Construction method of rock crushing damage model under impact loading and application thereof

Abstract

The invention relates to a method for constructing a rock crushing damage model under impact loading and application thereof, and belongs to the field of rock mass engineering. The method solves at least one of the problems that reliability and accuracy are insufficient when an existing rock model predicts the failure evolution law and / or strength under direct impact loading, and it is difficult to reveal the change law under direct impact loading. The method comprises the following steps: S1, based on a wing crack propagation model, obtaining a tensile damage model under quasi-static loading; s2, a correction factor is introduced to correct the tensioning damage model under static loading, and a tensioning damage model expression under direct impact loading is obtained; s3, determining the dynamic fracture toughness of the rock; s4, determining a correction factor; and S5, constructing a tension damage model under direct impact loading. According to the method, the accuracy and reliability of the model in predicting the strength of the rock under the direct impact loading and the damage evolution law are enhanced, and the obtained model can reveal the quantitative change law of the damage of the rock under the direct impact loading.

Description

Technical Field

[0001] This invention relates to the field of rock mass engineering technology, and in particular to a method for constructing a rock fracture damage model under impact loading and its application. Background Technology

[0002] Dynamic rock failure is a frequent problem in rock engineering fields such as tunnel excavation and mine blasting, as well as in geological disasters such as earthquakes, landslides, and rockbursts. Therefore, from an engineering perspective, studying rock failure under dynamic loads is essential. Research has found that rocks subjected to impact loads exhibit high strain rates during failure. Thus, from the perspective of laboratory experimental research, rock failure under impact loads can be abstracted as the study of damage and fracture of rocks under high strain rates. However, current research on rock failure under direct impact loading mostly relies on experimental studies of the dynamic strength characteristics of rocks or on deducing damage models from the dynamic stress-strain curves of rocks. However, these models often fail to accurately reflect the damage process in practical applications, especially when predicting the macroscopic evolution and strength of rock failure under direct impact loading. These models suffer from insufficient accuracy and reliability, and also struggle to reveal the quantitative changes in rocks under direct impact loading and the key factors influencing the damage process and strength of rocks. Summary of the Invention

[0003] In view of the above analysis, the present invention aims to provide a method for constructing a rock fracture damage model under impact loading and its application, in order to solve at least one of the following problems existing in rock damage models: (1) insufficient accuracy and reliability in predicting the macroscopic damage evolution law of rocks under direct impact loading; (2) insufficient accuracy and reliability in predicting the strength of rocks under direct impact loading; (3) difficulty in revealing the quantitative change law of rock damage under direct impact loading and the key factors affecting the rock damage process and strength.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] This invention provides a method for constructing a rock damage model under direct impact loading, comprising the following steps:

[0006] S1. Based on the interaction and superposition principle among multiple cracks, a wing crack propagation model is obtained when the initial oblique crack is fully opened under quasi-static loading. Based on the wing crack propagation model, and combined with uniaxial and triaxial tests and CCNBD experiments, a tensile damage model under quasi-static loading is obtained, i.e., K. I = f(σ1,σ3,L), where K If is the stress intensity factor value at the tip of the wing crack under static load. f is a polynomial function that includes multiple terms related to the concentrated force and / or far-field compressive stress acting on the crack. The multiple terms include the material properties of the rock, axial stress σ1, confining pressure σ3, and wing crack propagation length L.

[0007] S2. Introduce a correction factor k(v) related to the crack propagation rate, which includes a first correction factor k1(v) and a second correction factor k2(v), namely equation (1) and equation (2), to correct the tensile damage model under quasi-static loading and obtain the tensile damage model expression under direct impact loading.

[0008] Wherein, k1(v) is used to correct the terms in S1 related to the concentrated force acting on the crack, and k2(v) is used to correct the terms related to the far-field compressive stress acting on the crack.

[0009]

[0010] In equations (1) and (2), v r Let v be the Rayleigh wave velocity, v be the crack propagation rate, and v be a constant value. The average crack propagation rate is used as the reference value. replace;

[0011] S3. Conduct one-dimensional direct impact tests to obtain stress-strain curves of rock samples at different strain rates, thereby obtaining the peak strength σ at different strain rates. p That is, the measured strength; based on the measured strength and combined with the tensile damage model expression under direct impact loading described in S2, and setting the confining pressure σ3=0 and k(v)=1, the dynamic fracture toughness of the rock is calculated in the numerical calculation software. The value of is set as a series of point values, resulting in different values. Values ​​are taken at different strain rates The variation curve of σ1-L is used to obtain the theoretical strength, and the theoretical strength is found to be close to the measured strength at different strain rates. The values ​​of are fitted to obtain Relationship;

[0012] S4. Based on the tensile damage model expression under direct impact loading described in S2 and setting the circumference σ3 = 0, use numerical calculation software to fit and obtain the crack propagation length L corresponding to the maximum value of the axial stress σ1. i According to the peak strength σ measured at different strain rates in the one-dimensional direct impact test described in S3, p The corresponding time t i ,according to Obtain the average crack propagation rate Based on equations (1) and (2), determine the first correction factor k1(v) and the second correction factor k2(v) related to the crack propagation rate;

[0013] S5. Based on the tensile damage model expression under direct impact loading described in S2, and combined with the experimental data obtained from the uniaxial and triaxial tests and CCNBD experiments described in S1, as well as the values ​​determined in S3 and S4. By taking values ​​of k1(v) and k2(v), a tensile damage model for predicting rock failure mechanisms under direct impact loading is constructed.

[0014] Furthermore, the expression for the tensile damage model under direct impact loading is Equation (3):

[0015]

[0016] In equation (3), K Id σ1 is the stress intensity factor value at the tip of the wing crack under dynamic load, σ3 is the axial stress, σ4 is the confining pressure, L is the wing crack propagation length, λ is the crack length correction parameter, w is the crack spacing, b is the initial oblique crack length of the rock sample, and θ0 is the initial oblique crack inclination angle of the rock sample.

[0017] Furthermore, step S5 specifically includes the following steps:

[0018] S51. According to equation (3), when And when σ3=0, a one-dimensional tensile damage model under direct impact loading is constructed; and / or,

[0019] S52. According to equation (3), when When σ3 is a constant, a three-dimensional tensile damage model under direct impact loading is constructed.

