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

Abstract

The present invention relates to a method for constructing a rock crushing damage model and its application, belonging to the field of rock engineering, and solves at least one of the problems of existing rock damage models in predicting the macroscopic damage evolution law and / or strength under dynamic and static combined loading, namely, insufficient accuracy and reliability, and difficulty in revealing the quantitative change law of damage and destruction under dynamic and static combined loading. The construction method comprises: S1, obtaining a tension damage model under quasi-static loading; S2, introducing a correction factor for correction; S3, constructing a rock tension damage model under dynamic and static combined loading. The present invention performs a dynamic tension damage evolution model under dynamic and static combined loading conditions by micro-observing the extension of tension cracks, thereby enhancing the accuracy and reliability of the rock damage model in predicting the strength and / or evolution law of rock under dynamic and static combined loading, and accurately revealing the quantitative change law of rock damage and destruction under dynamic and static combined loading, as well as the key factors affecting the rock damage process and strength.

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 and application thereof. Background Art

[0002] Rock is a heterogeneous natural geological material with numerous natural micro-defects. During the construction and operation phases of rock and mine engineering, rock is often subjected to complex loading paths, not only to quasi-static loads but also to dynamic loads. Therefore, studying the evolution of rock damage and fracture under the combined action of in-situ stress and dynamic disturbance (i.e., combined static and dynamic loading) helps to correctly understand the failure mechanism of rock and is extremely important for the safe construction and disaster prediction of rock and mine engineering. From the perspective of indoor rock mechanics, the effects of rock under the combined action of in-situ stress and dynamic disturbance can be abstracted into impact tests of rock at different high strain rates.

[0003] At present, most of the research on the damage and fracture of rocks under combined dynamic and static loading has summarized the variation law of rock strength from experimental phenomena, or inverted the rock damage model by the dynamic stress-strain curve of the rock in the experiment. However, these models are often difficult to accurately reflect the damage process of rocks in practical applications. In particular, when predicting the strength of rocks and the evolution law of macroscopic damage under the more complex action of combined dynamic and static loading, these models all face the problem of insufficient accuracy and reliability. It is also difficult to reveal the quantitative variation law of rocks under combined dynamic and static loading and the key factors affecting the damage process and strength of rocks. 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 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 combined dynamic and static loading; (2) insufficient accuracy and reliability in predicting the strength of rocks under combined dynamic and static loading; and (3) difficulty in revealing the quantitative variation 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 purpose 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 is obtained when the initial oblique crack is closed 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, Equation (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 propagation 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 factors 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 loading, 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] Furthermore, 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 initial oblique crack inclination angle 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 σ 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 formula (5) is constructed and σ as =σ cc or σ 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] Furthermore, step S3 further 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, 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] Furthermore, step S3 further 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 formula (8) is constructed and σ as >σ ci Tensile damage model when ;

[0030]

[0031] Furthermore, step S3 further includes:

[0032] S34. When σ as =σ cc or σ 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 formula (9) is constructed and σ as =σ cc or σ 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 of axial static load σ as = 0 when the three-dimensional direct impact theoretical strength σ 31m According to the tensile damage model expressed in formula (9), that is, the peak strength of the constitutive model of σ1-L under a constant confining pressure, the axial static load σ is determined 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] Furthermore, the step S1 includes:

[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 the 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, elastic modulus E, and Poisson's ratio α described in step S11, obtain the relationship curve between the crack body strain and the axial strain under different confining pressures σ3;

[0044]

[0045] In formula (12), 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, 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 curves 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 expansion of tensile cracks. Specifically, by innovatively introducing correction factors related to the crack expansion 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 expansion 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 micro-observing 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 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

[0053] 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.

