Construction method and application of rock crushing damage model

Abstract

The invention relates to a construction method and application of a rock crushing damage model, and belongs to the field of rock mass engineering. The problem that at least one of the quantitative change rules of damage under dynamic and static combined loading is difficult to reveal due to the fact that accuracy and reliability are insufficient when an existing rock damage model predicts the evolution rule and / or strength of macroscopic damage under dynamic and static combined loading is solved. The construction method comprises the following steps: S1, obtaining a tension damage model under quasi-static loading; s2, introducing a correction factor for correction; and S3, constructing a rock tension damage model under dynamic and static combined loading. According to the method, the dynamic tension damage evolution model under the dynamic and static combined loading condition is positively performed through mesoscopic tension crack propagation, so that the accuracy and reliability of the rock damage model in predicting the strength and / or evolution law of the rock under the dynamic and static combined loading are enhanced; the quantitative change rule of damage of the rock under dynamic and static combined loading and key factors influencing the rock damage process and strength are accurately disclosed.

Description

Technical Field

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

[0002] Rock is a non-homogeneous natural geological material with numerous natural micro-defects inside. During the construction and operation phase of rock engineering and mine engineering, it is often faced with complex loading paths. It is not only subjected to quasi-static loads, but also often in a dynamic load state. Therefore, studying the evolution of rock damage and fracture under the combined action of in-situ stress and dynamic disturbance (i.e., combined dynamic and static loading) helps to correctly understand the failure mechanism of rock, which is extremely important for the safe construction and disaster prediction of rock engineering and mine engineering. From the perspective of indoor rock mechanics, the effect of rock under the combined action of in-situ stress and dynamic disturbance can be abstracted as an impact test study of rock at different high strain rates.

[0003] At present, most of the research on rock damage and fracture under dynamic and static combined loading summarizes the changing law of rock strength from experimental phenomena, or inverts the rock damage model through the dynamic stress-strain curve of rock in the experiment. However, these models are often difficult to accurately reflect the damage process of rock in practical applications, especially when predicting the strength of rock and the evolution law of macroscopic damage under the more complex action of dynamic and static combination. These models face the problem of insufficient accuracy and reliability, and it is difficult to reveal the quantitative change law of rock under dynamic and static combined loading and the key factors affecting the damage process and strength of rock. Summary of the invention

[0004] In view of the above analysis, the present invention aims to provide a method for constructing a rock crushing damage model and its application, so as to solve at least one of the following problems existing in the existing rock damage models: (1) the accuracy and reliability of predicting the evolution law of macroscopic damage and destruction of rocks under combined dynamic and static loading are insufficient; (2) the accuracy and reliability of predicting the strength of rocks under combined dynamic and static loading are insufficient; (3) it is difficult to reveal the quantitative change law of damage and destruction of rocks under combined dynamic and static loading and the key factors affecting the damage process and strength of rocks.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] The present invention provides a method for constructing a rock damage model, comprising the following steps:

[0007] S1. Based on the interaction between multiple cracks and the superposition principle, a wing crack growth model when the initial oblique crack is closed under quasi-static loading is obtained; 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, that is, formula (1):

[0008] K IC =K I =f(σ1,σ3,L) (1)

[0009] Among them, K IC is the quasi-static fracture toughness, K I is the stress intensity factor value of the wing crack tip under static load, f is a polynomial function, σ1 is the axial stress, σ3 is the confining pressure, and L is the wing crack extension length;

[0010] S2. By introducing a correction factor k(v) related to the crack growth rate, each term in the polynomial function described in S1 is corrected to obtain formula (2):

[0011] K Id =f'(σ1,σ3,L) (2)

[0012] Further introduction of correction factor After correction, we get formula (3):

[0013]

[0014] In formulas (2) and (3), K Id is the stress intensity factor value of the wing crack tip under dynamic load, and the damage variable β is the ratio of the crack body strain after crack initialization to the crack body strain at the peak strength of the rock;

[0015] S3. Based on formula (3), a rock tension damage model under dynamic and static combined loading is constructed. The rock tension damage model under dynamic and static combined loading is a constitutive model between the axial stress σ1 of the rock and the tension damage represented by the wing crack extension length L.

[0016] Further, the expression of formula (3) is formula (4):

[0017]

[0018] In formula (4), λ is the crack length correction parameter, w is the crack spacing, μ is the friction coefficient of the rock sample, b is the initial oblique crack length of the rock sample, θ0 is the inclination angle of the initial oblique crack of the rock sample; v r is the Rayleigh wave velocity, v is the crack growth rate, v is set to a constant value and is the average crack growth rate from the beginning of the crack to the maximum value of the axial stress replace.

[0019] Further, step S3 includes:

[0020] S31, when σ as =σ cc Or as =σ ci When , based on formula (4) and setting σ3=0 and β=0, the one-dimensional dynamic and static combined loading represented by equation (5) is constructed and σ as =σ cc Or as =σ ci Tensile damage model when ;

[0021]

[0022] Among them, σ as is the pre-applied axial static load, σ cc is the crack closure stress under quasi-static conditions, σ ci is the crack initialization stress under quasi-static conditions, is the dynamic fracture toughness of rock.

[0023] Further, step S3 also includes:

[0024] S32, when 0<σ as <σ cc When, according to formula (6) and combined The peak strength of the constitutive model of σ1-L under the condition of σ3=0 is used to determine the axial static load σ as =0 when the one-dimensional direct impact theoretical strength σ 11m According to the peak strength of the tensile damage model, i.e., the constitutive model of σ1-L, expressed in equation (5), the axial static load σ is determined as =σ cc Theoretical dynamic and static combined impact strength σ 12m ;

[0025]

[0026] σ 1m =(σ 12m -σ 11m )η+σ 11m (7)

[0027] According to formula (7) and combined with the determined σ 11m and σ 12m , obtain one-dimensional dynamic and static combined loading and 0<σ as <σ cc Theoretical dynamic and static combined impact strength σ 1m; The crack closure coefficient η is the ratio of the crack closure volume to the crack opening volume in the initial state.

[0028] Further, step S3 also includes:

[0029] S33. When σ as >σ ci When , based on formula (4) and setting When σ3 = 0, the one-dimensional dynamic and static combined loading represented by equation (8) is constructed and σ as >σ ci Tensile damage model when ;

[0030]

[0031] Further, step S3 also includes:

[0032] S34. When σ as =σ cc Or as =σ ci When , based on formula (4) and setting When β = 0 and σ3 is a constant, the three-dimensional dynamic and static combined loading represented by equation (9) is constructed and σ as =σ cc Or as =σ ci Tensile damage model when ;

[0033]

[0034] Furthermore, the step S3 further includes:

[0035] S35, when 0<σ as <σ cc When the confining pressure is constant, according to formula (6) and combined with The peak strength of the constitutive model of σ1-L under the condition is determined by the axial static load σ as = 0 when the three-dimensional direct impact theoretical strength σ 31m According to the tensile damage model expressed by formula (9), i.e., the peak strength of the constitutive model of σ1-L under a constant confining pressure, the axial static load σ as =σ cc Theoretical dynamic and static combined impact strength σ 32m ;

[0036]

[0037] According to formula (10) and combined with the determined σ 31m and σ 32m , obtain the three-dimensional dynamic and static combined loading and 0<σ as <σ ccTheoretical dynamic and static combined impact strength σ 3m .

