A method for constructing a rock crushing damage model under impact loading and its application

Abstract

The present invention relates to a method for constructing a rock crushing damage model under impact loading and its application, belonging to the field of rock engineering, and solving at least one of the problems of existing rock models in predicting the failure evolution law and / or strength under direct impact loading, namely, insufficient reliability and accuracy, and difficulty in revealing the change law under direct impact loading. The method comprises: S1, based on the wing crack propagation model, obtaining a tension damage model under quasi-static loading; S2, introducing a correction factor to correct the tension damage model under quasi-static loading, and obtaining an expression for the tension damage model under direct impact loading; S3, determining the dynamic fracture toughness of the rock; S4, determining the correction factor; S5, constructing a tension damage model under direct impact loading. The present invention enhances the accuracy and reliability of the model in predicting the strength and failure evolution law of rock under direct impact loading, and the obtained model can reveal the quantitative change law of the damage and destruction of rock under direct impact loading.

Description

Technical Field

[0001] The present invention relates to the technical field of rock mass engineering, and in particular to a method for constructing a rock crushing damage model under impact loading and an application thereof. Background Art

[0002] Dynamic rock failure is a common 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, studying rock failure under dynamic loading is essential from an engineering perspective. Studies have found that rocks subjected to impact loads experience high strain rates during failure. Therefore, from the perspective of laboratory experiments, rock failure under impact loading can be abstracted as a study of rock damage and fracture at high strain rates. However, current research on rock failure under direct impact loading mostly relies on experimental investigations of rock's dynamic strength patterns or inversion of rock damage models from its dynamic stress-strain curves. However, these models often struggle to accurately reflect the rock damage process in practical applications. In particular, these models suffer from insufficient accuracy and reliability when predicting the macroscopic failure evolution and strength of rocks under direct impact loading. Furthermore, they struggle to reveal the quantitative changes in rock under direct impact loading and the key factors influencing the rock damage process and strength. Summary of the Invention

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

[0004] The purpose of the present invention is achieved through the following technical solutions:

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

[0006] S1. Based on the interaction between multiple cracks and the superposition principle, a wing crack growth model is obtained when the initial oblique crack is fully opened under quasi-static loading. Based on the wing crack growth model, combined with uniaxial and triaxial tests and CCNBD experiments, a tensile damage model under quasi-static loading is obtained, namely, K I =f(σ1,σ3,L), where K Iis 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, axial stress σ1, confining pressure σ3, and wing crack extension length L;

[0007] 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 for the tensile damage model under direct impact loading;

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

[0009]

[0010] 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 the average crack growth rate is replace;

[0011] 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; 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 to a series of point values, and different At different strain rates The variation curve of σ1-L is obtained from it, and the theoretical strength is found to be close to the measured strength under different strain rates. The value of is fitted relationship;

[0012] 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 numerical calculation software fitting. 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;

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

[0014] Furthermore, the tensile damage model under direct impact loading is expressed as formula (3):

[0015]

[0016] 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.

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

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

[0019] S52, according to formula (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 represented by the wing crack extension length L when the initial inclined microcrack is fully opened.

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

[0022] Further, in step S3, in the one-dimensional direct impact test, the rock sample is yellow sandstone, and the The relationship is a power function.

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

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

[0025] 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 initiation stress σ ci , peak stress σ p ;

[0026] S12, according to the medium and high confining pressure σ p -σ3 linear fitting plot slope, CCNBD splitting experiment, σ ci -σ3 linear fitting graph, and 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 specimen, b is the length of the initial oblique crack of the rock specimen, and θ0 is the inclination angle of the initial oblique crack of the rock specimen;

[0027] S13, parameters μ, K determined based on S12 IC , b, θ0, according to the calculation that the crack initiation stress of the wing crack growth model under uniaxial compression is equal to the crack initialization stress, the parameter λ included in the tension damage model under quasi-static loading is obtained, and λ is the crack length correction parameter.

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

[0029] 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 growth model under uniaxial compression is equal to the experimental uniaxial compressive strength, the parameters w included in the tension damage model under quasi-static loading are obtained, where w is the crack spacing.

