Method for establishing rock dynamic triaxial statistical damage constitutive model

Abstract

The invention discloses a rock dynamic triaxial statistical damage constitutive model establishing method, and belongs to the technical field of rock dynamic constitutive model basic research of deep underground engineering. The method comprises the following steps: introducing a nonlinear Mohr-Coulomb and Hoek-Brown strength criterion, and deriving a nonlinear rock dynamic strength criterion considering a strain rate effect based on a rock dynamic strength and strain rate dependent strength criterion of a thermal activation and viscosity mechanism; constructing a rock infinitesimal strength measurement method capable of reflecting rock dynamic deformation characteristics, and establishing a rock dynamic triaxial statistical damage constitutive model; and carrying out sensitivity analysis on the rock dynamic triaxial statistical damage constitutive model. According to the method, the rock dynamic triaxial statistical damage constitutive model suitable for the high confining pressure and the high strain rate is effectively established, so that the nonlinear deformation process of the deep high confining pressure rock under the dynamic load effect is accurately simulated, and the method can be applied to the technical field of rock dynamic constitutive model basic research of deep underground engineering.

Description

Technical Field

[0001] The present invention belongs to the technical field of basic research on rock dynamic constitutive models for deep underground engineering, and specifically relates to a method for establishing a rock dynamic triaxial statistical damage constitutive model suitable for high confining pressure and high strain rate. Background Art

[0002] In water conservancy and hydropower, highway, railway, mining, civil engineering and other projects, deformation analysis and calculation of rock structures (such as slope engineering, underground structures and tunnels, foundation engineering, etc.) are indispensable in various engineering and structural designs, and are also important indicators for the stability control of various engineering and structural projects.

[0003] Deep rocks are usually in a high-in-situ stress environment characterized by high confining pressure. Their mechanical properties and deformation laws will change significantly, resulting in strong nonlinear characteristics of surrounding rock deformation. The damage behavior of rocks is directly related to the stability and safety of rock engineering. Therefore, it is of great significance to study the constitutive relationship of rocks in deep high-in-situ stress environments. However, the current research on rock constitutive relationships mainly focuses on constitutive models applicable to low confining pressure strength criteria, so it is difficult to ensure the calculation accuracy of the constitutive model obtained under high surrounding rock conditions. As a result, there may be a large deviation between the final analysis results and the actual engineering, and even misjudgment may occur. At the same time, rock engineering structures are often subjected to dynamic loads such as earthquakes, blasting and impact, which causes changes in the corresponding loading speed or strain rate. These factors will have an important impact on the mechanical behavior of rocks. Obviously, the existing constitutive model under static loads is difficult to reflect this dynamic effect.

[0004] Therefore, in order to more accurately describe and predict the dynamic mechanical behavior of rocks, it is particularly important to develop a dynamic constitutive model of rocks that can reflect the effects of actual loading speed and strain rate. Summary of the invention

[0005] The purpose of an embodiment of the present invention is to provide a method for establishing a dynamic triaxial statistical damage constitutive model of rock suitable for high confining pressure and high strain rate. To this end, a new nonlinear dynamic strength criterion is derived, a rock microelement strength measurement method that can reflect the dynamic deformation characteristics of rock is constructed, and the statistical damage theory is introduced into the dynamic constitutive model of rock. A method for calculating model parameters is proposed, and a dynamic triaxial statistical damage constitutive model of rock is established. The influence of different probability density distribution function forms on the constitutive model curve is considered, and a sensitivity analysis of the dynamic triaxial statistical damage constitutive model of rock is carried out, thereby solving at least one technical problem involved in the background technology.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0007] A method for establishing a dynamic triaxial statistical damage constitutive model of rock suitable for high confining pressure and high strain rate comprises the following steps:

[0008] Step S1, introducing nonlinear Mohr-Coulomb and Hoek-Brown strength criteria, based on the rock dynamic strength and strain rate-dependent strength criteria of thermal activation and viscosity mechanisms, and establishing a nonlinear rock dynamic strength criterion considering strain rate effect;

[0009] Step S2, calculating the rock dynamic yield strength parameters, and verifying the applicability of the nonlinear dynamic strength criterion in combination with the test data;

[0010] Step S3, constructing a rock micro-element strength measurement method that can reflect the dynamic deformation characteristics of rock, and introducing statistical damage theory into the dynamic constitutive model of rock;