[0038] Furthermore, the step S3 further includes:

[0039] S36, when σ as >σ ci When , based on formula (4) and setting When σ3 is a constant, the three-dimensional dynamic and static combined loading represented by formula (11) is constructed and σ as >σ ci Tensile damage model when ;

[0040]

[0041] Further, the step S1 comprises:

[0042] S11. Obtaining experimental data of the rock sample through uniaxial loading and conventional triaxial loading tests, including stress-strain curves and material characteristic parameters under different confining pressures σ3, wherein the material characteristic parameters include elastic modulus E and Poisson's ratio α of the rock sample;

[0043] S12, according to formula (12) and in combination with the stress-strain curve in step S11, as well as the elastic modulus E and the Poisson's ratio α, a curve of the relationship between the crack body strain and the axial strain under different confining pressures σ3 is obtained;

[0044]

[0045] In formula (12), ε axial is the axial strain, ε lateral is the hoop strain, ε V is the body strain, is the elastic body strain, is the inelastic body strain, i.e. the crack body strain, E is the elastic modulus of the rock sample, and α is the Poisson’s ratio of the rock sample;

[0046] S13, according to the axial static load σ pre-applied in the dynamic and static combined loading as and confining pressure σ bs , and accordingly, the values ​​of the damage variable β and / or the crack closure coefficient η are obtained from the relationship curve between the crack body strain and the axial strain under different confining pressures σ3.

[0047] The present invention also provides the application of the rock damage model obtained by the construction method described above in geotechnical engineering.

[0048] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0049] (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 dynamic and static combined loading conditions by micro-observing the extension of tensile cracks; specifically, by innovatively introducing correction factors related to the crack extension rate v and the damage variable β, the relevant items of the tensile damage model applicable to the quasi-static loading when the initial oblique crack is closed are appropriately corrected, ensuring that the constructed dynamic tensile damage evolution model can more accurately reflect the damage process of rock under dynamic and static combined loading, thereby enhancing the accuracy, reliability and stability of the rock damage model in predicting the strength of rock under dynamic and static combined loading.

[0050] (2) The present invention performs a dynamic tensile damage evolution model of rock under dynamic and static combined loading conditions by micro-observing the extension of tensile cracks, and combines appropriate correction factors to significantly improve the accuracy and reliability of the rock damage model in predicting the macroscopic damage evolution law of rock under dynamic and static combined loading.

[0051] (3) Based on the dynamic tensile damage evolution model of rock under dynamic and static combined loading conditions, which is performed by microscopic tensile crack expansion, and combined with appropriate correction factors, the accuracy and reliability of the macroscopic damage evolution law and strength prediction of rock under dynamic and static combined loading are significantly improved, thereby accurately revealing the quantitative change law of rock damage under dynamic and static combined loading and the key factors affecting the damage process and strength of rock.

[0052] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The 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 components throughout the drawings.

[0054] 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;

[0055] Figure 2 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 0 in the method provided in an embodiment of the present invention;

[0056] Figure 3A 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;

[0057] Figure 4 A curve showing the relationship between the peak stress and the confining pressure of a yellow sandstone sample under different confining pressures in the method provided in an embodiment of the present invention;

[0058] Figure 5 A curve showing the relationship between crack initialization stress and confining pressure of a yellow sandstone sample under different confining pressures in the method provided in an embodiment of the present invention;

[0059] Figure 6 A curve showing the relationship between crack closure stress and confining pressure of a yellow sandstone sample under different confining pressures in the method provided in an embodiment of the present invention;

[0060] Figure 7 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-L at m;

[0061] Figure 8 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;

[0062] Fig. 9 The stress-strain curves of the sandstone sample at different strain rates under one-dimensional dynamic load impact in the method provided in the embodiment of the present invention;

[0063] Fig.10 The morphological diagram of the sandstone sample after being destroyed at different impact strain rates in the method provided in the embodiment of the present invention;

[0064] Fig.11 A power function fitting diagram of dynamic fracture toughness versus strain rate provided by an embodiment of the present invention;

[0065] Fig.12 The method provided in the embodiment of the present invention is subjected to one-dimensional dynamic and static combined loading (σ as =σ ci =39MPa) Variation curve of σ1-L at different strain rates;

[0066] Fig.13 The method provided in the embodiment of the present invention is subjected to one-dimensional dynamic and static combined loading (σ as =σ ci =39MPa) stress-strain curves of sandstone at different strain rates;

[0067] Fig.14The stress-strain curves of sandstone under different axial static loads under one-dimensional dynamic and static combined loading in the method provided in the embodiment of the present invention (strain rate is 120 / s);

[0068] Fig.15 A result comparison diagram of the model predicted strength and actual strength of sandstone under different axial static loads under one-dimensional dynamic and static combined loading in the method provided in an embodiment of the present invention;

[0069] Fig.16 The morphological diagram of the sandstone sample after failure after one-dimensional dynamic and static combined loading in the method provided in the embodiment of the present invention (strain rate is 120 / s), (a) is axial static load = 5MPa, (b) is axial static load = 25MPa, (a) is axial static load = 50MPa;

[0070] Fig.17 The method provided in the embodiment of the present invention is subjected to three-dimensional dynamic and static combined loading (σ as =σ ci , strain rate is 170 / s) and the variation curve of σ1-L under different confining pressures;

[0071] Fig.18 The dynamic stress-strain curve (σ) of sandstone under different confining pressure conditions under three-dimensional dynamic and static combined loading in the method provided in the embodiment of the present invention as =σ ci , strain rate is 170 / s);

[0072] Fig.19 A comparison diagram of the theoretical predicted strength and the measured strength of sandstone at different confining pressures under three-dimensional dynamic and static combined loading in the method provided in an embodiment of the present invention (strain rate is 170 / s);

[0073] Fig. 20 Dynamic stress-strain curves of sandstone under different axial static loads under three-dimensional dynamic and static combined loading in the method provided in an embodiment of the present invention (confining pressure = 5 MPa, strain rate 170 / s);

[0074] Fig.21 This is a comparison chart of the theoretical predicted strength results and the measured strength results of sandstone under different axial static loads under three-dimensional dynamic and static combined loading in the method provided in an embodiment of the present invention (confining pressure = 5 MPa, strain rate 170 / s). DETAILED DESCRIPTION

[0075] The preferred embodiments of the present invention are 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, but are not used to limit the scope of the present invention.