[0020] The tensile damage model under direct impact loading is a constitutive model between the axial stress σ1 of the rock and the tensile damage characterized by the wing crack propagation length L when the initial inclined microcrack is fully opened.

[0021] Furthermore, in step S52, the confining pressure σ3 in the tensile damage model under three-dimensional direct impact loading is ≤ P. When the confining pressure σ3 is maintained at or below the threshold P, the dynamic failure of the rock exhibits a tensile failure mode.

[0022] Furthermore, in step S3, in the one-dimensional direct impact test, the rock sample is yellow sandstone. The relationship is an exponential function.

[0023] Furthermore, in step S3, the strain rate in the one-dimensional direct impact test ranges from 80 / s to 200 / s.

[0024] Furthermore, step S1 specifically includes the following steps:

[0025] S11. Experimental data of rock samples were obtained through uniaxial loading and conventional triaxial loading tests, including stress-strain curves, elastic modulus E and Poisson's ratio α under different confining pressures σ3, and characteristic stresses during the loading process; the characteristic stresses include: crack initialization stress σ. ci Peak stress σ p ;

[0026] S12, based on σ under medium to high confining pressure p -Slope of the linear fitting plot of σ3, CCNBD splitting experiment, σ ci The slope and intercept of the -σ3 linear fitting plot are used to determine the parameters μ and K in the wing crack propagation model under quasi-static loading when the initial oblique crack is fully opened. IC , b and θ0; μ is the friction coefficient of the rock sample, K IC denoted as quasi-static fracture toughness of the rock sample, b as the initial oblique crack length of the rock sample, and θ0 as the initial oblique crack inclination angle of the rock sample.

[0027] S13, Parameters μ and K determined based on S12 IC Based on the calculation of the crack initiation stress under uniaxial compression using the wing crack propagation model, which is equal to the crack initialization stress, the parameters λ included in the tensile damage model under quasi-static loading are obtained, where λ is the crack length correction parameter.

[0028] Furthermore, step S1 also includes the following steps:

[0029] S14, Parameters μ and K determined based on S12 and S13 IC Based on the calculation that the strength of the wing crack propagation model under uniaxial compression is equal to the experimental uniaxial compressive strength, the parameters w included in the tensile damage model under quasi-static loading are obtained, where w is the crack spacing.

[0030] Furthermore, step S1 also includes the following steps:

[0031] S15. Based on the elastic modulus E and Poisson's ratio α obtained in S11, and combined with the density ρ of the rock sample, the Rayleigh wave velocity v is determined by equation (4). r ;

[0032]

[0033] This invention also provides the application of the rock damage model under direct impact loading obtained by the construction method described above in geotechnical engineering. The application includes the study of the damage and crushing law of ore under impact loading and the study of the crushing / pulverizing law of ore in the grinding process.

[0034] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0035] (1) One of the innovations of the construction method provided by this invention is to elucidate the dynamic tensile damage evolution model of rock under direct impact loading by observing the propagation of tensile cracks. Specifically, by innovatively introducing a correction factor related to the crack propagation rate, the relevant terms of the tensile damage model applicable to the quasi-static loading when the initial oblique crack is fully opened are appropriately corrected, so as to ensure that the constructed dynamic tensile damage evolution model can more accurately reflect the physical properties and behavior of rock under direct impact dynamic loading, thereby enhancing the accuracy, reliability and stability of the rock damage model in predicting the strength of rock under direct impact loading.

[0036] (2) This invention uses microscopic tensile crack propagation to deduce the dynamic tensile damage evolution model of rock under direct impact loading. Combined with the determination method of key model parameters (such as the above-mentioned correction factor and dynamic fracture toughness), it significantly improves the accuracy and reliability of rock damage model in predicting the evolution law of macroscopic damage and failure of rock under direct impact loading.

[0037] (3) Based on the dynamic tensile damage evolution model of rock under direct impact loading provided by the present invention through microscopic tensile crack propagation, and combined with the method for determining key parameters, the accuracy and reliability of the macroscopic damage and failure evolution law and strength prediction of rock under direct impact loading have been significantly improved. In this way, it is possible to more accurately reveal the quantitative change law of rock damage and failure under direct impact loading and the key factors affecting the damage process and strength of rock.

[0038] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0039] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0040] Figure 1 The stress-strain curves of yellow sandstone samples under different confining pressures in the method provided in the embodiments of the present invention are shown.

[0041] Figure 2The stress-strain diagram, volumetric strain curve, and cracked volumetric strain curve of the yellow sandstone sample under a confining pressure of 0 provided in the embodiments of the present invention;

[0042] Figure 3 The stress-strain diagram, volumetric strain curve, and cracked volumetric strain curve of the yellow sandstone sample under a confining pressure of 20 MPa provided in the embodiments of the present invention;

[0043] Figure 4 The curves showing the relationship between peak stress and confining pressure of yellow sandstone samples under different confining pressures in the method provided in this embodiment of the invention;

[0044] Figure 5 The method provided in this embodiment of the invention includes a curve showing the relationship between the initial stress of cracks in a yellow sandstone sample under different confining pressures and the confining pressure.

[0045] Figure 6 In the method provided in this embodiment of the invention, the crack spacing w is equal to 2.4 × 10⁻⁶. -3 Curves showing the variation of σ1 and L at time m;

[0046] Figure 7 The theoretical uniaxial compressive strength value σ in the method provided in the embodiments of the present invention p,t Fitting plot with crack spacing w;

[0047] Figure 8 The stress-strain curves of sandstone samples under one-dimensional dynamic impact at different strain rates are shown in the method provided in the embodiments of the present invention.

[0048] Figure 9 These are morphological images of sandstone samples after failure under different impact strain rates in the method provided in this embodiment of the invention.

[0049] Figure 10 A power function fitting graph of dynamic fracture toughness as a function of strain rate provided in an embodiment of the present invention;

[0050] Figure 11 This is a graph showing the variation of σ1-L under different strain rates during one-dimensional direct loading in the method provided in this embodiment of the invention.

[0051] Figure 12 The graph shows the variation curves of σ1-L under different strain rates (confining pressure σ3 = 5 MPa) during three-dimensional direct loading in the method provided in the embodiment of the present invention.