[0011] Step S4, establishing a rock dynamic triaxial statistical damage constitutive model for simulating the dynamic deformation process of rock, and proposing a calculation formula for constitutive model parameters;

[0012] Step S5, verifying the rationality of the rock dynamic triaxial statistical damage constitutive model by comparative analysis with rock dynamic triaxial test data;

[0013] Step S6, based on the existing Weibull distribution function that describes the strength of rock micro-element, two probability density functions, Harris distribution and Gaussian distribution, are introduced, the influence of different probability density distribution function forms on the constitutive model curve is considered, and the sensitivity analysis of the dynamic triaxial statistical damage constitutive model of rock is carried out.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] 1. The present invention takes into account the nonlinear influence of rock dynamic strain rate on rock strength, introduces nonlinear Mohr-Coulomb and Hoek-Brown strength criteria, and establishes a nonlinear rock dynamic strength criterion suitable for high confining pressure conditions based on the uniaxial dynamic strength and strain rate dependence of rock based on thermal activation and viscosity mechanisms. This provides a new idea for the establishment of a statistical damage constitutive model for deep underground engineering and expands the application scope of the statistical damage constitutive model.

[0016] 2. The present invention establishes a rock micro-element strength measurement method that can reflect the dynamic deformation characteristics of rock, introduces statistical damage theory, and establishes a statistical damage constitutive model and a parameter determination method for simulating the dynamic triaxial deformation process of rock; through comparative analysis of the model theoretical curve and the experimental curve, it is shown that the present invention based on the nonlinear Mohr-Coulomb criterion and the Hoek-Brown criterion model can simulate the nonlinear deformation process, has a better simulation curve, and is reasonable and superior.

[0017] 3. On the basis of the established dynamic statistical damage model, the present invention introduces two distribution functions, Harris distribution and Gaussian distribution, to establish a dynamic triaxial statistical damage constitutive model of rock. Through comparative study with the existing Weibull distribution model, the model curve based on Weibull distribution and Gaussian distribution can better reflect the softening of rock and is more in line with the actual situation. Different probability distribution functions have advantages and limitations, and the probability distribution function can be selected and adjusted according to the specific situation.

[0018] 4. The method provided by the present invention has simple steps, fully considers the actual needs of the project, has a wide range of applicability and broad application prospects, and effectively makes up for the fact that the model curve of the existing technology cannot well simulate the process of nonlinear changes of rocks under deep high ground stress. It is of great significance to the simulation method of the dynamic deformation process of rocks in deep underground engineering structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0020] Figure 1 A flow chart of a method for establishing a dynamic triaxial statistical damage constitutive model of rock applicable to high confining pressure and high strain rate provided in an embodiment of the present invention;

[0021] Figure 2 The relationship diagram between the yield strength of rock and the strain rate under different confining pressures provided by the embodiment of the present invention (Mohr-Coulomb criterion, 0≤σ3≤σ c );in, Figure 2 (a) is a graph showing the relationship between rock yield strength and strain rate under a confining pressure of σ3=5 MPa provided in an embodiment of the present invention; Figure 2 (b) is a graph showing the relationship between rock yield strength and strain rate under a confining pressure of σ3=15 MPa provided in an embodiment of the present invention; Figure 2 (c) is a graph showing the relationship between rock yield strength and strain rate under a confining pressure of σ3=25 MPa provided in an embodiment of the present invention;

[0022] Figure 3 The relationship between the yield strength of rock and the strain rate under the confining pressure σ3=25Mpa provided in the embodiment of the present invention (Mohr-Coulomb criterion, σ3≥σ c );

[0023] Figure 4A relationship diagram between rock yield strength and strain rate under different confining pressures provided in an embodiment of the present invention (Hoek-Brown criterion); wherein, Figure 4 (a) is a graph showing the relationship between rock yield strength and strain rate under a confining pressure of σ3=5 MPa provided in an embodiment of the present invention; Figure 4 (b) is a graph showing the relationship between rock yield strength and strain rate under a confining pressure of σ3=15 MPa provided in an embodiment of the present invention; Figure 4 (c) is a graph showing the relationship between rock yield strength and strain rate under a confining pressure of σ3=25 MPa provided in an embodiment of the present invention;

[0024] Figure 5 (a) to (i) are comparison diagrams of theoretical and experimental curves provided in the embodiments of the present invention (Hoek-Brown criterion, Mohr-Coulomb criterion);