[0076] After in-depth research, the inventors of the present invention found that the existing rock damage models under dynamic and static combined loading obtained by inversion of experimental data have the following limitations: (1) Most of them ignore the opening and closing states of the initial cracks, and different initial crack states will directly affect the accuracy and reliability of the model prediction results; (2) Most of the existing damage models summarize the change law of rock strength from experimental phenomena, but ignore the tensile properties of damage under dynamic and static combined loading, and the determination methods of some model parameters are not reasonable; these problems lead to the existing models in predicting the strength and damage evolution law of rocks under more complex loading conditions such as dynamic and static combination. The model is not accurate and reliable enough, and it is difficult to reveal the quantitative change law of rock damage under dynamic and static combined loading and the key factors affecting the rock damage process and strength. Therefore, an innovative construction method is needed to overcome the above limitations of the existing models, so as to improve the model's prediction ability and explanatory power for rock damage under dynamic and static combined loading.

[0077] Based on this, the present invention provides a method for constructing a rock damage model, comprising the following steps:

[0078] S1. Based on the interaction between multiple cracks and the superposition principle, a wing crack growth model when the initial oblique crack is closed under quasi-static loading is obtained; 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, that is, formula (1):

[0079] K IC =K I =f(σ1,σ3,L) (1)

[0080] Among them, K IC is the quasi-static fracture toughness, K I is the stress intensity factor value of the wing crack tip under static load, f is a polynomial function, σ1 is the axial stress, σ3 is the confining pressure, and L is the wing crack extension length;

[0081] S2. By introducing a correction factor k(v) related to the crack growth rate, each item in the polynomial function in S1 is corrected to obtain formula (2):

[0082] K Id =f'(σ1,σ3,L) (2)

[0083] Further introduction of correction factor After correction, we get formula (3):

[0084]

[0085] In formulas (2) and (3), K Idis the stress intensity factor value of the wing crack tip under dynamic load, and the damage variable β is the ratio of the crack body strain after crack initialization to the crack body strain at the peak strength of the rock;

[0086] S3. Based on formula (3), a rock tension damage model under dynamic and static combined loading is constructed. The rock tension damage model under dynamic and static combined loading is a constitutive model between the axial stress σ1 of the rock and the tension damage represented by the wing crack extension length L.

[0087] Compared with the prior art, 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 dynamic and static combined loading conditions by micro-observing the extension of tensile cracks; specifically, by innovatively introducing correction factors related to the crack extension rate v and the damage variable β, the relevant items of the tensile damage model applicable to the quasi-static loading when the initial oblique crack is closed are properly corrected to ensure that the constructed dynamic tensile damage evolution model can more accurately reflect the damage process of rock under dynamic and static combined loading, thereby enhancing the accuracy, reliability and stability of the rock damage model in predicting the strength of rock under dynamic and static combined loading.

[0088] The present invention performs a dynamic tensile damage evolution model of rock under dynamic and static combined loading conditions by micro-observing the extension of tensile cracks, and combines appropriate correction factors to significantly improve the accuracy and reliability of the rock damage model in predicting the macroscopic damage evolution law of rock under dynamic and static combined loading.

[0089] Based on the dynamic tensile damage evolution model of rock under dynamic and static combined loading conditions, which is performed by micro-observation of tensile crack propagation, and combined with appropriate correction factors, the accuracy and reliability of the macroscopic damage evolution law and strength prediction of rock under dynamic and static combined loading are significantly improved, thereby being able to more accurately reveal the quantitative change law of rock damage under dynamic and static combined loading and the key factors affecting the damage process and strength of rock.

[0090] Specifically, in step S2, the expression of formula (3) is formula (4):

[0091]

[0092] In formula (4), λ is the crack length correction parameter, w is the crack spacing, μ is the friction coefficient of the rock sample, b is the initial oblique crack length of the rock sample, θ0 is the inclination angle of the initial oblique crack of the rock sample; v r is the Rayleigh wave velocity, v is the crack growth rate, v is set to a constant value and is the average crack growth rate from the beginning of the crack to the maximum value of the axial stress replace.

[0093] It can be understood that when studying the strength and damage evolution law of rocks under combined dynamic and static impacts, not only the influence of dynamic loads but also the influence of initial static loads should be considered. During quasi-static loading, the crack extension of the rock goes through the crack closure stage, linear elastic stage, crack extension stage, etc. For example, when the initial static load is equal to the crack closure stress, the stress intensity factor expression at the tip of the wing crack is completely different from that when the initial static load is equal to 0. Taking into account that the damage evolution process and strength of the rock under combined dynamic and static loading will change with the initial static load, the inventors of the present invention combined the characteristics of different crack extension stages of the rock and conducted a comprehensive analysis. According to the different situations of the relationship between the initial static load and the crack closure stress and the crack initialization stress, some specific implementation methods of constructing the tension damage model under combined dynamic and static loading in step S3 are further given, as follows:

[0094] In some specific preferred implementations, step S3 includes:

[0095] S31, when σ as =σ cc Or as =σ ci When , based on formula (4) and setting σ3=0 and β=0, the one-dimensional dynamic and static combined loading represented by equation (5) is constructed and σ as =σ cc Or as =σ ci Tensile damage model when ;

[0096]

[0097] Among them, σ as is the pre-applied axial static load, σ cc is the crack closure stress under quasi-static conditions, σ ci Initialize stress for a crack in quasi-static conditions.

[0098] S32, when 0<σ as <σ cc When, according to formula (6) and combined The peak strength of the constitutive model of σ1-L under the condition of σ3=0 is used to determine the axial static load σ as =0 when the one-dimensional direct impact theoretical strength σ 11m According to the peak strength of the tensile damage model, i.e., the constitutive model of σ1-L, expressed in equation (5), the axial static load σ is determined as =σ cc Theoretical dynamic and static combined impact strength σ 12m ;

[0099]

[0100] σ 1m =(σ 12m -σ 11m )η+σ 11m (7)

[0101] According to formula (7) and combined with the determined σ 11m and σ 12m , obtain one-dimensional dynamic and static combined loading and 0<σ as <σ cc Theoretical dynamic and static combined impact strength σ 1m ; The crack closure coefficient η is the ratio of the crack closure volume to the crack opening volume in the initial state.