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

[0031] 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 formula (4): r ;

[0032]

[0033] The present invention also provides the application of the rock damage model under direct impact loading obtained by the construction method as described above in geotechnical engineering, wherein the application includes the study of the damage and crushing laws of ore under impact load and the study of the crushing / crushing laws 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 innovative points of the construction method provided by the present invention is to perform a dynamic tensile damage evolution model of rock under direct impact loading by micro-observing the expansion of tensile cracks. Specifically, by innovatively introducing a correction factor related to the crack expansion rate, the relevant items of the tensile damage model applicable to the quasi-static loading when the initial oblique crack is fully opened are appropriately corrected, ensuring that the constructed dynamic tensile damage evolution model can more accurately reflect the physical properties and behavior of rock under direct impact dynamic load, thereby enhancing the accuracy, reliability and stability of the rock damage model in predicting the strength of rock under direct impact loading.

[0036] (2) The present invention performs a dynamic tensile damage evolution model of rock under direct impact loading by micro-observing the expansion of tensile cracks, and combines the method for determining key model parameters (such as the above-mentioned correction factor and dynamic fracture toughness), which significantly improves the accuracy and reliability of the rock damage model in predicting the evolution law of macroscopic damage and destruction of rock under direct impact loading.

[0037] (3) Based on the dynamic tensile damage evolution model of rock under direct impact loading by microscopic tensile crack expansion provided by the present invention, 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 have been significantly improved, thereby being able to more accurately reveal the quantitative change law of rock damage under direct impact loading and the key factors affecting the damage process and strength of rock.

[0038] In the present invention, the above-mentioned technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of the present invention will be described in the following description, and some advantages will become apparent from the description or be learned through practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0040] Figure 1 A stress-strain curve diagram of a yellow sandstone sample under different confining pressures in the method provided in an embodiment of the present invention;

[0041] Figure 2A stress-strain diagram including characteristic stress, a volume strain curve diagram, and a crack volume strain curve diagram of a yellow sandstone sample under a confining pressure of 0 in the method provided in an embodiment of the present invention;

[0042] Figure 3 A stress-strain diagram including characteristic stress, a volume strain curve diagram, and a crack volume strain curve diagram of a yellow sandstone sample under a confining pressure of 20 MPa in the method provided in an embodiment of the present invention;

[0043] Figure 4 A curve showing the relationship between peak stress and confining pressure of a yellow sandstone sample under different confining pressures in the method provided in an embodiment of the present invention;

[0044] Figure 5 A curve showing the relationship between crack initiation stress and confining pressure of a yellow sandstone sample under different confining pressures in the method provided in an embodiment of the present invention;

[0045] Figure 6 In the method provided in the embodiment of the present invention, the crack spacing w is equal to 2.4×10 -3 The variation curve of σ1 and L at m;

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

[0047] Figure 8 A stress-strain curve diagram of a sandstone sample at different strain rates under one-dimensional dynamic load impact in the method provided in an embodiment of the present invention;

[0048] Figure 9 This is a morphological diagram of a sandstone sample after failure at different impact strain rates in the method provided by an embodiment of the present invention;

[0049] Figure 10 A power function fitting diagram of dynamic fracture toughness versus strain rate provided by an embodiment of the present invention;

[0050] Figure 11 A graph showing the variation of σ1-L at different strain rates during one-dimensional direct loading in the method provided in an embodiment of the present invention;

[0051] Figure 12 A graph showing the change of σ1-L at different strain rates (confining pressure σ3 = 5 MPa) during three-dimensional direct loading in the method provided in an embodiment of the present invention;

[0052] Figure 13 The stress-strain curves of the sandstone specimens at different strain rates under dynamic triaxial conditions (confining pressure σ3 = 5 MPa) in the method provided in an embodiment of the present invention;

[0053] Figure 14A comparison chart of the theoretical strength and measured strength of sandstone specimens at different strain rates under dynamic triaxial conditions (confining pressure σ3 = 5 MPa) in the method provided in an embodiment of the present invention;

[0054] Figure 15 A graph showing the change of σ1-L under different confining pressures (strain rate = 170 / s) during three-dimensional direct loading in the method provided in an embodiment of the present invention;

[0055] Figure 16 This is a stress-strain curve diagram of a sandstone sample under different confining pressures (strain rate = 170 / s) under dynamic triaxial conditions in the method provided in an embodiment of the present invention;

[0056] Figure 17 This is a comparison chart of the theoretical strength and measured strength of sandstone at different confining pressures (strain rate = 170 / s) under dynamic triaxial conditions in the method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, and are not used to limit the scope of the present invention.