[0025] Figure 6 The influence diagram of strain rate on rock deformation process under different confining pressures provided by the embodiment of the present invention (Mohr-Coulomb criterion, 0≤σ3≤σ c );in, Figure 6 (a) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=5 MPa provided in an embodiment of the present invention; Figure 6 (b) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=15 MPa provided in an embodiment of the present invention; Figure 6 (c) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=25 MPa provided in an embodiment of the present invention;

[0026] Figure 7 The influence diagram of strain rate on rock deformation process under confining pressure σ3=25Mpa provided in the embodiment of the present invention (Mohr-Coulomb criterion, σ3≥σ c );

[0027] Figure 8 The influence diagram of strain rate on rock deformation process under different confining pressures provided by the embodiment of the present invention (Hoek-Brown criterion); wherein, Figure 8 (a) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=5 MPa provided in an embodiment of the present invention; Figure 8 (b) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=15 MPa provided in an embodiment of the present invention; Figure 8 (c) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=25 MPa provided in an embodiment of the present invention;

[0028] Fig. 9A comparison diagram of the Harris distribution theory and experimental curves provided by the embodiment of the present invention (Hoek-Brown criterion, σ3 = 25Mpa, );

[0029] Fig.10 (a) to (f) are comparison diagrams of Gaussian distribution theory and experimental curves (Hoek-Brown criterion) provided in the embodiments of the present invention;

[0030] Fig.11 The influence diagram of strain rate on rock deformation process under different confining pressures provided by the embodiment of the present invention (Hoek-Brown criterion); wherein, Fig.11 (a) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=5 MPa provided in an embodiment of the present invention; Fig.11 (b) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=15 MPa provided in an embodiment of the present invention; Fig.11 (c) is a diagram showing the influence of strain rate on rock deformation process under confining pressure σ3=25 MPa provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0032] See also Figure 1 As shown, an embodiment of the present invention provides a method for establishing a dynamic triaxial statistical damage constitutive model of rock, comprising the following steps:

[0033] Step S1, introducing nonlinear Mohr-Coulomb and Hoek-Brown strength criteria, based on the rock dynamic strength and strain rate-dependent strength criteria of thermal activation and viscosity mechanisms, and establishing a nonlinear rock dynamic strength criterion considering strain rate effect;

[0034] Step S2, calculating the rock dynamic yield strength parameters, and verifying the applicability of the nonlinear dynamic strength criterion in combination with the test data;

[0035] Step S3, constructing a rock micro-element strength measurement method that can reflect the dynamic deformation characteristics of rock, and introducing statistical damage theory into the dynamic constitutive model of rock;

[0036] Step S4, establishing a rock dynamic triaxial statistical damage constitutive model for simulating the dynamic deformation process of rock, and proposing a calculation formula for constitutive model parameters;

[0037] Step S5, verifying the rationality of the rock dynamic triaxial statistical damage constitutive model by comparative analysis with rock dynamic triaxial test data;

[0038] Step S6, based on the existing Weibull distribution function that describes the strength of rock micro-element, two probability density functions, Harris distribution and Gaussian distribution, are introduced, the influence of different probability density distribution function forms on the constitutive model curve is considered, and the sensitivity analysis of the dynamic triaxial statistical damage constitutive model of rock is carried out.

[0039] In step S1, a nonlinear rock dynamic strength criterion considering the strain rate effect is established, which specifically includes:

[0040] The dynamic strength-strain rate relationship criterion of rock based on thermal activation and viscosity mechanism is established and expressed as follows:

[0041]

[0042] The nonlinear Mohr-Coulomb criterion is introduced and expressed as:

[0043]

[0044]

[0045] In the formula, σ1 and σ3 represent the maximum and minimum principal stresses of rock respectively; c is the static cohesion of rock; is the internal friction angle; σ c Represents the uniaxial compressive strength of rock.