[0102] S33. When σ as >σ ci When , based on formula (4) and setting When σ3 = 0, the one-dimensional dynamic and static combined loading represented by equation (8) is constructed and σ as >σ ci Tensile damage model when ;

[0103]

[0104] S34. When σ as =σ cc Or as =σ ci When , based on formula (4) and setting When β = 0 and σ3 is a constant, the three-dimensional dynamic and static combined loading represented by equation (9) is constructed and σ as =σ cc Or as =σ ci Tensile damage model when ;

[0105]

[0106] S35, when 0<σ as <σ cc When the confining pressure is constant, according to formula (6) and combined with The peak strength of the constitutive model of σ1-L under the condition is determined by the axial static load σ as = 0 when the three-dimensional direct impact theoretical strength σ 31m According to the tensile damage model expressed by formula (9), i.e., the peak strength of the constitutive model of σ1-L under a constant confining pressure, the axial static load σ as =σ cc Theoretical dynamic and static combined impact strength σ 32m ;

[0107]

[0108] According to formula (10) and combined with the determined σ 31m and σ 32m , obtain the three-dimensional dynamic and static combined loading and 0<σ as <σ cc Theoretical dynamic and static combined impact strength σ 3m .

[0109] S36, when σ as >σ ci When , based on formula (4) and setting When σ3 is a constant, the three-dimensional dynamic and static combined loading represented by formula (11) is constructed and σ as >σ ci Tensile damage model when ;

[0110]

[0111] In some preferred embodiments, step S1 specifically includes the following steps:

[0112] S10. Based on the interaction between multiple cracks and the superposition principle, a wing crack propagation model is obtained when the initial oblique crack is closed under quasi-static loading.

[0113] 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, material property parameters, characteristic stresses during loading, and quasi-static fracture toughness K IC ; The material characteristic parameters include the elastic modulus E and Poisson's ratio α of the rock sample;

[0114] The characteristic stresses in the loading process include: crack initiation stress σ ci , peak stress σ p , crack closure stress σ cc , crack damage stress σ cd .

[0115] The material characteristic parameters also include: the internal friction angle of the rock sample The friction coefficient μ, the initial oblique crack length b, and the initial oblique crack inclination angle θ0 are determined by the following steps:

[0116] S111, according to σ under medium and high confining pressure p -σ3 linear fit graph slope k1 and combined Determining the internal friction angle of a rock specimen according to Determine the friction coefficient μ of the rock sample; preferably, the medium-high confining pressure is σ3≥15Mpa.

[0117] S112. Determine the peak load P according to the load-displacement curve of the sample under compression load in the CCNBD splitting test. max , and through K IC =f(P max ) Calculate K IC ;

[0118] S113, according to σ ci -The slope k2 and intercept d2 of the linear fit graph of σ3, combined with and The initial oblique crack length b and the initial oblique crack inclination angle θ0 of the rock sample are calculated and determined.

[0119] It can be understood that the CCNBD cleavage test refers to a Cracked Chevron Notched Brazilian Disc cleavage test.

[0120] S12, according to formula (12) and in combination with the stress-strain curve in step S11, as well as the elastic modulus E and the Poisson's ratio α, obtain a curve of the relationship between the crack volume strain and the axial strain under different confining pressures σ3, and / or a curve of the relationship between the crack volume strain and the axial strain;

[0121]

[0122] In formula (12), ε axial is the axial strain, ε lateral is the hoop strain, ε V is the body strain, is the elastic body strain, is the inelastic body strain, i.e. the crack body strain, E is the elastic modulus of the rock sample, and α is the Poisson's ratio of the rock sample.

[0123] S13, according to the axial static load σ pre-applied in the dynamic and static combined loading as and confining pressure σ bs , and accordingly, the values ​​of the damage variable β and / or the crack closure coefficient η are obtained from the relationship curve between the crack body strain and the axial strain under different confining pressures σ3.

[0124] It should be noted that when σ cc <σ as <σ ci When the crack body strain curve (e.g. Figure 2 or Figure 3 ), we can determine the crack closure coefficient η = 1, that is, the dynamic and static combined strength of the rock remains unchanged, where σ as is the pre-applied axial static load, σ ci is the crack initialization stress under quasi-static conditions, σ ccis the crack closure stress under quasi-static conditions.

[0125] In some preferred embodiments, step S1 specifically further includes the following steps:

[0126] S14, based on the material characteristic parameters determined in S11, and according to the wing crack extension model under uniaxial compression, the crack initiation stress is equal to the crack initialization stress, and the parameter λ included in the tension damage model under quasi-static loading is calculated, where λ is a crack length correction parameter;

[0127] S15, based on the material characteristic parameters determined in S11, and according to the fact that the strength of the wing crack extension model under uniaxial compression is equal to the experimental uniaxial compressive strength, the parameter w included in the tensile damage model under quasi-static loading is calculated, where w is the crack spacing;

[0128] S16, through the material characteristic parameters determined by S11, combined with the density ρ of the rock sample, the Rayleigh wave velocity v is determined by formula (13): r ;

[0129]

[0130] In some preferred embodiments, S14 specifically includes the following steps: according to the wing crack extension model, the crack initiation stress is equal to the crack initialization stress during uniaxial compression, and formula (14) is derived:

[0131]

[0132] In formula (14), 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 initial oblique crack length of the rock sample, θ0 is the inclination angle of the initial oblique crack of the rock sample, and the material characteristic parameters determined by S11, including μ, b, θ0, K IC Substitute into formula (14) and calculate the value of λ.

[0133] In some preferred embodiments, S15 specifically includes the following steps:

[0134] S151, according to the formula (15) derived from the wing crack growth model under uniaxial compression, based on the determined λ and the material characteristic parameters determined by S11 including μ, b, θ0, K IC , draw the variation curves of σ1 and L for different w values, and obtain the axial stress peak σ in each σ1-L variation curve p,t That is, the theoretical uniaxial compressive strength value, based on the σ corresponding to different w values p,t , we get p,t -w fitting graph;

[0135]

[0136] S152. Based on the stress-strain curve of the rock sample under uniaxial compression (σ3=0) in S11, the experimental uniaxial compressive strength value σ of the rock sample is obtained. p,exp ; From the σ p,t -w In the fitting graph, find σ p,t =σ p,exp The corresponding horizontal coordinate point value is the crack spacing w.

[0137] In some specific embodiments, in step S2, the correction factor k(v) related to the crack growth rate includes a first correction factor k1(v) and a second correction factor k2(v), i.e., equation (16) and equation (17), wherein k1(v) is used to correct the term related to the concentrated force borne by the crack in the polynomial function in S1, and k2(v) is used to correct the term related to the far-field compressive stress borne by the crack in the polynomial function in S1;

[0138]

[0139] In formula (16) and formula (17), 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;

[0140] Specifically, the dynamic fracture toughness of the rock The method for determining σ includes the following steps: conducting 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 formula (6) and the formula (18) obtained when the confining pressure σ3 = 0 and k1(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.

[0141]

[0142] In formula (18), 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.