[0058] Based on in-depth research, the inventors discovered that existing rock damage models for direct impact loading, derived through inversion of measured data, have the following limitations: First, existing models ignore the tensile failure properties of rock under direct dynamic loading; and second, the determination methods for some model parameters are not rational. These issues result in insufficient accuracy and reliability in predicting the strength and damage evolution of rock under direct dynamic impact loading. They are unable to accurately reveal the true failure mechanism of rock under direct impact loading, and also hinder effective quantitative analysis of rock damage under direct impact loading. Therefore, an innovative construction method is needed to overcome the above limitations of existing models and improve their predictive and explanatory power for rock damage under direct impact loading. After analyzing numerous experimental results, the inventors found that when direct impact loading is applied, the initial segment of the rock dynamic stress-strain curve does not exhibit a concave depression, indicating that the rock does not undergo a crack closure phase under direct impact loading. Therefore, when constructing the model, assuming that the initial crack is open is more reasonable and closer to reality.

[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 between multiple cracks and the superposition principle, a wing crack growth model is obtained when the initial oblique crack is fully opened under quasi-static loading. Based on the wing crack growth model, combined with uniaxial and triaxial tests and CCNBD experiments, a tensile damage model under quasi-static loading is obtained, namely, 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, which includes 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, axial stress σ1, confining pressure σ3, and wing crack extension length L;

[0061] 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 for the tensile damage model under direct impact loading;

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

[0063]

[0064] 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 the average crack growth rate is replace;

[0065] 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 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 it, and the theoretical strength is found to be close to the measured strength under different strain rates. The value of is fitted relationship;

[0066] 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 numerical calculation software fitting.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;

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

[0068] Compared with the existing technology, one of the innovative points of the construction method provided by the present invention is to perform a dynamic tensile damage evolution model of rock under direct impact loading by micro-observing the expansion of tensile cracks; specifically, by innovatively introducing a correction factor related to the crack expansion rate, the relevant items of the tensile damage model applicable to the quasi-static loading when the initial oblique crack is fully opened are appropriately corrected 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 loads, 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 the present invention, can improve the accuracy and applicability of the tension damage model in predicting the strength change trend of rock 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 and help reduce risks, thereby ensuring the safety and reliability of rock engineering. Specifically, unlike the CCNBD splitting test commonly used in the prior art to determine the fracture toughness of rock, the present invention adopts an indirect method. Based on the peak strength of rock specimens at different strain rates obtained from a one-dimensional direct impact test, and combined with the expression of the tensile damage model under one-dimensional direct impact loading, the present invention adopts an indirect method. That is, the dynamic fracture toughness at different strain rates is obtained by combining experiments with theory and numerical analysis software. Here, it is assumed that the dynamic fracture toughness of rock is a single function of strain rate. This is because although the dynamic fracture toughness of rock is affected by crack length and changes with crack propagation, the crack lengths within each rock are equal, so the influence of crack length can be ignored. In addition, 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 is unchanged during the propagation of the wing crack. Based on the above, the correction factor k(v) = 1 is assumed when calculating the dynamic fracture toughness of rock.

[0070] By micro-observing the propagation of tensile cracks, the present invention demonstrates a dynamic tensile damage evolution model of rock under direct impact loading. Combined with the method for determining key model parameters (such as correction factors and dynamic fracture toughness), the accuracy and reliability of the rock damage model in predicting the evolution law of macroscopic damage and destruction of rock under direct impact loading are significantly improved.

[0071] Based on the dynamic tensile damage evolution model of rock under direct impact loading provided by the present invention, which is performed by micro-observing tensile crack expansion, and combined with the method for determining key parameters, the accuracy and reliability of the macroscopic damage and destruction evolution law and strength prediction of rock under direct impact loading have been significantly improved, thereby being able to more accurately reveal the quantitative change law of rock damage and destruction under direct impact loading and the key factors affecting the damage process and strength of rock.

[0072] Specifically, the tensile damage model under direct impact loading is expressed as formula (3):

[0073]

[0074] 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.

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

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

[0077] S52, according to formula (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 represented by the wing crack extension length L when the initial inclined microcrack is fully opened.