[0046] When 0≤σ3≤σ c When σ3=0 is substituted into formula (2), the cohesion of rock under uniaxial compression condition can be expressed as:

[0047]

[0048] Considering that the change of dynamic strength of rock under dynamic load is determined by the change of cohesion, and the change of internal friction angle with loading rate is very small, it can be ignored. Therefore, the uniaxial dynamic stress Y in formula (1) is used to replace the uniaxial static stress σ1 in formula (4), and the dynamic cohesion c is obtained. d , that is:

[0049]

[0050] Let c = c d , and substitute it into formula (2), we get the dynamic strength criterion of rock under complex stress conditions σ 1d , that is:

[0051]

[0052] Since equation (6) must satisfy the rock strength standard under static conditions, the last two terms on the right side of equation (6) must be 0 in static problems, that is:

[0053]

[0054] Therefore, by comparing equation (2) and equation (7), we can get:

[0055]

[0056] Substituting formula (8) into formula (6), formula (6) can also be rewritten as:

[0057]

[0058] In general rock engineering, since the temperature change is very small, the temperature T can be regarded as a constant, and A1 = C2T (constant). By using it in equation (9), the proposed nonlinear dynamic strength standard can be obtained, which can be expressed as:

[0059]

[0060] in:

[0061]

[0062]

[0063]

[0064] When σ3≥σ c When σ3=0 is substituted into formula (3), the cohesion of rock under uniaxial compression condition can be expressed as:

[0065]

[0066] By replacing the uniaxial static stress σ1 in equation (14) with the uniaxial dynamic stress Y, the dynamic cohesion can be obtained, that is,

[0067]

[0068] Therefore, let c = c d , and substitute it into formula (3) to obtain the dynamic strength criterion of rock under complex stress conditions, namely:

[0069]

[0070] Considering that formula (16) must also meet the rock strength standard under static conditions, the last two terms on the right side of formula (16) must be 0 in static problems, that is:

[0071] σ1=σ3+C1 (17)

[0072] Therefore, comparing equation (3) and equation (17), we can get:

[0073]

[0074] Further replacing equation (18) into equation (16), equation (16) is rewritten as:

[0075]

[0076] In general rock engineering, since the temperature change is very small, the temperature T can be regarded as a constant, so A2 = C2T (constant) can be used in formula (19) to obtain the nonlinear dynamic strength standard, which is expressed as follows:

[0077]

[0078] in:

[0079]

[0080] Introducing the failure criterion based on Hoek-Brown, we can obtain:

[0081]

[0082] In the formula, σ1 and σ3 are the maximum and minimum principal stresses of rock respectively; m and s are constants related to rock characteristics;

[0083] Substituting σ3=0 into equation (2), we can obtain s under uniaxial compression of rock, which can be expressed as:

[0084]

[0085] Substituting the uniaxial static stress σ1 in equation (23) with the uniaxial dynamic stress Y, we can obtain the dynamic s d , that is:

[0086]

[0087] Let s = s d , and substituting it into formula (22), we can get the dynamic strength criterion of rock under complex stress state, which can be expressed as:

[0088]

[0089] Considering that formula (25) must also meet the rock strength standard under static conditions, the last term on the right side of formula (25) must be 0 in static problems, that is:

[0090]

[0091] Therefore, comparing equation (22) and equation (26), we can get:

[0092]

[0093] Substituting formula (27) into formula (25), formula (25) can also be rewritten as:

[0094]

[0095] In common rock engineering, since the temperature change is very small, the temperature T can be regarded as a constant, and A3 = C2T (constant) is substituted into formula (28) to obtain the nonlinear dynamic strength standard, which is expressed as follows:

[0096]

[0097] α3=m (30)

[0098]

[0099] In step S2, the dynamic yield strength parameters of the rock are calculated and combined with the test data to verify the nonlinear dynamic strength criterion, which specifically includes:

[0100] The experimental study on the uniaxial dynamic characteristics of rock under 5-25Mpa confining pressure was introduced, and the static and dynamic stress-strain curves of rock under different confining pressures were obtained. On this basis, the yield strength of rock under different confining pressures was determined, and the specific data are shown in Table 1.

[0101] Table 1 Static yield stress of rock under different confining pressures

[0102] <![CDATA[σ3 / Mpa]]> Static yield stress / Mpa 5 19.52 15 29.62 25 41.89

[0103] The static yield strength index of rock is calculated by nonlinear fitting of static stress-strain curve, where cohesion c y is 6.04Mpa, internal friction angle The correlation coefficient of the fitting is as high as 0.9941. The constant m related to rock characteristics is 0.1307, s is 0.2911, and the fitting coefficient is as high as 0.9961. By studying the dynamic stress-strain curves of rocks under different confining pressures and loading rates, the dynamic yield stress of rocks under the above conditions is obtained, as shown in Table 2.