[0052] Figure 13 Stress-strain curves of sandstone samples under dynamic triaxial conditions at different strain rates (confining pressure σ3 = 5 MPa) provided in the embodiments of the present invention;

[0053] Figure 14A comparison of the theoretical and measured strengths of sandstone samples under dynamic triaxial conditions at different strain rates (confining pressure σ3 = 5 MPa) provided in the embodiments of the present invention;

[0054] Figure 15 The graph shows the variation of σ1-L under different confining pressures (strain rate = 170 / s) during three-dimensional direct loading in the method provided in the embodiment of the present invention.

[0055] Figure 16 Stress-strain curves of sandstone samples under different confining pressures (strain rate = 170 / s) under dynamic triaxial conditions provided in the embodiments of the present invention;

[0056] Figure 17 This is a comparison chart of the theoretical and measured strengths of sandstone under different confining pressures (strain rate = 170 / s) in the method provided in this embodiment of the invention. Detailed Implementation

[0057] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0058] Based on in-depth research, the inventors of this invention discovered that existing rock damage models obtained through inversion from measured data under direct impact loading have the following limitations: First, existing models neglect the tensile failure properties of rocks under direct dynamic impact; second, the methods for determining some model parameters are not reasonable enough. These problems result in insufficient accuracy and reliability of existing models in predicting the strength and damage evolution of rocks under direct impact dynamic loading, failing to accurately reveal the true failure mechanism of rocks under direct impact loading, and also making it difficult to effectively quantify the damage and failure of rocks under direct impact loading. Therefore, an innovative construction method is needed to overcome the above-mentioned limitations of existing models to improve the model's predictive ability and explanatory power for rock damage under direct impact loading. After analyzing numerous experimental results, the inventors found that the initial segment of the dynamic stress-strain curve of the rock did not show a concave phenomenon when a direct impact load was applied, which means that the rock did not experience a crack closure stage under direct impact loading. Therefore, assuming that the initial crack is in an open state when constructing the model is more reasonable and closer to the actual situation.

[0059] Based on this, the present invention provides a method for constructing a rock damage model under direct impact loading, comprising the following steps:

[0060] S1. Based on the interaction and superposition principle among multiple cracks, a wing crack propagation model is obtained when the initial oblique crack is fully opened under quasi-static loading. Based on the wing crack propagation model, and combined with uniaxial and triaxial tests and CCNBD experiments, a tensile damage model under quasi-static loading is obtained, i.e., K. I = f(σ1,σ3,L), where K I f is the stress intensity factor value at the tip of the wing crack under static load. f is a polynomial function that includes multiple terms related to the concentrated force and / or far-field compressive stress acting on the crack. The multiple terms include the material properties of the rock, axial stress σ1, confining pressure σ3, and wing crack propagation length L.

[0061] S2. Introduce a correction factor k(v) related to the crack propagation rate, which includes a first correction factor k1(v) and a second correction factor k2(v), namely equation (1) and equation (2), to correct the tensile damage model under quasi-static loading and obtain the tensile damage model expression under direct impact loading.

[0062] Wherein, k1(v) is used to correct the terms in S1 related to the concentrated force acting on the crack, and k2(v) is used to correct the terms related to the far-field compressive stress acting on the crack.

[0063]

[0064] In equations (1) and (2), v r Let v be the Rayleigh wave velocity, v be the crack propagation rate, and v be a constant value. The average crack propagation rate is used as the reference value. replace;

[0065] S3. Conduct one-dimensional direct impact tests to obtain stress-strain curves of rock samples at different strain rates, thereby obtaining the peak strength σ at different strain rates. p That is, the measured strength. Based on the measured strength and combined with the tensile damage model expression under direct impact loading described in S2, and setting the confining pressure σ3 = 0 and k(v) = 1, the dynamic fracture toughness of the rock is calculated in the numerical calculation software. The value of is set as a series of point values, resulting in different values. Values ​​are taken at different strain rates The variation curve of σ1-L is used to obtain the theoretical strength, and the theoretical strength is found to be close to the measured strength at different strain rates. The values ​​of are fitted to obtain Relationship;

[0066] S4. Based on the tensile damage model expression under direct impact loading described in S2 and setting the circumference σ3 = 0, use numerical calculation software to fit and obtain the crack propagation length L corresponding to the maximum value of the axial stress σ1.i According to the peak strength σ measured at different strain rates in the one-dimensional direct impact test described in S3, p The corresponding time t i ,according to Obtain the average crack propagation rate Based on equations (1) and (2), determine the first correction factor k1(v) and the second correction factor k2(v) related to the crack propagation rate;

[0067] S5. Based on the tensile damage model expression under direct impact loading described in S2, and combined with the experimental data obtained from the uniaxial and triaxial tests and CCNBD experiments described in S1, as well as the values ​​determined in S3 and S4. By taking values ​​of k1(v) and k2(v), a tensile damage model for predicting rock failure mechanisms under direct impact loading is constructed.

[0068] Compared with existing technologies, one of the innovations of the construction method provided by this invention is to elucidate the dynamic tensile damage evolution model of rock under direct impact loading by observing the propagation of tensile cracks at a microscopic level. Specifically, by innovatively introducing a correction factor related to the crack propagation rate, the relevant terms of the tensile damage model applicable to the quasi-static loading when the initial oblique crack is fully open are appropriately modified, ensuring that the constructed dynamic tensile damage evolution model can more accurately reflect the physical properties and behavior of rock under direct impact dynamic loading, thereby enhancing the accuracy, reliability and stability of the rock damage model in predicting the strength of rock under direct impact loading.

[0069] It should be noted that the method for determining dynamic fracture toughness, as one of the innovations of this invention, can improve the accuracy and applicability of the tensile damage model in predicting the strength change trend of rocks under direct impact loading. At the same time, the strength predicted by the model is slightly lower than the measured strength, which can provide an additional safety margin, help reduce risks, and thus ensure the safety and reliability of rock engineering. Specifically, unlike the existing method of determining rock fracture toughness using CCNBD splitting tests, this invention employs an indirect method. It utilizes the peak strength of rock samples at different strain rates obtained from one-dimensional direct impact tests, combined with the tensile damage model expression under one-dimensional direct impact loading. This approach combines experimental and theoretical methods, using numerical analysis software to obtain the dynamic fracture toughness at different strain rates. Here, it is assumed that the dynamic fracture toughness of the rock is a single function of the strain rate. This is because, although the dynamic fracture toughness of the rock is affected by the crack length and changes with crack propagation, the crack length within each rock is equal, thus the influence of crack length can be ignored. Furthermore, under microscopic conditions, the total propagation length of the wing crack is relatively small, and the crack propagation time is relatively short. Therefore, it can be considered that the dynamic fracture toughness remains constant during wing crack propagation. Based on the above, a correction factor k(v) = 1 is assumed when calculating the dynamic fracture toughness of the rock.