[0079] Preferably, in step S52, the confining pressure σ3 in the tension damage model under the three-dimensional direct impact loading is ≤P. When the confining pressure σ3 is maintained at a threshold value P or lower, the dynamic failure of the rock manifests as a tension failure mode.

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

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

[0082] 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 initiation stress σ ci , peak stress σ p , crack closure stress σ cc , crack damage stress σ cd ;

[0083] S12, according to the medium and high confining pressure σ p -σ3 linear fitting plot slope, CCNBD splitting experiment, σ ci -σ3 linear fitting graph, and 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 specimen, b is the length of the initial oblique crack of the rock specimen, and θ0 is the inclination angle of the initial oblique crack of the rock specimen;

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

[0085] S13, parameters μ, K determined based on S12 IC , b, θ0, calculated based on the crack initiation stress equal to the crack initialization stress of the wing crack growth model under uniaxial compression, the parameters λ included in the tension damage model under quasi-static loading are obtained, λ is the crack length correction parameter;

[0086] S14, parameters μ, K determined based on S12 and S13 IC , b, θ0, λ, calculated based on the strength of the wing crack growth model under uniaxial compression being 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 the density ρ of the rock sample, the Rayleigh wave velocity v is determined by formula (4): r ;

[0088]

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

[0090] S121, according to the σ under medium and high confining pressure p -σ3 linear fitting graph slope k1 and combined Determine the internal friction angle of a rock specimen according to Determine the friction coefficient μ, σ of the rock sample p is the peak stress;

[0091] S122. Determine the peak load P based on the load-displacement curve of the CCNBD specimen under compression load. max and through K IC =f(P max ) Calculate K IC ;

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

[0093] It can be understood that the CCNBD cracking test refers to a cracked chevron notched Brazilian disc cracking test.

[0094] In some preferred embodiments, S13 specifically includes the following steps: according to the wing crack growth model, the crack initiation stress is equal to the crack initialization stress during uniaxial compression, and formula (5) is derived:

[0095]

[0096] In formula (5), σ ci-I is the crack initialization stress obtained from the uniaxial test, μ is the friction coefficient of the rock sample, b is the length of the initial oblique crack of the rock sample, θ0 is the inclination angle of the initial oblique crack of the rock sample, and the parameters μ, K determined based on the experimental data obtained from the uniaxial and triaxial tests and CCNBD experiments described in S1 are IC Substitute , b, and θ0 into formula (5) to calculate the value of λ.

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

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

[0099]

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

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

[0102] The strength characteristics include the maximum value σ of the axial stress σ1 max That is, the dynamic strength of the rock, the axial stress σ1 value when the wing crack extension length L=0 is the dynamic crack initialization stress; the wing crack extension length characteristics include σ max The corresponding L value is the critical wing crack extension length.

[0103] The applications also include research on the damage and crushing laws of ores under impact loads, and research on the crushing / comminution laws of ores in grinding processes.

[0104] The technical solution of the present invention is 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, comprising the following steps:

[0107] S1. Based on the interaction between multiple cracks and the superposition principle, a wing crack growth model is obtained when the initial oblique crack is fully opened under quasi-static loading. Based on the wing crack growth model, combined with uniaxial and triaxial tests and CCNBD experiments, a tensile damage model under quasi-static loading is obtained, namely, 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; σ1 is the axial stress, σ3 is the confining pressure, and L is the wing crack propagation length. The specific steps include:

[0108] S10. Based on the interaction between multiple cracks and the superposition principle, the wing crack propagation model when the initial oblique crack is fully opened under quasi-static loading is obtained, which is expressed as formula (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 carried out under room 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 and circumferential strain gauges, respectively. During uniaxial loading, the specimen was placed in a suitable position and loaded until macroscopic fractures occurred in the rock specimen. During conventional triaxial loading, the axial stress and confining pressure were first loaded to the target hydrostatic stress state at a loading rate of 1 MPa / min, and then loaded at an axial strain rate of 0.02 mm / min until a macroscopic fracture surface was generated in the rock specimen. Acoustic emission signals were simultaneously collected during this process.

[0111] The rock sample used in this test was a yellow sandstone sample. The yellow sandstone sample was cylindrical and primarily composed of quartz, accounting for 70% of the mineral particles. The percentages of plagioclase, microcline, chlorite, dolomite, ankerite, calcite, and muscovite were 11%, 8%, 3%, 2%, 2%, 2%, and 2%, respectively. The mineral crystallinity was 89%. The basic physical parameters and loading confining pressure of the yellow sandstone sample are shown in Table 1.