[0143] Specifically, the average crack growth rate The method for determining the first correction factor k1(v) and the second correction factor k2(v) comprises the following steps: According to the right side of formula (5): The wing crack extension length L corresponding to the maximum axial stress σ1 is obtained by numerical calculation software fitting. i ; Combined with the peak strength σ at different strain rates measured in the one-dimensional dynamic and static combined impact test p The corresponding time t i ,according to The average crack growth rate According to equations (16) and (17), the first correction factor k1(v) and the second correction factor k2(v) related to the crack growth rate are determined.

[0144] The present invention also provides an application of the rock damage model obtained by the construction method as described above in geotechnical engineering, the application comprising: obtaining, according to the rock damage model, the evolution law of the wing crack extension length L with the axial stress σ1 under different dynamic load strain rates and / or different confining pressures and / or different static loads, the strength characteristics, and the wing crack extension length characteristics;

[0145] The strength characteristics include: the axial stress σ1 value when the wing crack extension length L=0, i.e., the dynamic crack initialization stress, the maximum value σ of the axial stress σ1 max That is, the dynamic and static combined strength of the rock. The wing crack extension length characteristics include σ max The corresponding L value is the critical wing crack extension length.

[0146] The applications also include research on the damage and crushing laws of ores under combined dynamic and static impact loads, and research on the crushing / grinding laws of ores in grinding processes.

[0147] The technical solution of the present invention is further described in detail below in conjunction with specific embodiments.

[0148] Example 1

[0149] This embodiment provides a method for constructing a rock damage model and its application, comprising the following steps:

[0150] S1. Based on the interaction between multiple cracks and the superposition principle, a wing crack growth model when the initial oblique crack is closed under quasi-static loading is obtained; based on the wing crack growth model, combined with uniaxial and triaxial tests and CCNBD experiments, a tension damage model under quasi-static loading is obtained; S1 specifically includes the following steps:

[0151] S10. Based on the interaction between multiple cracks and the superposition principle, the wing crack propagation model when the initial oblique crack is closed under quasi-static loading is obtained, and its expression is formula (19);

[0152]

[0153] 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 at room temperature. Specifically, the axial strain-controlled loading method was adopted with a loading rate of 0.02 mm per minute. The axial strain and circumferential strain were measured by the axial strain gauge and the circumferential strain gauge, 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 occurred in the rock specimen, and the acoustic emission signal in this process was simultaneously collected.

[0154] The rock sample used in this test is a yellow sandstone sample. The yellow sandstone sample is cylindrical, and its main mineral particles are quartz, with a content percentage of 70%; the content percentages of plagioclase, microcline, chlorite, dolomite, ankerite, calcite, and muscovite are: 11%, 8%, 3%, 2%, 2%, 2%, 2%, and 2%, respectively, and the mineral crystallinity is 89%. The basic physical parameters and loading confining pressure of the yellow sandstone sample are shown in Table 1;

[0155] Table 1 Basic physical parameters, loading and confining pressure settings, and macroscopic failure types of yellow sandstone specimens

[0156]

[0157] 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 ), elastic modulus E and Poisson's ratio α (as shown in Table 2 below) included in the material characteristic parameters, 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 ;

[0158] Table 2 Elastic modulus and Poisson's ratio of yellow sandstone samples under different confining pressures

[0159]

[0160] Where, the peak stress σ p The size of can be directly obtained through the stress-strain curve; 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 size is equal to the volume strain of the rock minus the elastic volume strain. The method of determining the rock volume strain and crack volume strain according to formula (12) and combining Figure 1 The stress-strain data of the sandstone specimens are taken as an example when the specimen is subjected to uniaxial loading (i.e., specimen S1 in Table 1) and the confining pressure is 20 MPa (i.e., specimen S6 in Table 1). The calculation results are as follows: Figure 2 and 3 As shown; the characteristic stresses of the remaining six specimens (i.e., S2-S5 and S7-S8) can be obtained using a similar method.

[0161] Further, the material characteristic parameters also include the internal friction angle of the sandstone sample. The friction coefficient μ, the initial oblique crack length b, and the initial oblique crack inclination angle θ0 are determined by the following steps:

[0162] S111, according to the peak stress σ under different confining pressures obtained in S11 p , we can get the following through data fitting: 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 sample was determined to be μ = 0.62;

[0163] S112. Determine the peak load P according to 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 (20):

[0164]

[0165] In formula (20), Pmax 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 (20) can be obtained by using a0 and a B The numerical value is obtained by linear interpolation calculation;

[0166]

[0167] S113, based on the crack initialization stress σ under different confining pressures obtained in S11 ci , we can get the following through data fitting: 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 sample is calculated to be b = 3.3 × 10 -4 m and the initial oblique crack inclination angle θ0 = 65.36°.

[0168] S12, according to formula (12) and in combination with the stress-strain curve in step S11, as well as the elastic modulus E and the Poisson's ratio α, obtain the relationship curve between the crack volume strain and the axial strain under different confining pressures σ3, and the relationship curve between the volume strain and the axial strain; as Figure 2 and Figure 3 As shown;

[0169] S13, according to the axial static load σ pre-applied in the dynamic and static combined loading as and confining pressure σ bs , the values ​​of damage variable β and / or crack closure coefficient η are obtained from the relationship curve between crack body strain and axial strain under different confining pressures σ3. bs = 0, from Figure 2 In the above example, we find σ as , peak stress σ p The ordinate corresponding to the crack body strain curve and the ratio of the two ordinates are obtained, that is, the confining pressure σ bs = 0 and σ as >σ ci The damage variable β is taken when the axial stress σ1 is equal to σ as The ordinate corresponds to the crack body strain curve, that is, the confining pressure σ bs =0 and 0<σ as <σ cc The value of crack closure coefficient η when ;

[0170] For example, when the confining pressure σ bs =20MPa, from Figure 3 In the above example, we find σ as , peak stress σ p The ordinate corresponding to the crack body strain curve and the ratio of the two ordinates are obtained, that is, the confining pressure σ bs =20MPa and σ as >σ ci The value of the damage variable β at time ; Figure 3 , find that the axial stress σ1 is equal to σ as The ordinate corresponds to the crack body strain curve, that is, the confining pressure σ bs =0 and 0<σ as <σ cc The crack closure coefficient η is taken when the pre-applied confining pressure σ bs Set to other values, similar to σ bs =20MPa method to obtain the values ​​of β and / or η.

[0171] S14, the crack initiation stress under confining pressure = 0, i.e., σ under uniaxial compression, included in the material characteristic parameters determined in S11 ci-I =39MPa(from Figure 2 Get) and K IC =0.38MPa·m 1 / 2 , μ = 0.62, b = 3.3 × 10 -4 Substituting m and θ0=65.36° into equation (14), we obtain λ=0.05.