[0104] Table 2 Dynamic yield stress of rock under different confining pressures and strain rates

[0105]

[0106]

[0107] Formula (10), Formula (20) and Formula (29) are used to fit the dynamic yield strength of rock under different confining pressures, and the dynamic yield strength parameters of rock under different strength standards are obtained, as shown in Tables 3, 4 and 5.

[0108] Table 3 Dynamic yield strength parameters of rocks (Mohr-Coulomb criterion, 0≤σ3≤σ c )

[0109]

[0110] Table 4 Dynamic yield strength parameters of rocks (Mohr-Coulomb criterion, σ3≥σ c )

[0111]

[0112] Table 5 Dynamic yield strength parameters of rocks (Hoek-Brown criterion)

[0113]

[0114] Substituting these static and dynamic yield strength parameters into equations (10), (20), and (29), the dynamic strength curves of rocks under different confining pressures and different strength criteria are constructed. Figure 2 , Figure 3 , Figure 4 For the convenience of comparison, the test data of dynamic strength are also included in the figure to verify the rationality of the nonlinear dynamic strength criterion.

[0115] Step S3 specifically includes:

[0116] The model is further improved on the basis of Lemaitre strain equivalence hypothesis. On this basis, the rock under dynamic loading is regarded as two parts: damaged and undamaged. It is further assumed that the rock no longer has bearing capacity after failure, and the entire load is borne by the undamaged rock.

[0117] The dynamic damage model of rock is constructed. The expression of the model can be expressed as:

[0118] 0≤σ3≤σ c

[0119] (i=1,2 or 3)(32)

[0120] In the formula, σ id is the dynamic macroscopic nominal stress of rock, σ id is the dynamic effective stress of rock (stress in the rock mass without undamaged parts), D d is the dynamic damage variable or damage factor of rock (i.e., the ratio of the cross-sectional area of ​​the damaged part of the rock to the total area of ​​the rock). id is the stress on the undamaged part of the rock. Assuming that the undamaged part of the rock obeys the generalized Hooke's law, then:

[0121]

[0122] In the formula, E d and μ d are the dynamic elastic modulus and dynamic Poisson’s ratio of rock, respectively; is the microscopic strain of the undamaged part of the material; i, j, k = 1, 2, 3 or 2, 3, 1 or 3, 2, 1. Since the damaged and undamaged materials are closely overlapped, their deformation can be regarded as a synergistic relationship, that is:

[0123]

[0124] In the formula, ε i is the dynamic macroscopic strain of rock. Substituting equations (32) and (34) into equation (33), we can obtain:

[0125] σ id =E d ε i (1-D d )+μ d (σ jd +σ kd )(35)

[0126] First, assuming that the rock micro-element strength or rock micro-element failure obeys Weibull distribution, its probability density function can be expressed as:

[0127] P(F)=m / F0(F / F0) m-1 exp[-(F d / F0) m ] (36)

[0128] Where F is the distribution variable of the infinitesimal destruction Weibull distribution, and m and F0 are the Weibull distribution parameters.

[0129] The damage variable is:

[0130]

[0131] The triaxial dynamic statistical damage evolution model of rock can be expressed as:

[0132]

[0133] The two nonlinear rock dynamic yield strength criteria proposed above, namely, equation (10), equation (20), and equation (29), are used to establish the following rock dynamic micro-element strength measurement method, which can be expressed as:

[0134] (MC criterion, 0≤σ3≤σ c ) (39)

[0135] (MC criterion, σ3≥σ c )(40)

[0136] (HB criteria) (41)

[0138] In the formula, are the maximum and minimum principal stresses on the undamaged part of the rock, i.e., the maximum and minimum effective stresses; other parameters or variables have the physical meanings mentioned above. Therefore, the dynamic micro-element strength of rock F can also be expressed by equations (32) and (35). d It is expressed as:

[0139]

[0140] (MC criterion, 0≤σ3≤σ c )(42)

[0141] (MC criterion, σ3≥σ c ) (43)

[0143] (HB criteria)(44).

[0144] Step S4 specifically includes:

[0145] Based on the above-mentioned rock dynamic damage model and damage evolution model, by substituting equation (38) into equation (35), we can obtain a rock dynamic triaxial statistical damage constitutive model that can describe the dynamic deformation of rock.