[0070] This invention, by observing the propagation of tensile cracks, elucidates the dynamic tensile damage evolution model of rocks under direct impact loading. Combined with methods for determining key model parameters (such as correction factors and dynamic fracture toughness), it significantly improves the accuracy and reliability of rock damage models in predicting the macroscopic damage and failure evolution of rocks under direct impact loading.

[0071] Based on the dynamic tensile damage evolution model of rock under direct impact loading provided by this invention, which uses microscopic tensile crack propagation to predict the growth of the crack, and combined with the method for determining key parameters, the accuracy and reliability of the macroscopic damage evolution law and strength prediction of rock under direct impact loading are significantly improved. This allows for a more accurate revelation of the quantitative variation law of rock damage under direct impact loading and the key factors affecting the damage process and strength of the rock.

[0072] Specifically, the expression for the tensile damage model under direct impact loading is Equation (3):

[0073]

[0074] In equation (3), K Id σ1 is the stress intensity factor value at the tip of the wing crack under dynamic load, σ3 is the axial stress, σ4 is the confining pressure, L is the wing crack propagation length, λ is the crack length correction parameter, w is the crack spacing, b is the initial oblique crack length of the rock sample, and θ0 is the initial oblique crack inclination angle of the rock sample.

[0075] In some preferred embodiments, step S5 specifically includes the following steps:

[0076] S51. According to equation (3), when And when σ3=0, a one-dimensional tensile damage model under direct impact loading is constructed; and / or,

[0077] S52. According to equation (3), when When σ3 is a constant, a three-dimensional tensile damage model under direct impact loading is constructed.

[0078] The tensile damage model under direct impact loading is a constitutive model between the axial stress σ1 of the rock and the tensile damage characterized by the wing crack propagation length L when the initial inclined microcrack is fully opened.

[0079] Preferably, in step S52, the confining pressure σ3 in the three-dimensional direct impact loading tensile damage model is ≤ P. When the confining pressure σ3 is maintained at or below the threshold P, the dynamic failure of the rock exhibits a tensile failure mode.

[0080] In some specific embodiments, in step S3, during the one-dimensional direct impact test, the rock sample is yellow sandstone. The relationship is a power function; and / or, the strain rate ranges from 80 / s to 200 / s.

[0081] In some preferred embodiments, step S1 specifically includes the following steps:

[0082] S11. Experimental data of rock samples were obtained through uniaxial loading and conventional triaxial loading tests, including stress-strain curves, elastic modulus E and Poisson's ratio α under different confining pressures σ3, and characteristic stresses during the loading process; the characteristic stresses include: crack initialization stress σ. ci Peak stress σ p Crack closure stress σ cc Crack damage stress σ cd ;

[0083] S12, based on σ under medium to high confining pressure p -Slope of the linear fitting plot of σ3, CCNBD splitting experiment, σ ci The slope and intercept of the -σ3 linear fitting plot are used to determine the parameters μ and K in the wing crack propagation model under quasi-static loading when the initial oblique crack is fully opened. IC , b and θ0; μ is the friction coefficient of the rock sample, K IC denoted as quasi-static fracture toughness of the rock sample, b as the initial oblique crack length of the rock sample, and θ0 as the initial oblique crack inclination angle of the rock sample.

[0084] Preferably, in step S12, the medium-high confining pressure is σ3 ≥ 15 MPa.

[0085] S13, Parameters μ and K determined based on S12 IC b, θ0, based on the calculation that the initiation stress of the crack propagation model under uniaxial compression is equal to the crack initialization stress, the parameters λ included in the tensile damage model under quasi-static loading are obtained, where λ is the crack length correction parameter;

[0086] S14, Parameters μ and K determined based on S12 and S13 IC b, θ0, λ, based on the calculation that the strength of the wing crack propagation model under uniaxial compression is equal to the experimental uniaxial compressive strength, the parameters w included in the tensile damage model under quasi-static loading are obtained, where w is the crack spacing;

[0087] S15. Based on the elastic modulus E and Poisson's ratio α obtained in S11, and combined with the density ρ of the rock sample, the Rayleigh wave velocity v is determined by equation (4). r ;

[0088]

[0089] In some preferred embodiments, S12 specifically includes the following steps:

[0090] S121, based on σ under medium to high confining pressure p -σ3 linear fitting plot slope k1 and combined with Determine the internal friction angle of the rock sample according to Determine the friction coefficients μ and σ of the rock sample. p This represents the peak stress.

[0091] S122. Determine the peak load P based on the load-displacement curve of the CCNBD specimen under compressive load. max And through K IC =f(P max K was calculated. IC ;

[0092] S123, according to σ ci The slope k2 and intercept d2 of the linear fit plot of -σ3, combined with and Calculate and determine the initial oblique crack length b and the initial oblique crack inclination angle θ0, σ of the rock sample. ci Initialize the stress for the crack.

[0093] It is understood that the CCNBD splitting test refers to the splitting test of the Cracked Chevron Notched Brazilian Disc with herringbone slits.

[0094] In some preferred embodiments, S13 specifically includes the following steps: based on the crack propagation model, the initiation stress under uniaxial compression is equal to the crack initialization stress, and equation (5) is derived:

[0095]

[0096] In equation (5), σ ci-I The initial stress for crack formation is given by uniaxial test, μ is the friction coefficient of the rock specimen, b is the initial oblique crack length of the rock specimen, and θ0 is the initial oblique crack inclination angle of the rock specimen. The parameters μ and K, determined based on the experimental data obtained from the uniaxial and triaxial tests described in S1 and the CCNBD experiment, are used. IC Substituting b and θ0 into equation (5), we can calculate the value of λ.