[0172] S15, according to formula (15), based on the determined λ=0.05 and the material characteristic parameters determined in S11, μ=0.62, b=3.3×10 -4 m and θ0=65.36°, K IC =0.38MPa·m 1 / 2 , plot the curve of L changing with σ1 for different w values. For example, when w = 2.4×10 -3 When m, the variation curve of σ1 and L is as follows Figure 7 As shown, from Figure 7 We get w = 2.4 × 10 -3 The peak axial stress σ at m p,t =90MPa; σ corresponding to different w values p,t , we get p,t -w fitting graph, see Figure 8 ;

[0173] Furthermore, based on the stress-strain curve of the sandstone sample in S11 under uniaxial compression (i.e. Figure 1 and 2 ), and the experimental uniaxial compressive strength value σ of the sandstone sample is obtained p,exp =68MPa; Figure 8 The σ shown p,t -w In the fitting graph, find σ p,t =σ p,exp =68MPa, the corresponding abscissa value is the crack spacing w=1.6×10 -3 m.

[0174] S16, 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 , the Rayleigh wave velocity v corresponding to samples S1-S8 under different confining pressures is determined by formula (13): r .

[0175] Based on the wing crack growth model described in S10, and combined with μ = 0.62, b = 3.3 × 10 -4 m and θ0=65.36°, λ=0.05, w=1.6×10 -3 m, K IC =0.38MPa·m 1 / 2 , the tensile damage model when the initial oblique crack is closed under quasi-static loading is obtained, that is, formula (22):

[0176]

[0177] S2. Introducing the first correction factor k1(v) and the second correction factor k2(v), namely, equations (16) and (17), the tensile damage model when the initial oblique crack is closed under quasi-static loading represented by equation (22) is corrected; the dynamic fracture toughness of the rock is The method for determining k1(v) and k2(v) specifically includes:

[0178] S201. 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 specimens at different strain rates, such as Fig. 9 The morphology of the sandstone specimens after failure at three strain rates is shown in Fig.10 As shown;

[0179] from Fig. 9 The peak strength σ at different strain rates is obtained pThat is, the measured strength. According to the measured strength and combined with formula (18), MATLAB software is used to find the theoretical strength close to the measured strength under different strain rates. The value of is fitted. The power function relationship of Fig.11 As shown,

[0180] S202, using MATLAB software, the right side of equation (5) The wing crack extension length L corresponding to the maximum axial stress σ1 is obtained by data fitting i , combined with the time t corresponding to the rock peak strength measured in the one-dimensional dynamic and static combined impact test 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 S16 r According to equations (16) and (17), k1(v) and k2(v) are obtained. 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 the Rayleigh wave velocity, it is much smaller. The present 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, to ensure that the model expression is more rigorous and more widely applicable.

[0181] Further introduction of correction factor After correction, we get formula (23):

[0182]

[0183] S3. Based on formula (23), a rock tension damage model under dynamic and static combined loading is constructed, which specifically includes the following steps:

[0184] S31, from Figure 2 , Figure 5 and Figure 6 It can be seen that σ under confining pressure of 0 cc =25MPa,σ ci =39MPa, when σ as =25MPa or σ as =39MPa, based on formula (23) and set σ3=0 and β=0, and the one-dimensional dynamic and static combined loading and σ as =25MPa or σ as=39MPa tensile damage model is equation (24), where based on the Determine different strain rates Next Take the value and substitute it into formula (24); based on the different strains determined in S202 Substituting the value of k1(v) under the condition into equation (24), we can obtain the variation law of axial stress σ1-L, as follows: Fig.12 shown.

[0185]

[0186] According to the experimental results, the sandstone specimen has a pre-applied axial stress equal to σ ci = Dynamic stress-strain curve when 39MPa, such as Fig.13 As shown. Fig.12 and Fig.13 The one-dimensional dynamic-static combined strength obtained according to the model prediction results is basically consistent with the one-dimensional dynamic-static combined strength obtained from the experimental results, and both gradually increase with the increase of strain rate.

[0187] S32, when 0<σ as <25MPa, based on the different strains determined in S202 The value of k1(v) under , according to formula (25) and set The peak strength of the constitutive model of σ1-L under σ3=0 is used to determine the axial static load σ as =0 when the one-dimensional direct impact theoretical strength σ 11m According to the tensile damage model expressed by equation (24), i.e., the constitutive model of σ1-L, the axial static load σ is determined as =σ cc =Theoretical dynamic and static combined impact strength σ at 25MPa 12m ;

[0188]

[0189] σ 1m =(σ 12m -σ 11m )η+σ 11m (7)

[0190] According to formula (7) and combined with the determined σ 11m , σ 12m and S13 from Figure 2 σ1=σ obtained from the strain curve of the medium crack body as The value of η under the one-dimensional dynamic and static combined loading is obtained and 0<σ as Theoretical dynamic and static combined impact strength σ when <25MPa 1m ;

[0191] S33. When σ as >σ ci =39MPa, based on formula (23) and set When σ3 = 0, the one-dimensional dynamic and static combined loading represented by equation (26) is constructed and σ as >39MPa tensile damage model; based on the S201 Determine different strain rates Next Take the value and substitute it into formula (26); based on the different strains determined in S202 Substituting the value of k1(v) under the condition into equation (26), the confining pressure σ is determined based on the S13 method. bs = 0 and σ as >σ ci The damage variable β is taken when σ is substituted into formula (26) to obtain the variation curve of axial stress σ1-L. From the peak strength in the variation curve of σ1-L, the damage variable β under one-dimensional dynamic and static combined loading and σ as >σ ci = Theoretical dynamic and static combined impact strength at 39MPa;

[0192]

[0193] When the dynamic strain rate of the sandstone specimen is 120 / s, the stress-strain curves of the sandstone specimen under different axial static load conditions obtained experimentally are as follows: Fig.14 As shown in the figure, the theoretical dynamic and static combined strength of rock derived from the tension damage model under the one-dimensional dynamic and static combined loading obtained in the above steps S31-S33 is similar to Fig.14 The dynamic and static combined strength of rocks obtained in the experiment were compared. The results are as follows: Fig.15 ,from Fig.15 It can be seen that the dynamic and static combined strength predicted by the model is basically consistent with the experimental results, which shows that the rock tension damage model under the one-dimensional dynamic and static combined loading obtained by the construction method provided by the present invention is accurate and reliable for predicting the strength of rock. Fig.16 It can be seen that when the strain rate is 120 / s, the failure mode of the sandstone specimens under different axial static load conditions is tension failure, which also shows that the dynamic tension damage evolution model of rock under dynamic and static combined loading conditions based on the microscopic tension crack extension of the present invention is reasonable.