[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 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;

[0058] 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;

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

[0063] Figure 10 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;

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

[0065] Figure 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] Figure 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] Figure 14The stress-strain curves 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 (strain rate is 120 / s);

[0068] Figure 15 A comparison chart 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] Figure 16 Figure 3 shows the morphology of a sandstone specimen after failure after one-dimensional static and dynamic combined loading in the method provided in an embodiment of the present invention (strain rate is 120 / s), (a) is an axial static load = 5 MPa, (b) is an axial static load = 25 MPa, and (a) is an axial static load = 50 MPa;

[0070] Figure 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) under different confining pressures;

[0071] Figure 18 The dynamic stress-strain curves (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 are shown in FIG. as =σ ci , strain rate is 170 / s);

[0072] Figure 19 A comparison chart of the theoretical predicted strength and 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] Figure 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] Figure 21 This is a comparison chart of the theoretically 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 by an embodiment of the present invention (confining pressure = 5 MPa, strain rate 170 / s). DETAILED DESCRIPTION

[0075] 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.

[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 being inaccurate and unreliable when predicting the strength and damage evolution law of rocks under more complex loading conditions such as dynamic and static combined loading, 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 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 is obtained when the initial oblique crack is closed 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, Equation (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 propagation length;

[0081] S2. By introducing a correction factor k(v) related to the crack growth rate, each term 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 factors 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 loading, 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 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 dynamic and static combined loading conditions by micro-observing the expansion of tensile cracks; specifically, by innovatively introducing correction factors related to the crack expansion 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.

[0088] By micro-observing the expansion of tensile cracks, the present invention performs a dynamic tensile damage evolution model of rock under dynamic and static combined loading conditions, 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-observing 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 more 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.

[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 initial oblique crack inclination angle 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 of rocks under dynamic and static combined impact, 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 wing crack tip is completely different from when the initial static load is equal to 0. Taking into account that the damage evolution process and strength of the rock under dynamic and static combined loading will change with the difference in 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 dynamic and static combined loading in step S3 are further given, as follows:

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

[0095] S31, when σ as =σ cc or σ 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 formula (5) is constructed and σ as =σ cc or σ 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 the stress for the crack in quasi-static conditions.

[0098] 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, 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 formula (8) is constructed and σ as >σ ci Tensile damage model when ;

[0103]

[0104] S34. When σ as =σ cc or σ 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 formula (9) is constructed and σ as =σ cc or σ 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 of axial static load σ as = 0 when the three-dimensional direct impact theoretical strength σ 31m According to the tensile damage model expressed in formula (9), that is, the peak strength of the constitutive model of σ1-L under a constant confining pressure, the axial static load σ is determined 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 during 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 the σ under medium and high confining pressure p -σ3 linear fitting 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 -σ3 linear fit graph slope k2 and intercept d2, combined with and The initial oblique crack length b and the initial oblique crack inclination angle θ0 of the rock specimen are calculated and determined.

[0119] It can be understood that the CCNBD cracking test refers to a cracked chevron notched Brazilian disc cracking test.

[0120] S12. According to formula (12) and in combination with the stress-strain curve, elastic modulus E, and Poisson's ratio α described in step S11, 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 volume 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 curves 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 of step S1 (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 further includes the following steps:

[0126] S14, based on the material characteristic parameters determined in S11, and according to the wing crack growth model under uniaxial compression, the crack initiation stress is equal to the crack initialization stress, and the parameter λ included in the tensile 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 growth 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 in 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 growth 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 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 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 wing crack growth model in uniaxial compression derived from the formula (15), based on the determined λ and S11 determined material characteristic parameters including μ, b, θ0, K IC , draw the curve of σ1 and L for different w values, and get the axial stress peak σ in each σ1-L 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;

[0135]

[0136] S152. Based on the stress-strain curve of the rock sample in S11 under uniaxial compression (σ3 = 0), the experimental uniaxial compressive strength value of the rock sample σ is obtained. 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.

[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., equations (16) and (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 the average crack growth rate is replace;

[0140] Specifically, the dynamic fracture toughness of the rock The determination method 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 it, and the theoretical strength is found to be 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) includes the following steps: According to the right side of formula (5) The wing crack extension length L corresponding to the maximum value of axial stress σ1 is obtained by fitting using numerical calculation software. 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 described above in geotechnical engineering, the application comprising: obtaining, based on the rock damage model, 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 and / or different static loads;

[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 σ1 of the axial stress σ 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 / comminution laws of ores in grinding processes.

[0147] The technical solution of the present invention is further described in detail below with reference to 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 is obtained when the initial oblique crack is closed under quasi-static loading. Based on the wing crack growth model, and in combination with uniaxial and triaxial tests and CCNBD experiments, a tensile 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 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.