[0097] In some preferred embodiments, S14 specifically includes the following steps:

[0098] S141. Based on the wing crack propagation model derived from equation (6) under uniaxial compression (i.e., uniaxial loading, confining pressure σ3=0), and based on the determined λ and other parameters μ, b, θ0, K IC Plot the curves of L versus σ1 for different values ​​of w, and obtain the peak axial stress σ in each σ1-L curve. p,t That is, the theoretical uniaxial compressive strength value, based on the σ corresponding to different values ​​of w. p,t σ p,t -w fitting plot;

[0099]

[0100] S142. Based on the stress-strain curve of the rock specimen under the uniaxial test (i.e., uniaxial loading) described in S1, obtain the experimental uniaxial compressive strength value σ of the rock specimen. p,exp ; from the σ p,t -w fitting plot, find σ p,t =σ p,exp The corresponding horizontal coordinate point value is the crack spacing w.

[0101] The present invention also provides the application of the rock damage model under direct impact loading obtained by the above construction method in geotechnical engineering. The application includes: obtaining the evolution law, strength characteristics, and wing crack propagation length characteristics of the wing crack length L with axial stress σ1 under different dynamic load strain rates and / or different confining pressures based on the rock damage model under direct impact loading.

[0102] The strength characteristics include the maximum value of the axial stress σ1 σ max This refers to the dynamic strength of the rock, the axial stress σ1 when the wing crack propagation length L = 0, which is the dynamic crack initialization stress; the wing crack propagation length characteristic includes σ max The corresponding L value is the critical wing crack propagation length.

[0103] The applications also include the study of damage and crushing patterns of ores under impact loads, and the study of crushing / pulverizing patterns of ores in grinding processes.

[0104] The technical solution of the present invention will be further described in detail below with reference to specific embodiments.

[0105] Example 1

[0106] This embodiment provides a method for constructing a rock damage model under direct impact loading, including the following steps:

[0107] S1. Based on the interaction and superposition principle among multiple cracks, a wing crack propagation model is obtained when the initial oblique crack is fully opened under quasi-static loading. Based on the wing crack propagation model, and combined with uniaxial and triaxial tests and CCNBD experiments, a tensile damage model under quasi-static loading is obtained, i.e., K. I = f(σ1,σ3,L), where K I The stress intensity factor at the crack tip of the flange under static load is given by f, which is a polynomial function including multiple terms related to the concentrated force and / or far-field compressive stress acting on the crack; σ1 is the axial stress, σ3 is the confining pressure, and L is the crack propagation length; the specific steps include:

[0108] S10. Based on the interaction and superposition principle between multiple cracks, the crack propagation model of the wing when the initial oblique crack is fully opened under quasi-static loading is obtained, and its expression is Equation (7):

[0109]

[0110] S11. Using the TAW-2000 rock mechanics testing system independently developed by the Institute of Geology and Geophysics, Chinese Academy of Sciences, uniaxial loading and conventional triaxial loading tests were conducted under ambient temperature conditions. Specifically, an axial strain-controlled loading method was adopted, with a loading rate of 0.02 mm / min. The axial strain and circumferential strain were measured by axial strain gauges and circumferential strain gauges, respectively. During uniaxial loading, the sample was placed in a suitable position and loaded until macroscopic fracture occurred in the rock sample. During conventional triaxial loading, the axial stress and confining pressure were first applied to the target hydrostatic stress state at a loading rate of 1 MPa / min, and then the axial strain rate was 0.02 mm / min until macroscopic fracture surfaces occurred in the rock sample. Acoustic emission signals were collected simultaneously during this process.

[0111] The rock sample used in this experiment was a yellow sandstone sample. The yellow sandstone sample was cylindrical, and its main constituent mineral grains were quartz (70%); the percentages of plagioclase, microcline, chlorite, dolomite, ferrodolithite, calcite, and muscovite were 11%, 8%, 3%, 2%, 2%, 2%, and 2%, respectively, with a mineral crystallinity of 89%. The basic physical parameters and confining pressure of the yellow sandstone sample are shown in Table 1.

[0112] Table 1. Basic physical parameters, confining pressure settings, and macroscopic failure types of yellow sandstone samples.

[0113]

[0114] Experimental data for yellow sandstone samples were obtained through the aforementioned uniaxial loading and conventional triaxial loading tests, including stress-strain curves under different confining pressures σ3 (e.g., Figure 1 The material property parameters include the elastic modulus E and Poisson's ratio α (as shown in Table 2 below), and the characteristic stresses during the loading process; the characteristic stresses include: crack initialization stress σ. ci Peak stress σ p Crack closure stress σ cc Crack damage stress σ cd ;

[0115] Table 2 Elastic modulus and Poisson's ratio of yellow sandstone samples under different confining pressures.

[0116]

[0117] Wherein, peak stress σ pThe magnitude of the stress can be directly obtained from the stress-strain curve. Other characteristic stresses need to be obtained indirectly by calculating the volumetric strain and crack strain. For brittle rocks, the volumetric strain reflects the ratio of the total volume change to the total volume in the rock. The crack strain is equal to the non-elastic strain of the rock during loading, and its magnitude is equal to the volumetric strain of the rock minus the elastic strain. The calculation formula is shown in the following formula (8):

[0118]

[0119] In equation (8), ε axial For axial strain, ε lateral For circumferential strain, ε V For the body to adapt to strain, It is the strain of an elastic body. For non-elastic body strain, i.e. crack strain, σ1 is the axial stress, σ3 is the confining pressure, E is the elastic modulus, and α is Poisson's ratio;

[0120] The method for determining rock mass strain and crack body strain according to equation (8) and combined with Figure 1 The stress-strain data of the sandstone samples in the table are shown below, taking the samples under uniaxial loading (i.e., sample S1 in Table 1) and confining pressure of 20 MPa (i.e., sample S6 in Table 1) as an example. The calculation results are as follows: Figure 2 and Figure 3 As shown; the characteristic stresses of the remaining 6 specimens (i.e., S2-S5 and S7-S8) can be obtained using a similar method.