[0194] S34, from Figure 5 It can be seen that the σ under the confining pressure of 0MPa, 5MPa, 10MPa, and 15MPa is ci =39MPa, 55MPa, 74MPa, 89MPa, for example, the confining pressure is 5MPa and σ as =σci =55MPa, based on formula (23) and set When β=0 and σ3=5MPa, the confining pressure under the three-dimensional dynamic and static combined loading is 5Mpa and σ as =σ ci =55MPa tensile damage model, where the tensile damage model is based on the tensile damage model obtained in S201. Determine different strain rates Next Take the value and substitute it into formula (27); based on the different strains determined in S202 Substituting the values ​​of k1(v) and k2(v) under the condition into equation (27), we can obtain the variation law of axial stress σ1-L, as follows: Fig.17 , which shows the variation law of σ1-L when the strain rate is 170 / s and the confining pressures are 0MPa, 5MPa, 10MPa, and 15MPa respectively and the initial static load = the crack initialization stress under the corresponding confining pressure;

[0195]

[0196] According to the experimental results, when the pre-applied axial static pressure of the sandstone specimen is equal to the static load crack initialization stress under the corresponding confining pressure, the stress-strain curves under different confining pressure conditions are as follows: Fig.18 As shown. Fig.17 Dynamic strength of rock predicted by mesoscopic tensile damage model and Fig.18 The measured intensity is compared with that in Fig.19 As shown, the strain rate is 170 / s. Fig.19 It can be seen that when the axial static pressure is equal to the static load crack initialization stress under the corresponding confining pressure, the theoretically predicted strength and the experimentally measured dynamic-static combined strength values ​​both increase with the increase of the confining pressure, and their values ​​are very close. This shows that the three-dimensional tensile damage model under dynamic-static combined loading obtained by the construction method provided by the present invention is accurate and reliable for predicting the dynamic-static combined strength of rock.

[0197] S35, from Figure 6 It can be seen that when the confining pressure = 5MPa, σ cc =35MPa, when 0<σ as <σ cc =35MPa, based on the different strains determined in S202 The values ​​of k1(v) and k2(v) under the condition are set according to equation (28) The peak strength of the constitutive model of σ1-L under σ3 = 5 MPa is used to determine the axial static load σ as = 0 when the three-dimensional direct impact theoretical strength σ 31mAccording to the tensile damage model expressed in equation (27), i.e., the peak strength of the constitutive model of σ1-L at a confining pressure of σ3 = 5 MPa, the axial static load σ as =σ cc =Theoretical dynamic and static combined impact strength σ at 35MPa 32m ;

[0198]

[0199] σ 3m =(σ 32m -σ 31m )η+σ 31m (10)

[0200] According to formula (10) and combined with the determined σ 31m and σ 32m and σ1=σ obtained from the crack body strain curve under confining pressure σ3=5MPa in S13 as The value of η under the three-dimensional dynamic and static combined loading and 0<σ as <σ cc =Theoretical dynamic and static combined impact strength σ at 35MPa 3m .

[0201] S36, when σ as >σ ci =55MPa, based on formula (23) and set When σ3 = 5 MPa, the three-dimensional dynamic and static combined loading represented by equation (29) is constructed and σ as >σ ci =55MPa tensile damage model; based on the results obtained in S201 Determine different strain rates Next Take the value and substitute it into formula (29); based on the different strains determined in S202 Substituting the values ​​of k1(v) and k2(v) into equation (29), the confining pressure σ is determined based on the S13 method. bs =5MPa and σ as >σ ci The damage variable β is taken when σ is substituted into formula (29) to obtain the variation curve of axial stress σ1-L. The peak strength is determined from the variation curve of σ1-L, and the ... as >σ ci =Theoretical dynamic and static combined impact strength at 55MPa;

[0202]

[0203] In order to further study the influence of different axial static pressures on the three-dimensional dynamic and static combined strength of rock, the confining pressure σ3 = 5MPa and the strain rate are set to 170 / s. The stress-strain curves of the sandstone specimens obtained in the experiment under different axial static pressures are shown in Fig. 20 As shown in FIG. 1 , the theoretical dynamic and static combined strength of rock derived from the tension damage model under the three-dimensional dynamic and static combined loading obtained in the above steps S34-S36 is similar to that in FIG. Fig. 20 The dynamic and static combined strength of rocks obtained in the experiment were compared. The results are as follows: Fig.21 , the strain rate is 170 / s, the confining pressure σ3 is 5MPa, Fig.21 It can be seen that the theoretical prediction strength is consistent with the experimental measured dynamic and static combined strength, and the strength values ​​are relatively consistent. This shows that the three-dimensional dynamic and static combined loading tensile damage model obtained by the construction method provided by the present invention has strong applicability and high reliability for predicting the dynamic and static combined strength of rock.

[0204] This embodiment also provides an application of the rock tension damage model under dynamic and static combined loading obtained by the construction method as described above in geotechnical engineering, and the application includes:

[0205] (a) According to the rock tension damage model under dynamic and static combined loading, the evolution law of the wing crack extension length L with the axial stress σ1 under different dynamic load strain rates, different confining pressures, and different static loads is obtained, as shown in Fig.12 , Fig.17 As shown;

[0206] according to Fig.12 , when the static load is the quasi-static crack initiation stress, the sandstone crack initiation stress under dynamic load conditions gradually increases with the increase of strain rate, from 100MPa at a strain rate of 85 / s to 117MPa at a strain rate of 131 / s;

[0207] according to Fig.17 When the axial static load is the crack initiation stress of quasi-static loading under respective confining pressures, the dynamic crack initiation stress increases slightly with the increase of confining pressure: when the confining pressure is 0MPa, the dynamic crack initiation stress is 180MPa; when the confining pressure is 15MPa, the dynamic crack initiation stress is 197MPa.

[0208] (b) according to the rock tension damage model under the dynamic and static combined loading, the strength characteristics under different dynamic load strain rates, different confining pressures, and different axial static pressures are obtained;

[0209] For example, according to Fig.12When the static load is the quasi-static crack initialization stress, the dynamic-static combined strength of sandstone under one-dimensional dynamic-static combined loading gradually increases with the increase of strain rate, and the dynamic-static combined strength gradually increases from 188MPa at a strain rate of 85 / s to 220MPa at a strain rate of 131 / s. Fig.15 The theoretical prediction values ​​of the combined dynamic and static strength at different axial static pressures were obtained.

[0210] For example, according to Fig.17 , when the axial static load is the crack initialization stress of quasi-static loading under respective confining pressures, the dynamic-static combined strength of sandstone under three-dimensional dynamic-static combined loading gradually increases with the increase of confining pressure. Fig.19 The theoretical prediction values ​​of the combined dynamic and static strength at different confining pressures were obtained. Fig.21 The theoretical prediction values ​​of the combined dynamic and static strength at different axial static pressures were obtained.

[0211] (c) according to the rock tension damage model under the dynamic and static combined loading, the wing crack extension length characteristics under different dynamic load strain rates, different confining pressures, and different axial static pressures are obtained;

[0212] For example, according to Fig.12 When the axial static load is equal to the quasi-static crack initialization stress, the wing cracks under different loading conditions are all extended to a length of 1.25×10 -4 m, the dynamic load peak strength of the rock is reached, that is, the critical wing crack extension length is 1.25×10 -4 m.