[0146]

[0147] The above-mentioned rock dynamic triaxial statistical damage constitutive model containing multiple parameters to simulate the dynamic deformation process of rock has been established, namely, Equation (45). Next, we will discuss in detail how to determine these model parameters.

[0148] First, the constitutive model based on the nonlinear Mohr-Coulomb criterion:

[0149] When 0≤σ3≤σ c Since the conventional dynamic triaxial test is usually conducted with constant confining pressure (σ 2d =σ 3d =σ3, σ3 is the static confining pressure), the first equation in equation (45) can be rewritten as:

[0150] σ 1d =E d ε i exp[-(F d / F0) m ]+2μ d σ3 (46)

[0151] Among them, F d From equation (42), let σ 2d =σ 3d =σ3, which can be expressed as:

[0152]

[0153] Therefore, according to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, formula (47) can be obtained:

[0154]

[0155] In the formula, σ 1dc , ε 1dc are respectively the dynamic stress and dynamic strain at the peak of the conventional rock dynamic triaxial stress-strain curve measured by the test curve. In addition, the peak stress σ 1dc and strain ε 1dc It must also satisfy formula (46), that is:

[0156] σ 1dc =E d ε 1dc exp[-(F dc / F0) m ]+2μ d σ3 (49)

[0157] Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (47), we get:

[0158]

[0159] Therefore, combining equation (48) and equation (49) yields:

[0160]

[0161]

[0162] When σ3≥σ c Since the conventional dynamic triaxial test is usually conducted with constant confining pressure (σ 2d =σ 3d =σ3, σ3 is the static confining pressure), the first equation in equation (45) can be rewritten as:

[0163] σ 1d =E d ε i exp[-(F d / F0) m ]+2μ d σ3 (46)

[0164] Among them, F d From equation (43) and let σ 2d =σ 3d =σ3, which can be expressed as:

[0165]

[0166] Therefore, according to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, formula (46) can be obtained:

[0167]

[0168] In the formula, σ 1dc , ε 1dc are respectively the dynamic stress and dynamic strain at the peak of the conventional rock dynamic triaxial stress-strain curve measured by the test curve. In addition, the peak stress σ 1dc and strain ε 1dc It must also satisfy formula (46), that is:

[0169] σ 1dc =E d ε 1dc exp[-(F dc / F0) m ]+2μ d σ3 (49)

[0170] Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (53), we get:

[0171]

[0172] Therefore, combining equations (48) and (49) yields:

[0173]

[0174]

[0175] Second, the constitutive model based on the nonlinear Hoek-Brown criterion:

[0176] Since conventional dynamic triaxial tests are usually performed with constant confining pressure (σ 2d =σ 3d =σ3, σ3 is the static confining pressure), the first equation in equation (45) can be rewritten as:

[0177] σ 1d =E d ε i exp[-(F d / F0) m ]+2μ d σ3 (46)

[0178] Among them, F d From formula (3-12) and let σ 2d =σ 3d =σ3, which can be expressed as:

[0179]

[0180] Therefore, according to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, formula (46) can be obtained:

[0181]

[0182] In the formula, σ 1dc , ε 1dc are respectively the dynamic stress and dynamic strain corresponding to the peak point of the conventional rock dynamic triaxial stress-strain curve, which can be obtained from the test curve. In addition, the peak point stress σ 1dc and strain ε 1dc It must also satisfy formula (46), that is:

[0183] σ 1dc =E d ε 1dc exp[-(F dc / F0) m ]+2μ d σ3 (49)

[0184] Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (57), we get:

[0185]

[0186] Therefore, combining equation (48) and equation (49) yields:

[0187]

[0188]

[0189] Among them, D d σ 1d =σ 1dc and ε i =ε 1dc Substitute into equation (35) and let σ 2d =σ 3d =σ3, which can be expressed as:

[0190]

[0191] The above formulas (51) and (52), (55) and (56), (59) and (60) are the determination methods of the model parameters m and F0 proposed in the present invention. However, the dynamic stress-strain curve obtained from the traditional rock dynamic triaxial test is usually a deviatoric stress and deviatoric strain relationship curve, which cannot be directly obtained from the test data, so it needs to be converted. Therefore, through the conventional rock dynamic triaxial test, the peak stress of the rock dynamic triaxial dynamic stress-strain curve is obtained. strain but:

[0192]

[0193]