[0121] S12, based on σ under medium to high confining pressure p -Slope of the linear fitting plot of σ3, CCNBD splitting experiment, σ ci The slope and intercept of the -σ3 linear fitting plot are used to determine the b, θ0, and other parameters K included in the wing crack propagation model when the initial oblique crack is fully opened under quasi-static loading. IC μ; μ is the friction coefficient of the rock sample, K IC Let be the quasi-static fracture toughness of the rock sample, b be the initial oblique crack length of the rock sample, and θ0 be the initial oblique crack inclination angle of the rock sample; S12 specifically includes the following steps:

[0122] S121, Based on the peak stress σ under different confining pressures obtained in S11 p Data fitting yields results such as Figure 4 The σ shown p The relationship curve of -σ3, from Figure 4 It can be seen that the linear fit is good at confining pressures of 15MPa, 20MPa, 25MPa, and 30MPa. Based on the σ under medium to high confining pressures (i.e., confining pressure σ3 ≥ 15MPa),... pThe slope k1 = 3.22 of the -σ3 linear fitting plot is combined with... Determine the internal friction angle of the sandstone sample according to The friction coefficient of the sandstone sample was determined to be μ = 0.62;

[0123] S122. Determine the peak load P based on the load-displacement curve of the CCNBD specimen under compressive load. max And through K IC =f(P max K was calculated. IC =0.38MPa·m 1 / 2 ;K IC =f(P max The specific calculation formula for ) is Equation (9):

[0124]

[0125] In equation (9), P max Let B be the peak load at which the CCNBD specimen fails, B be the thickness of the Brazilian disk specimen, and R be the radius of the Brazilian disk specimen. According to the method recommended by the International Society for Rock Mechanics (ISRM), four dimensionless constants are defined to characterize the geometry of the rock, namely a0, a1, a2, and a3 as shown in equation (10). B a s In equation (9), u and ω can be obtained by utilizing a0 and a0 from existing technologies. B The numerical values ​​were obtained through linear interpolation.

[0126]

[0127] S123. Crack initialization stress σ under different confining pressures obtained in S11 ci Data fitting yields results such as Figure 5 The σ shown ci The -σ3 relationship curve and its slope k2 = 3.2113 and intercept d2 = 39.799, combined with... and The initial diagonal crack length of the sandstone sample was calculated to be b = 3.3 × 10⁻⁶. -4 m and the initial diagonal crack inclination angle θ0 = 65.36°.

[0128] S13. The initial crack stress under confining pressure σ3 = 0, i.e., σ under uniaxial compression, is included in the experimental data of S11. ci-I =39MPa (from Figure 2 and Figure 5 (can be obtained) and K IC =0.38MPa·m 1 / 2 μ = 0.62, b = 3.3 × 10-4 Substituting m and θ0 = 65.36° into equation (5), we get λ = 0.05.

[0129] S14. According to equation (6), based on the determined λ = 0.05 and other parameters μ = 0.62 and b = 3.3 × 10⁻⁶, -4 m and θ0 = 65.36°, K IC =0.38MPa·m 1 / 2 Plot the curves of L versus σ1 for different values ​​of w. For example, when w = 2.4 × 10 -3 When m, the curve of L changing with σ1 is as follows: Figure 6 As shown, from Figure 6 Therefore, w = 2.4 × 10 -3 Peak axial stress σ at m p,t =90MPa; based on different values ​​of w corresponding to σ p,t σ p,t -w fitting plot, see Figure 7 ;

[0130] Furthermore, based on the stress-strain curves of the sandstone sample in S11 under uniaxial compression ( Figure 2 )as well as Figure 4 The experimental uniaxial compressive strength value σ of the sandstone sample was obtained. p,exp =68MPa; from Figure 7 The σ shown p,t -w fitting plot, find σ p,t =σ p,exp The x-axis value corresponding to 68 MPa is the crack spacing w = 1.6 × 10⁻⁶. -3 m.

[0131] S15. The elastic modulus E and Poisson's ratio α obtained from Table 2 in S11, combined with the density ρ of the sandstone sample ρ = 2.30 g / cm³. 3 Using equation (4), the Rayleigh wave velocities v corresponding to samples S1-S8 under different confining pressures are determined. r .

[0132] Based on the expression (7) of the wing crack propagation model, and combined with the parameters determined by S12-S14, the tensile damage model when the initial oblique crack is fully opened under quasi-static loading is obtained, namely, equation (11):

[0133]

[0134] S2. Introduce the first correction factor k1(v) and the second correction factor k2(v) to modify the tensile damage model under quasi-static loading, and obtain the expression (12) of the tensile damage model under direct impact loading.

[0135]

[0136] S3. A one-dimensional direct impact test was conducted on a disk-shaped specimen with a diameter of 50 mm and a thickness of 25 mm using a split Hopkinson pressure bar (SHPB) experimental setup. The stress-strain curves of the sandstone specimen at different strain rates were obtained, as shown below. Figure 8 As shown, the morphology of the sandstone samples after failure at three strain rates is as follows: Figure 9 As shown;

[0137] from Figure 8 To obtain the peak strength σ at different strain rates p That is, the measured strength. Based on the measured strength and combined with the tensile damage model expression (12) under direct impact loading, and setting the confining pressure σ3=0 and k1(v)=1, using MATLAB software, we find the strain rates corresponding to the theoretical strength that are close to the measured strength. The values ​​of are fitted to obtain The power function relationship, such as Figure 10 As shown, that is

[0138] S4. Based on equation (3) and setting the confining pressure σ3 = 0, we obtain equation (13).

[0139]

[0140] Using MATLAB software, the part containing variables on the right side of equation (13) is... Data fitting yields the crack propagation length L corresponding to the maximum value of axial stress σ1. i According to the time t corresponding to the peak rock strength measured in the one-dimensional direct impact test described in S3 i ,according to Obtain the average crack propagation rate Furthermore, combining the Rayleigh wave velocities v corresponding to samples S1-S8 under different confining pressures determined by S15, r According to equations (1) and (2), k1(v) and k2(v) are obtained. In this embodiment, the values ​​of k1(v) and k2(v) are very close to 1, because w = 1.6 × 10 in this embodiment. -3 A smaller m indicates a lower average crack propagation rate. The wave velocity is much smaller than that of Ruili.

[0141] This invention introduces a correction factor to improve the universality and accuracy of the model, especially when the spacing w between the wing cracks is large, ensuring that the model expression is more rigorous and more widely applicable.