[0213] according to Fig.17 When the axial static load is the crack initialization stress of the quasi-static loading under the respective confining pressures, the critical wing crack length when the sandstone reaches the dynamic strength gradually increases with the increase of the confining pressure: when the confining pressure is 0 MPa, the critical wing crack extension length is 1.08×10 -4 m; when the confining pressure is 15 MPa, the critical wing crack extension length is 1.36×10 -4 m.

[0214] Based on the comparison and analysis of the prediction results of the above model provided in this embodiment and the experimental results, 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 evolution law of rock under dynamic and static combined loading conditions, which helps to more accurately reveal the quantitative change law of rock damage and destruction under dynamic and static combined loading conditions and the key factors affecting the damage process and strength of rock, such as dynamic load strain rate, confining pressure, and axial static pressure.

[0215] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for constructing a rock damage model, 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 when the initial oblique crack is closed under quasi-static loading is obtained; 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, that is, formula (1): K IC =K I =f(σ1,σ3,L) (1) Among them, K IC is the quasi-static fracture toughness, K I is the stress intensity factor value of the wing crack tip under static load, f is a polynomial function, σ1 is the axial stress, σ3 is the confining pressure, and L is the wing crack extension length; S2. By introducing a correction factor k(v) related to the crack growth rate, each term in the polynomial function described in S1 is corrected to obtain formula (2): K Id =f'(σ1,σ3,L) (2) Further introduction of correction factor After correction, we get formula (3): In formulas (2) and (3), K Id is the stress intensity factor value of the wing crack tip under dynamic load, and the damage variable β is the ratio of the crack body strain after crack initialization to the crack body strain at the peak strength of the rock; S3. Based on formula (3), a rock tension damage model under dynamic and static combined loading is constructed. The rock tension damage model under dynamic and static combined loading is a constitutive model between the axial stress σ1 of the rock and the tension damage represented by the wing crack extension length L.

2. The construction method according to claim 1, characterized in that: The expression of formula (3) is formula (4): In formula (4), λ is the crack length correction parameter, w is the crack spacing, μ is the friction coefficient of the rock sample, b is the initial oblique crack length of the rock sample, θ0 is the inclination angle of the initial oblique crack of the rock sample; v r is the Rayleigh wave velocity, v is the crack growth rate, v is set to a constant value and is the average crack growth rate from the beginning of the crack to the maximum value of the axial stress replace.

3. The construction method according to claim 2, characterized in that: Step S3 includes: S31, when σ as =σ cc Or as =σ ci When , based on formula (4) and setting σ3=0 and β=0, the one-dimensional dynamic and static combined loading represented by equation (5) is constructed and σ as =σ cc Or as =σ ci Tensile damage model when ; Among them, σ as is the pre-applied axial static load, σ cc is the crack closure stress under quasi-static conditions, σ ci is the crack initialization stress under quasi-static conditions, is the dynamic fracture toughness of rock.

4. The construction method according to claim 3, characterized in that: Step S3 also includes: S32, when 0<σ as <σ cc When, according to formula (6) and combined with The peak strength of the constitutive model of σ1-L under the condition of σ3=0 is used to determine the axial static load σ as =0 when the one-dimensional direct impact theoretical strength σ 11m According to the peak strength of the tensile damage model, i.e., the constitutive model of σ1-L, expressed in equation (5), the axial static load σ is determined. as =σ cc Theoretical dynamic and static combined impact strength σ 12m ; s 1m =(s 12m -s 11m )η+σ 11m (7) According to formula (7) and combined with the determined σ 11m and σ 12m , obtain one-dimensional dynamic and static combined loading and 0<σ as <σ cc Theoretical dynamic and static combined impact strength σ 1m ; The crack closure coefficient η is the ratio of the crack closure volume to the crack opening volume in the initial state.

5. The construction method according to claim 4, characterized in that: Step S3 also includes: S33. When σ as >σ ci When , based on formula (4) and setting When σ3 = 0, the one-dimensional dynamic and static combined loading represented by equation (8) is constructed and σ as >σ ci Tensile damage model when ; 6. The construction method according to claim 5, characterized in that: Step S3 also includes: S34. When σ as =σ cc Or as =σ ci When , based on formula (4) and setting When β = 0 and σ3 is a constant, the three-dimensional dynamic and static combined loading represented by equation (9) is constructed and σ as =σ cc Or as =σ ci Tensile damage model when ; 7. The construction method according to claim 6, characterized in that: The step S3 further comprises: S35, when 0<σ as <σ cc When the confining pressure is constant, according to formula (6) and combined with The peak strength of the constitutive model of σ1-L under the condition is determined by the axial static load σ as = 0 when the three-dimensional direct impact theoretical strength σ 31m According to the tensile damage model expressed by formula (9), i.e., the peak strength of the constitutive model of σ1-L under a constant confining pressure, the axial static load σ as =σ cc Theoretical dynamic and static combined impact strength σ 32m ; s 3m =(s 32m -s 31m )η+σ 31m (10) According to formula (10) and combined with the determined σ 31m and σ 32m , obtain the three-dimensional dynamic and static combined loading and 0<σ as <σ cc Theoretical dynamic and static combined impact strength σ 3m .

8. The construction method according to claim 7, characterized in that: The step S3 further comprises: S36, when σ as >σ ci When , based on formula (4) and setting When σ3 is a constant, the three-dimensional dynamic and static combined loading represented by formula (11) is constructed and σ as >σ ci Tensile damage model when ; 9. The construction method according to claim 1, characterized in that: The step S1 comprises: S11. Obtaining experimental data of the rock sample through uniaxial loading and conventional triaxial loading tests, including stress-strain curves and material characteristic parameters under different confining pressures σ3, wherein the material characteristic parameters include elastic modulus E and Poisson's ratio α of the rock sample; S12, according to formula (12) and in combination with the stress-strain curve in step S11, as well as the elastic modulus E and the Poisson's ratio α, a curve of the relationship between the crack body strain and the axial strain under different confining pressures σ3 is obtained; In formula (12), ε axial is the axial strain, ε lateral is the hoop strain, ε V is the body strain, is the elastic body strain, is the inelastic body strain, i.e. the crack body strain, E is the elastic modulus of the rock sample, and α is the Poisson’s ratio of the rock sample; S13, according to the axial static load σ pre-applied in the dynamic and static combined loading as and confining pressure σ bs , and accordingly, the values ​​of the damage variable β and / or the crack closure coefficient η are obtained from the relationship curve between the crack body strain and the axial strain under different confining pressures σ3.

10. Application of the rock damage model obtained by the construction method according to any one of claims 1 to 9 in geotechnical engineering.

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