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

[0113]

[0114] Through the above uniaxial loading and conventional triaxial loading tests, the experimental data of the yellow sandstone specimens were obtained, including the stress-strain curves under different confining pressures σ3 (such as Figure 1 ), the material characteristic parameters including elastic modulus E and Poisson's ratio α (see Table 2 below), characteristic stress during loading; the characteristic stress includes: 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] Where, the peak stress σ pThe magnitude of can be directly obtained from the stress-strain curve, while the other characteristic stresses need to be obtained indirectly by calculating the volume strain and the crack volume strain. For brittle rocks, the volume strain reflects the ratio of the total volume change in the rock to the total volume. The crack volume strain is equal to the inelastic volume strain of the rock during loading, and its magnitude is equal to the volume strain of the rock minus the elastic volume strain. The calculation formula is shown in the following formula (8):

[0118]

[0119] In formula (8), ε axial is the axial strain, ε lateral is the hoop strain, ε V is the volume strain, is the elastic body strain, is the inelastic body strain, i.e. the crack body strain, σ1 is the axial stress, σ3 is the confining pressure, E is the elastic modulus, and α is the Poisson’s ratio;

[0120] According to the method of determining rock volume strain and crack volume strain according to formula (8) and combining Figure 1 The stress and strain data of the sandstone specimen in Table 1 are taken as an example. The specimen is loaded uniaxially (i.e., specimen S1 in Table 1) and has a confining pressure of 20 MPa (i.e., specimen S6 in Table 1). The calculation results are as follows: Figure 2 and Figure 3 The characteristic stresses of the remaining six specimens (i.e., S2-S5 and S7-S8) can be obtained using a similar method.

[0121] S12, according to the medium and high confining pressure σ p -σ3 linear fitting plot slope, CCNBD splitting experiment, σ ci -σ3The slope and intercept of the linear fitting graph are used to determine the wing crack growth model including b and θ0 and other parameters K when the initial oblique crack is fully opened under the quasi-static loading. IC , μ; 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; S12 specifically includes the following steps:

[0122] S121, according to the peak stress σ under different confining pressures obtained in S11 p , obtained by data fitting as Figure 4 The σ shown p -σ3 relationship curve, from Figure 4 It can be seen that the linear fit is good when the confining pressure is 15MPa, 20MPa, 25MPa and 30MPa. According to the σ under medium and high confining pressure (i.e., confining pressure σ3 ≥ 15MPa), p-σ3 linear fitting graph slope k1 = 3.22 and combined Determining the internal friction angle of sandstone specimens according to The friction coefficient of the sandstone specimen 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 compression load. max and through K IC =f(P max ) Calculate K IC =0.38MPa·m 1 / 2 ;K IC =f(P max The specific calculation formula of ) is formula (9):

[0124]

[0125] In formula (9), P max is the peak load of the CCNBD specimen, B is the thickness of the Brazilian disc specimen, R is the radius of the Brazilian disc specimen, and according to the method recommended by the International Society of Rock Mechanics (ISRM), four dimensionless constants are defined to characterize the geometric dimensions of the rock, namely a0, a1, a B 、a s ; u and ω in formula (9) can be obtained by using a0 and a B The values ​​are obtained by linear interpolation calculation;

[0126]

[0127] S123, based on the crack initialization stress σ under different confining pressures obtained in S11 ci , obtained by data fitting as Figure 5 As shown ci -σ3 relationship curve and its slope k2=3.2113 and intercept d2=39.799, combined with and The initial oblique crack length of the sandstone specimen is calculated to be b = 3.3 × 10 -4 m and the initial oblique crack inclination angle θ0 = 65.36°.

[0128] S13, the crack initiation stress under confining pressure σ3 = 0 included in the experimental data of S11, that is, σ under uniaxial compression 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 obtain λ = 0.05.

