypothesis, the average strain rate of the filling specimen is obtained Stress σ S and strain ε S The relationship over time is as follows

[0157] ε T (t) = ε I (t)+ε R (t) = -1.7 × 10 -6

[0158]

[0159]

[0160]

[0161] ε calculated according to the SHPB test principle R (t) is the reflected strain, ε T (t) is the transmission strain and ε I (t) is the incident strain. Based on the stress wave theory and the law of conservation of energy, the incident energy W of the filling specimen under the dynamic load test is I (t), reflected energy W R (t), transmission energy W T (t) and absorbed energy W S (t) satisfies the following calculation formula

[0162] W S (t) = W I (t)-W R (t)-W T (t) = 1.4679 (J)

[0163]

[0164]

[0165]

[0166] Where W S (t) is the absorbed energy, W I (t) is the incident energy, W R (t) is the reflected energy, W T (t) is the transmitted energy, A is the cross-sectional area of ​​the incident rod, and A S is the cross-sectional area of ​​the specimen, E is the elastic modulus of the rod, l S is the thickness of the specimen, C0 is the velocity of the elastic stress wave, σ S (t) is the dynamic stress of the specimen, ε S (t) is the strain of the specimen, is the strain rate of the specimen, ε R (t) is the reflected strain, ε T (t) is the transmission strain, ε I (t) is the incident strain;

[0167] The calculation method of the dynamic fracture toughness of the filling body is

[0168] The absorbed energy mainly acts on the deformation and destruction of the filling specimen. In order to better study its energy dissipation law, the following hypothesis is proposed:

[0169] ① No heat energy is dissipated during the deformation and destruction of the filling body;

[0170] ② All the absorbed energy is used to expand the crack of the specimen;

[0171] ③The fracture process of the material is quasi-static, that is, the absorbed energy is equal to the fracture energy;

[0172] Under this assumption, the fracture energy G F (which characterizes the energy required to produce a crack per unit area) is equal to the absorbed energy W S , which is also equal to the critical strain energy release rate G IC (which characterizes the energy consumed per unit area at the crack tip when the crack expands), that is,

[0173] W S =G F =G IC

[0174] Because the three-point bending beam method and wedge splitting method for measuring the fracture energy of materials are inevitably affected by the size effect, when the crack of the material propagates, its G IC Satisfies the following relationship

[0175] G F ≥G IC

[0176]

[0177] Since the filling body is a mixture of tailings, cement and water, the research method of the fracture energy of concrete can be referred to. The fracture toughness is used to characterize the ability of the material to prevent crack propagation, that is, the ability of the material to resist brittle fracture. Therefore, the expansion law of the fracture toughness of the filling body specimen is as follows:

[0178]

[0179] Therefore

[0180]

[0181] When the material fracture process is quasi-static or the specimen size is large enough, G F =G IC , that is, the fracture toughness calculation formula of the filling body under this condition is

[0182]

[0183] Where: W S is the absorbed energy, J; E is the Young's elastic modulus, MPa; G F is the fracture energy, J; G IC is the critical strain energy release rate, J; K IC is the fracture toughness, kPa·m 0.5 ;

[0184] The dynamic fracture toughness of the filling specimen in this embodiment is 14.867 kPa·m 0.5 .

[0185] The above describes the specific embodiments of the present invention in detail, but the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

Claims

1. A method for calculating the dynamic fracture toughness of a filling body, characterized by: The specific steps are as follows: (1) Preparation of filling specimens; (2) A split-Hopkinson pressure bar (SHPB) testing system was used to conduct uniaxial impact tests on the filling specimens, and the experimental data during the uniaxial impact tests were recorded. The experimental data included the incident wave, reflected wave, transmitted wave, stress and strain of the filling specimens, sampling time, and voltage signals. (3) Perform dynamic stress equilibrium test on the experimental data of each uniaxial impact test, and screen the stress and strain test data of the filling specimen under dynamic stress equilibrium; (4) Calculate the absorption energy of the filling body under impact load , and draw the stress-strain curve of the filling specimen. The slope of the tangent line of the loading curve at 0.5 times the uniaxial strength is the Young's elastic modulus. The dynamic fracture toughness of the filling is calculated based on the absorbed energy of the filling and the Young's elastic modulus. Specifically, the calculation method of the dynamic fracture toughness of the filling body is: Assumptions: ① No heat energy is dissipated during the deformation and failure of the filling body; ② All absorbed energy is used for the expansion of the specimen crack; ③ The fracture process of the material is quasi-static, that is, the absorbed energy is equal to the fracture energy; Fracture energy G of filling body F Equal to absorbed energy W S , which is also equal to the critical strain energy release rate G IC ,Right now ； The calculation formula of the dynamic fracture toughness of the filling body is: ； Where: is the absorbed energy, J; E is Young's elastic modulus, ; is the fracture toughness, .

2. The method for calculating the dynamic fracture toughness of a filling body according to claim 1, characterized in that: Step (3) The method for dynamic stress balance test is: 1) Draw the curves of the incident wave voltage, reflected wave voltage, transmitted wave voltage, and the sum of the incident wave voltage and reflected wave voltage over time for each uniaxial impact test; 2) Using stress balance factor Characterizes the degree of balance of the specimen under impact load. If the stress difference at both ends of the specimen is less than 5% of the average stress inside the specimen, it is in a stress equilibrium state, that is, the stress balance factor is When the time-varying curve of the sum of the incident wave voltage and the reflected wave voltage tends to overlap with the time-varying curve of the transmitted wave voltage, it is determined that the filling specimen is in a dynamic stress equilibrium state under the impact condition, where the stress balance factor is The calculation method is: ； Where, is the incident wave voltage, is the reflected wave voltage, is the transmitted wave voltage.

3. The method for calculating the dynamic fracture toughness of a filling body according to claim 1, characterized in that: Step (4) Absorption energy of filling body The calculation method is ； in ; ； ； However, according to the one-dimensional stress wave theory and stress equilibrium assumption, the average strain rate of the filling specimen is obtained. ,stress and strain The relationship over time is as follows ； ； ； ； Where, For absorption energy, is the incident energy, is the reflected energy, is the transmitted energy, A is the cross-sectional area of ​​the incident rod, is the cross-sectional area of ​​the specimen, E is the elastic modulus of the rod, is the thickness of the specimen, is the velocity of the elastic stress wave, is the dynamic stress of the specimen, is the strain of the specimen, is the strain rate of the specimen, is the reflected strain, is the transmission strain, is the incident strain.

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