[0154] 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.

[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 ), 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 ;

[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 the loading process, and its size is equal to the volume strain of the rock minus the elastic volume strain. According to the method of determining the rock volume strain and crack volume strain according to formula (12) and combining Figure 1 The stress and strain data of the medium sandstone specimen are taken as an example when the specimen is under 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 The characteristic stresses of the remaining six specimens (i.e., S2-S5 and S7-S8) can be obtained using a similar method.

[0161] Furthermore, 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, 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;

[0163] S112. 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 (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 values ​​are obtained by linear interpolation calculation;

[0166]

[0167] S113, 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°.

[0168] S12. According to formula (12) and in combination with the stress-strain curve, elastic modulus E, and Poisson's ratio α described in step S11, the relationship curves of the crack body strain and axial strain under different confining pressures σ3, as well as the relationship curves of the crack body strain and axial strain are obtained; 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 of crack body strain with axial strain under different confining pressures σ3. For example, when the confining pressure σ bs = 0, from Figure 2 In the equation, find σ respectively. 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 vertical coordinate corresponding to the crack body strain curve is obtained when the confining pressure σ bs =0 and 0<σ as <σ cc The value of the crack closure coefficient η when ;

[0170] For example, when the confining pressure σ bs =20MPa, from Figure 3 In the equation, find σ respectively. 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 when Figure 3 , find the axial stress σ1 equal to σ as The vertical coordinate corresponding to the crack body strain curve is obtained when 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, you can use similar 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, including 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 changing 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; based on the corresponding σ for different w values p,t , we get σ p,t -w fitting graph, see Figure 8 ;

[0173] Furthermore, based on the stress-strain curve of the sandstone specimen 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; from Figure 8 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.

[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 , using formula (13), determine the Rayleigh wave velocity v corresponding to samples S1-S8 under different confining pressures 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 , we obtain the tensile damage model when the initial oblique crack is closed under quasi-static loading, that is, Equation (22):

[0176]

[0177] S2. Introducing the first correction factor k1(v) and the second correction factor k2(v), i.e., equations (16) and (17), to correct the tensile damage model when the initial oblique crack is closed under quasi-static loading represented by equation (22); the dynamic fracture toughness of the rock The specific method for determining k1(v) and k2(v) 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 specimen at different strain rates, such as Figure 9 As shown in the figure, the morphology of the sandstone specimens after failure at three strain rates is shown in Figure 10 As shown;

[0179] from Figure 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), using MATLAB software, we can find the theoretical strength close to the measured strength under different strain rates. The value of is fitted The power function relationship of Figure 11 As shown,

[0180] S202, using MATLAB software, the right side of equation (5) The wing crack extension length L corresponding to the maximum value of 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 , k1(v) and k2(v) are obtained according to equations (16) and (17). 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 The wave velocity is much smaller than that of the Rayleigh wave. 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 factors 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, the one-dimensional dynamic and static combined loading and σ as =25MPa or σ as=39MPa tensile damage model is formula (24), where based on the obtained 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 equation (24), we can obtain the variation law of the axial stress σ1-L, as follows: Figure 12 shown.

[0185]