[0129] S14, according to formula (6), based on the determined λ = 0.05 and other parameters μ = 0.62, b = 3.3 × 10 -4 m and θ0=65.36°, K IC =0.38MPa·m 1 / 2 , draw the curve of L changing with σ1 for different w values. 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 We get w = 2.4 × 10 -3 The peak axial stress σ at m p,t =90MPa; based on the corresponding σ of different w values p,t , we get σ p,t -w fitting graph, see Figure 7 ;

[0130] Furthermore, based on the stress-strain curve 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 is obtained p,exp =68MPa; from Figure 7 The σ shown p,t -w fitting graph, find σ p,t =σ p,exp =68MPa, the corresponding abscissa value is the crack spacing w=1.6×10 -3 m.

[0131] S15, the elastic modulus E and Poisson's ratio α listed in Table 2 obtained in S11, combined with the density of the sandstone sample ρ = 2.30 g / cm 3 , using formula (4), determine the Rayleigh wave velocity v corresponding to samples S1-S8 under different confining pressures r .

[0132] Based on the expression (7) of the wing crack growth 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, introducing a first correction factor k1(v) and a second correction factor k2(v) to correct the tensile damage model under quasi-static loading, and obtaining 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 device to obtain the stress-strain curves of the sandstone specimen at different strain rates, such as Figure 8 As shown in the figure, the morphology of the sandstone specimens after failure at three strain rates is as follows: Figure 9 As shown;

[0137] from Figure 8 The peak strength σ at different strain rates is obtained p That is, the measured strength. According to 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, the theoretical strength under different strain rates corresponding to the measured strength is found using MATLAB software. The value of is fitted The power function relationship of Figure 10 As shown,

[0138] S4. According to formula (3) and setting the confining pressure σ3 = 0, we get formula (13),

[0139]

[0140] Using MATLAB software, the part on the right side of equation (13) containing variables is The wing crack extension length L corresponding to the maximum value of axial stress σ1 is obtained by data fitting i , according to the time t corresponding to the peak strength of the rock measured in the one-dimensional direct impact test described in S3 i ,according to The average crack growth rate Further combined with the Rayleigh wave velocity v corresponding to samples S1-S8 under different confining pressures determined by S15 r , k1(v) and k2(v) are obtained according to equations (1) and (2). The values ​​of k1(v) and k2(v) obtained in this embodiment are very close to 1. This is because w=1.6×10 -3 m is small, and the average crack growth rate Compared with Ruili, the wave speed is much smaller.

[0141] The present invention introduces a correction factor to improve the universality and accuracy of the model, especially when the spacing w between wing cracks is large, to ensure 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 k1(v)=1, k2(v)=1 and different strain rates determined by S3 and S4 The tensile damage model for predicting the failure mechanism of sandstone under direct impact loading is constructed by taking values ​​of

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

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

[0145] The SHPB experimental device was used to conduct a three-dimensional direct impact test on a disc-shaped specimen with a diameter of 50 mm and a thickness of 25 mm. Figure 13 (σ3=5MPa) and Figure 16 (strain rate = 170 / s) stress-strain curve.

[0146] Will Figure 12 The dynamic strength of sandstone under dynamic triaxial impact loading (different strain rates) is derived from the microscopic tensile damage model under three-dimensional direct impact loading. Figure 13 The measured intensity is compared with that in Figure 14 shown; from Figure 14 It can be seen that both the dynamic triaxial strength values ​​measured in the experiment and predicted by the mesoscopic tensile damage model reflect that the dynamic strength of the sandstone specimen increases with increasing strain rate when the confining pressure is maintained at 5 MPa. This demonstrates that the mesoscopic tensile damage model under direct impact loading, constructed using the method of the present invention, can accurately predict the variation of rock strength under direct impact loading with dynamic strain rate. Furthermore, the model-predicted strength is slightly lower than the measured strength, providing an additional safety margin, helping to reduce risk and thus ensuring the safety and reliability of rock mass engineering.

[0147] Will Figure 15 The dynamic strength of sandstone under dynamic triaxial impact load (with different confining pressures) is derived from the microscopic tensile damage model under three-dimensional direct impact loading. Figure 16 The measured intensity is compared with that in Figure 17 shown; from Figure 17 It can be seen that both the predictions from the mesoscopic tensile damage model and the experimental measurements indicate that the dynamic strength of sandstone specimens increases significantly with increasing confining pressure. This demonstrates that the mesoscopic tensile damage model for direct impact loading, constructed using the method of the present invention, can accurately predict the strength variation of rock under direct impact loading with confining pressure. Furthermore, the model-predicted strength is slightly lower than the measured strength, providing an additional safety margin, helping to reduce risk and thus ensuring the safety and reliability of rock mass engineering.