[0142] S5, the expression (12) of the tensile damage model under direct impact loading obtained based on S2, and the values ​​of k1(v) = 1, k2(v) = 1 and different strain rates determined by S3 and S4. By selecting values, a tensile damage model for predicting the failure mechanism of sandstone under direct impact loading is constructed, which includes:

[0143] S51. According to equation (12), when When σ3 = 0, a one-dimensional tensile damage model under direct impact loading is constructed, and the following results are obtained: Figure 11 The curves showing the variation of σ1-L under different strain rates are shown.

[0144] S52, when Furthermore, when the confining pressure σ3 = 5 MPa, a three-dimensional tensile damage model under direct impact loading was constructed, and thus the following results were obtained: Figure 12 The curves showing the variation of σ1-L under different strain rates (σ3=5MPa) are shown, and as follows... Figure 15 The curves shown are the variation curves of σ1-L under confining pressures σ3 of 0MPa, 5MPa, 10MPa, and 15MPa at a strain rate of 170 / s.

[0145] Three-dimensional direct impact tests were conducted on a disc-shaped specimen with a diameter of 50 mm and a thickness of 25 mm using an SHPB experimental setup, and the results were obtained. Figure 13 (σ3=5MPa) and Figure 16 Stress-strain curve (strain rate = 170 / s).

[0146] Will Figure 12 The dynamic strength of sandstone under dynamic triaxial impact loading (with different strain rates) is derived from a three-dimensional direct impact loading micro-tensile damage model. Figure 13 Compare the measured intensity in the data, such as Figure 14 As shown; from Figure 14 It can be seen that both the experimentally measured dynamic triaxial strength values ​​and the predicted dynamic triaxial strength values ​​from the micro-tensile damage model reflect the increase in dynamic strength of the sandstone sample with increasing strain rate when the confining pressure is maintained at 5 MPa. This indicates that the micro-tensile damage model under direct impact loading obtained by the method of this invention can accurately predict the trend of rock strength under direct impact loading with dynamic strain rate. Furthermore, the model-predicted strength is slightly lower than the measured strength, which provides an additional safety margin, helps to reduce risks, and thus ensures the safety and reliability of rock engineering.

[0147] Will Figure 15 The dynamic strength of sandstone under dynamic triaxial impact load (with different confining pressures) is derived from a three-dimensional direct impact loading micro-tensile damage model. Figure 16 Compare the measured intensity in the data, such as Figure 17 As shown; from Figure 17 It can be seen that both the predicted results of the micro-tensile damage model and the experimental results show that the dynamic strength of the sandstone sample increases significantly with increasing confining pressure. This indicates that the micro-tensile damage model under direct impact loading obtained by the method of this invention can accurately predict the trend of rock strength variation with confining pressure under direct impact loading. Furthermore, the model-predicted strength is slightly lower than the measured strength, which can provide an additional safety margin, help reduce risks, and thus ensure the safety and reliability of rock engineering.

[0148] This embodiment also provides the application of the rock tension damage model under direct impact loading obtained by the construction method described above in geotechnical engineering, the application including:

[0149] (a) Based on the tension damage model under one-dimensional and / or three-dimensional direct impact loading described in S5, the evolution law of crack propagation length L of the flange with axial stress σ1 under different dynamic load strain rates and different confining pressures is obtained, such as... Figure 11 , Figure 12 and Figure 15 As shown;

[0150] according to Figure 11 The stress at which the crack begins to propagate under high strain rate increases slightly with increasing strain rate, gradually increasing from 35 MPa at a strain rate of 83 / s to 48 MPa at a strain rate of 196 / s.

[0151] according to Figure 12 When the confining pressure is 5 MPa, the initial stress of cracks in the sandstone sample gradually increases with the increase of strain rate: when the strain rate is 98 / s, the initial stress of cracks is 52 MPa; when the strain rate is 193 / s, the initial stress of cracks is 62 MPa.

[0152] according to Figure 15 The stress at which the wing crack begins to propagate (i.e., the initial stress of the dynamic crack) gradually increases with the increase of the confining pressure: when the confining pressure is 0 MPa, the initial stress of the dynamic crack is 46 MPa; when the confining pressure is 15 MPa, the initial stress of the dynamic crack is 89 MPa.

[0153] (b) Based on the tension damage model under one-dimensional and / or three-dimensional direct impact loading described in S5, obtain the strength characteristics under different dynamic load strain rates; for example... Figure 14 The theoretical predicted strength shown is from Figure 12 The maximum value of axial stress σ1 under different strain rates is shown. max In addition, strength characteristics under different confining pressures were obtained, such as... Figure 17 The theoretical predicted strength shown is from Figure 15 The maximum value of axial stress σ1 under different confining pressures is shown. max Obtained; in addition, from Figure 11 It can be seen that the J-stage of the nonlinear segment of the σ1-L curve of sandstone under one-dimensional direct impact loading lasts longer, which is consistent with the experimental observation results.

[0154] (c) Based on the tension damage model under one-dimensional and / or three-dimensional direct impact loading described in S5, obtain the crack propagation length characteristics of the wing under different dynamic load strain rates and confining pressures. For example, according to... Figure 11 At high strain rates, the wing crack propagation length of sandstone increases to 1.74 × 10⁻⁶ at different strain rates. -4 At m, the axial stress reaches its maximum value, i.e., the dynamic compressive strength, and the critical wing crack propagation length is 1.74 × 10⁻⁶. -4 m.

[0155] according to Figure 12 At different strain rates, the crack propagation length of the wing increased to 1.79 × 10⁻⁶. -4 At m, the dynamic peak strength of the sandstone was reached, that is, the critical wing crack propagation length was 1.79 × 10⁻⁶. -4 m.

[0156] according to Figure 15 The wing crack propagation length at which the dynamic peak strength of sandstone is reached increases slightly with increasing confining pressure: when the confining pressure is 0 MPa, the critical wing crack propagation length is 1.76 × 10⁻⁶ MPa. -4 m; when the confining pressure is 15 MPa, the critical wing crack propagation length is 1.84 × 10 m. -4 m.

[0157] Based on the comparison and analysis of the model prediction results and experimental results provided in this embodiment, it is further verified that the micro-tensile damage model obtained by the construction method provided by the present invention has higher accuracy, reliability and stability in predicting the strength and damage evolution law of rocks under direct impact loading. This helps to more accurately reveal the quantitative change law of damage and failure of rocks under direct impact loading and the key factors affecting the damage process and strength of rocks, such as dynamic load strain rate and confining pressure.