[0186] According to the experimental results, the sandstone specimen has a pre-applied axial stress equal to σ ci =39MPa when the dynamic stress-strain curve, such as Figure 13 As shown. Figure 12 and Figure 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 When <25MPa, based on the different strains determined in S202 The value of k1(v) under the condition is set according to formula (25) 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 formula (24), that is, the constitutive model of σ1-L, the axial static load σ is determined as =σ cc =Theoretical dynamic and static combined impact strength σ when 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 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 formula (26) is constructed and σ as >39MPa tensile damage model; based on the results obtained in S201 Determine different strain rates Next Take the value and substitute it into formula (26); based on the different strains determined in S202 The value of k1(v) under the condition of σ is substituted into formula (26). The confining pressure σ is determined based on the S13 method. bs =0 and σ as >σ ci The damage variable β is substituted into formula (26) to obtain the variation curve of axial stress σ1-L. From the peak strength of 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 by the experiment are as follows: Figure 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 consistent with the following Figure 14 The dynamic and static combined strength of rocks obtained in the experiment were compared. The results are as follows: Figure 15 ,from Figure 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 one-dimensional rock tensile damage model under 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. Figure 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 illustrates that the dynamic tension damage evolution model of rock under dynamic and static combined loading conditions based on the microscopic tension crack propagation in 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 above equation into (27), we can obtain the variation law of axial stress σ1-L, as follows: Figure 17 , which shows the variation of σ1-L when the strain rate is 170 / s and the confining pressures are 0 MPa, 5 MPa, 10 MPa, and 15 MPa, respectively, and the initial static load = the crack initiation 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: Figure 18 As shown. Figure 17 The dynamic strength of rock predicted by the microscopic tensile damage model is Figure 18 The measured intensity is compared with that in Figure 19 As shown, the strain rate is 170 / s. Figure 19 It can be seen that when the axial static pressure is equal to the static crack initialization stress under the corresponding confining pressure, both the theoretically predicted strength and the experimentally measured dynamic-static combined strength values ​​increase with the increase of the confining pressure, and the two 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 formula (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 formula (27), that is, the peak strength of the constitutive model of σ1-L at a confining pressure σ3 = 5 MPa, the axial static load σ is determined as =σ cc =Theoretical dynamic and static combined impact strength σ when 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 the σ1=σ obtained from the crack body strain curve under the 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 when 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 formula (29) is constructed and σ as >σ ci =55MPa tensile damage model; wherein, based on the 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 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 damage variable β is substituted into formula (29) to obtain the variation curve of axial stress σ1-L. as >σ ci =Theoretical dynamic and static combined impact strength at 55MPa;

[0202]

[0203] In order to further study the effect 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 under different axial static pressures obtained in the experiment are shown in Figure 2. Figure 20 As shown in the figure, 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 consistent with the following Figure 20 The dynamic and static combined strength of rocks obtained in the experiment were compared. The results are as follows: Figure 21 , the strain rate is 170 / s, the confining pressure σ3 is 5MPa, Figure 21 It can be seen that the theoretically predicted strength and the experimentally measured dynamic and static combined strength show consistent trends and are in good agreement with each other. This demonstrates that the three-dimensional tensile damage model under dynamic and static combined loading 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 described above in geotechnical engineering, the application including:

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

[0206] according to Figure 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 100 MPa at a strain rate of 85 / s to 117 MPa at a strain rate of 131 / s;

[0207] according to Figure 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 0 MPa, the dynamic crack initiation stress is 180 MPa; when the confining pressure is 15 MPa, the dynamic crack initiation stress is 197 MPa.

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

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

[0210] For example, according to Figure 17 , when the axial static load is the crack initialization stress of quasi-static loading under respective confining pressures, the dynamic and static combined strength of sandstone under three-dimensional dynamic and static combined loading gradually increases with the increase of confining pressure. Figure 19 The theoretical prediction values ​​of the dynamic and static combined strength at different confining pressures were obtained. Figure 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 tensile damage model under 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 Figure 12 When the axial static load is equal to the quasi-static crack initialization stress, the wing cracks under different loading conditions are all at the extension 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 Figure 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 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 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 rock damage process and strength, such as dynamic load strain rate, confining pressure, and axial static pressure.

[0215] 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, 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 closed 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, Equation (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 propagation 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 factors 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 loading, 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 initial oblique crack inclination angle 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 σ 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 formula (5) is constructed and σ as =σ cc or σ 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 further includes: 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, 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 further 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 formula (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 further includes: S34. When σ as =σ cc or σ 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 formula (9) is constructed and σ as =σ cc or σ as =σ ci Tensile damage model when ; 7. The construction method according to claim 6, characterized in that: The step S3 further includes: 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 of axial static load σ as = 0 when the three-dimensional direct impact theoretical strength σ 31m According to the tensile damage model expressed in formula (9), that is, the peak strength of the constitutive model of σ1-L under a constant confining pressure, the axial static load σ is determined 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 includes: 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 the 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, elastic modulus E, and Poisson's ratio α described in step S11, obtain the relationship curve between the crack body strain and the axial strain under different confining pressures σ3; In formula (12), 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, 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 curves 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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