[0148] This embodiment also provides an 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) According to the tensile damage model under one-dimensional and / or three-dimensional direct impact loading described in S5, the evolution law of the wing crack extension length L with the axial stress σ1 under different dynamic load strain rates and different confining pressures is obtained, as shown in Figure 11 、 Figure 12 and Figure 15 As shown;

[0150] according to Figure 11 , the stress at the beginning of wing crack propagation at high strain rate increases slightly with the increase of strain rate, gradually increasing from 35MPa at strain rate of 83 / s to 48MPa at strain rate of 196 / s;

[0151] according to Figure 12 , when the confining pressure is 5MPa, the crack initiation stress of the sandstone specimen gradually increases with the increase of strain rate: when the strain rate is 98 / s, the crack initiation stress is 52MPa; when the strain rate is 193 / s, the crack initiation stress is 62MPa;

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

[0153] (b) Obtaining strength characteristics at different dynamic load strain rates according to the tensile damage model under one-dimensional and / or three-dimensional direct impact loading described in S5; for example, Figure 14 The theoretically predicted strength shown is obtained from Figure 12 The maximum value σ of the axial stress σ1 at different strain rates is shown max In addition, the strength characteristics under different confining pressures are also obtained, such as Figure 17 The theoretically predicted strength shown is obtained from Figure 15 The maximum value σ of the axial stress σ1 under different confining pressures is shown max obtained; in addition, from Figure 11 It can be seen that the nonlinear section of the sandstone σ1-L curve under one-dimensional direct impact loading lasts longer in the J stage, which is consistent with the experimental observations.

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

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

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

[0157] Based on the comparison and analysis of the above-mentioned model prediction results and experimental results provided in this embodiment, it is further verified that the microscopic 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 rock under direct impact loading, which helps to more accurately reveal the quantitative change law of rock damage under direct impact loading and the key factors affecting the damage process and strength of rock, such as dynamic load strain rate and confining pressure.

[0158] The above description is only a preferred specific 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 thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by 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 between multiple cracks and the superposition principle, a wing crack growth model is obtained when the initial oblique crack is fully opened under quasi-static loading. Based on the wing crack growth model, combined with uniaxial and triaxial tests and CCNBD experiments, a tensile damage model under quasi-static loading is obtained, namely, 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, axial stress σ1, confining pressure σ3, and 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 for the tensile damage model under direct impact loading; Wherein, k1(v) is used to correct the term related to the concentrated force on the crack in S1, and k2(v) is used to correct the term related to the far-field compressive stress 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 the average crack growth rate is 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; 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 to a series of point values, and different At different strain rates The variation curve of σ1-L is obtained from it, and the theoretical strength is found to be 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 numerical calculation software fitting. 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 experimental data obtained from the uniaxial and triaxial tests and CCNBD experiments described in S1 and the data determined in S3 and S4 By taking the 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 three-dimensional tensile damage model under 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 in the tension damage model under the three-dimensional direct impact loading is ≤P. When the confining pressure σ3 is maintained at a threshold value P or lower, the dynamic failure of the rock is manifested in 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, and the 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 initiation stress σ ci , peak stress σ p ; S12, according to the medium and high confining pressure σ p -σ3 linear fitting plot slope, CCNBD splitting experiment, σ ci -σ3 linear fitting graph, and 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 specimen, b is the length of the initial oblique crack of the rock specimen, and θ0 is the inclination angle of the initial oblique crack of the rock specimen; S13, parameters μ, K determined based on S12 IC , b, θ0, according to the calculation that the crack initiation stress of the wing crack growth model under uniaxial compression is equal to the crack initialization stress, the parameter λ included in the tension damage model under quasi-static loading is obtained, and λ is the crack length correction parameter.

8. The construction method according to claim 7, characterized in that: Step S1 further 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 growth model under uniaxial compression is equal to the experimental uniaxial compressive strength, the parameters w included in the tension damage model under quasi-static loading are obtained, where w is the crack spacing.

9. The construction method according to claim 8, characterized in that: Step S1 further 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 formula (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, wherein the application includes studying the damage and crushing laws of ore under impact load and studying the crushing / comminution laws of ore in grinding process.

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