[0158] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a rock damage model under direct impact loading, characterized in that: The following steps are involved: S1. Based on the interaction and superposition principle between multiple cracks, the wing crack growth model under quasi-static loading when the initial oblique crack is fully opened is obtained; based on the wing crack growth model, combined with uniaxial and triaxial tests and CCNBD experiments, the tensile damage model under quasi-static loading is obtained, that is, K I =f(σ1,σ3,L), where K I is the stress intensity factor value of the wing crack tip under static load, f is a polynomial function, including multiple factors related to the concentrated force and / or remote compressive stress borne by the crack; the multiple factors include the material characteristic parameters of the rock, the axial stress σ1, the confining pressure σ3, and the wing crack extension length L; S2. Introducing a correction factor k(v) related to the crack growth rate, which includes a first correction factor k1(v) and a second correction factor k2(v), i.e., equations (1) and (2), to correct the tensile damage model under quasi-static loading, and obtain an expression of the tensile damage model under direct impact loading; Wherein, k1(v) is used to correct the term related to the concentrated force action on the crack described in S1, and k2(v) is used to correct the term related to the far-field compressive stress action on the crack; In formula (1) and formula (2), v r is the Rayleigh wave velocity, v is the crack growth rate, v is set to a constant value and is calculated as the average crack growth rate replace; S3. Conduct a one-dimensional direct impact test to obtain the stress-strain curve of the rock sample at different strain rates, thereby obtaining the peak strength σ at different strain rates. p That is, the measured strength; according to the measured strength and combined with the tensile damage model expression under direct impact loading described in S2 and setting the confining pressure σ3 = 0 and k(v) = 1, the dynamic fracture toughness of the rock is calculated in the numerical calculation software. The value of is set to a series of point values, and different At different strain rates The variation curve of σ1-L is obtained from the theoretical strength, and the theoretical strength is close to the measured strength under different strain rates. The value of is fitted. relationship; S4. According to the tensile damage model expression under direct impact loading described in S2 and setting σ3 = 0, the wing crack extension length L corresponding to the maximum value of axial stress σ1 is obtained by fitting using numerical calculation software. i , according to the peak strength σ at different strain rates measured in the one-dimensional direct impact test described in S3 p The corresponding time t i ,according to The average crack growth rate According to equations (1) and (2), the first correction factor k1(v) and the second correction factor k2(v) related to the crack growth rate are determined; S5, based on the tensile damage model expression under direct impact loading described in S2, combined with the test data obtained from the uniaxial and triaxial tests and CCNBD experiments described in S1 and the values ​​determined in S3 and S4 By taking values ​​of k1(v) and k2(v), a tensile damage model is constructed to predict the rock failure mechanism under direct impact loading.

2. The construction method according to claim 1, characterized in that: The tensile damage model under direct impact loading is expressed as formula (3): In formula (3), K Id is the stress intensity factor value of the wing crack tip under dynamic load, σ1 is the axial stress, σ3 is the confining pressure, L is the wing crack extension length; λ is the crack length correction parameter, w is the crack spacing; b is the initial oblique crack length of the rock specimen, and θ0 is the inclination angle of the initial oblique crack of the rock specimen.

3. The construction method according to claim 2, characterized in that: Step S5 specifically includes the following steps: S51, according to formula (3), when When σ3=0, a tensile damage model under one-dimensional direct impact loading is constructed; and / or, S52, according to formula (3), when When σ3 is a constant, a tensile damage model under three-dimensional direct impact loading is constructed; The tensile damage model under direct impact loading is a constitutive model between the axial stress σ1 of the rock and the tensile damage represented by the wing crack extension length L when the initial inclined microcrack is fully opened.

4. The construction method according to claim 3, characterized in that: In step S52, the confining pressure σ3≤P in the tension damage model under the three-dimensional direct impact loading, when the confining pressure σ3 is maintained at a threshold value P or lower, the dynamic failure of the rock is manifested as a tension failure mode.

5. The construction method according to claim 1, characterized in that: In step S3, in the one-dimensional direct impact test, the rock sample is yellow sandstone, The relationship is a power function.

6. The construction method according to claim 1, characterized in that: In step S3, in the one-dimensional direct impact test, the strain rate ranges from 80 / s to 200 / s.

7. The construction method according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Through uniaxial loading and conventional triaxial loading tests, experimental data of rock samples are obtained, including stress-strain curves under different confining pressures σ3, elastic modulus E and Poisson's ratio α, and characteristic stresses during loading; the characteristic stresses include: crack initialization stress σ ci , peak stress σ p ; S12, according to the medium and high confining pressure σ p -σ3 linear fitting curve slope, CCNBD splitting experiment, σ ci The slope and intercept of the linear fitting graph of -σ3 are used to determine the parameters μ, K, and IC , b and θ0; μ is the friction coefficient of the rock sample, K IC is the quasi-static fracture toughness of the rock sample, b is the length of the initial oblique crack of the rock sample, and θ0 is the inclination angle of the initial oblique crack of the rock sample; S13, parameters μ, K determined based on S12 IC , b, θ0, according to the calculation that the crack initiation stress of the wing crack extension model under uniaxial compression is equal to the crack initialization stress, the tension damage model under quasi-static loading includes the parameter λ, λ is the crack length correction parameter.

8. The construction method according to claim 7, characterized in that: Step S1 also includes the following steps: S14, parameters μ, K determined based on S12 and S13 IC , b, θ0, λ, according to the calculation that the strength of the wing crack extension model under uniaxial compression is equal to the experimental uniaxial compressive strength, the tension damage model under quasi-static loading includes the parameter w, where w is the crack spacing.

9. The construction method according to claim 8, characterized in that: Step S1 also includes the following steps: S15. Based on the elastic modulus E and Poisson's ratio α obtained in S11 and the density ρ of the rock sample, the Rayleigh wave velocity v is determined by equation (4): r ; 10. Application of the rock damage model under direct impact loading obtained by the construction method according to any one of claims 1 to 9 in geotechnical engineering, the application includes studying the damage and crushing laws of ore under impact load, and studying the crushing / crushing laws of ore in grinding process.

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