[0194] In the formula, ε c The rock specimen is subjected to hydrostatic pressure σ3, that is, axial stress σ 1d The initial strain generated by loading to the confining pressure σ3; It is directly obtained from the stress and strain at the peak point of the test curve. It is generally believed that rock is not damaged under hydrostatic pressure, so according to the second equation in equation (45), σ 1d =σ 2d =σ 3d =σ3, we can get the method of determining the initial strain, that is:

[0195] ε c =(1-2μ d )σ3 / E d (64)

[0196] In step S5, the constructed dynamic triaxial statistical damage constitutive model of deep rock is verified in combination with the test data, which specifically includes:

[0197] The test data and test curves are introduced, and the parameter values ​​under different confining pressure conditions and strain rate conditions are calculated according to the test data and the theoretical formula in step S5. The parameter values ​​are determined by the method proposed in the present invention. The determination results of these parameters are listed in Table 6, Table 7, and Table 8.

[0198] Table 6 Constitutive model parameters (Mohr-Coulomb criterion, 0≤σ3≤σ) under different confining pressures and strain rates c )

[0199]

[0200] Table 7 Constitutive model parameters (Mohr-Coulomb criterion, σ3≥σ c )

[0201]

[0202] Table 8 Constitutive model parameters under different confining pressures and strain rates (Hoek-Brown criterion)

[0203]

[0204]

[0205] Substituting the above parameters into the model analysis and calculation provided by the present invention can obtain the theoretical curve of the model of the present invention. The theoretical curve of the Hoek-Brown criterion model and the theoretical curve of the Mohr-Coulomb criterion model of the present invention are listed in the same curve graph with the experimental curve. Figure 5 (a)~ Figure 5 (i) It can be seen that both models of the present invention can reflect the nonlinear deformation of the dynamic deformation process of rock. With the increase of loading rate and confining pressure, the dynamic strength of the rock mass also increases, which is in good agreement with the actual situation, thus verifying the rationality of the established mechanical model.

[0206] In addition, the present invention plots the model theoretical curve under the same confining pressure condition in the same diagram, see Figure 6 , Figure 7 , Figure 8 The results are shown in Figure 2 for intuitive comparison. By comparison, it can be found that under the same confining pressure, the deformation behavior of rock will show significant differences due to changes in strain rate. Specifically, as the strain rate increases, the strength of the rock increases accordingly, and this trend is consistent with the actual geological phenomenon. This change trend verifies the rationality of the model theoretical curve and provides strong support for the understanding of the dynamic deformation process of rock.

[0207] In summary, the model provided by the present invention simulates the dynamic deformation process of rock under high confining pressure better than the existing ones, reflects the nonlinearity of rock deformation well, and has obvious rationality and superiority.

[0208] In step S6, Harris distribution and Gaussian distribution are introduced to further explore the influence of probability distribution function on rock dynamic deformation, including:

[0209] Assuming that the micro-element strength of rock obeys the improved Harris probability density distribution, Li Xiaofeng et al. obtained the rock statistical damage softening model, which can be expressed as:

[0210]

[0211] In the formula, D is the rock damage variable, F is the random distribution variable of the micro-element strength, and a and b are model parameters greater than 0. Since a and b are both greater than 0, p(F)>0, and the first formula of formula (65) is monotonically increasing; when the random distribution variable of the rock micro-element strength F=0, D=0, which is equivalent to intact rock material; when F→∞, D→1, all the micro-elements are destroyed, and the rock loses its bearing capacity. It can be seen that the change law of the rock damage parameter reflected by the first formula in formula (65) is close to the real situation.

[0212] The following rock dynamic micro-element strength measurement method is established by using the Hoek-Brown nonlinear rock dynamic yield strength criterion, i.e., formula (43), which can be expressed as:

[0213] (HB criteria) (66)

[0215] In the formula, are the maximum and minimum principal stresses, i.e., the maximum and minimum effective stresses, respectively, on the undamaged part of the rock; the physical meanings of other parameters or variables are as described above. Therefore, using equations (32) and (34), the dynamic micro-element strength of rock F d It is expressed as:

[0216] (HB criteria) (67)

[0218] Based on the above-mentioned rock dynamic damage model and damage evolution model, by substituting equation (65) into equation (34), we can obtain the dynamic-statistical damage constitutive model that can describe the dynamic deformation of rock, namely:

[0219]

[0220] The above-mentioned rock dynamic triaxial statistical damage constitutive model containing multiple parameters to simulate the dynamic deformation process of rock has been established, namely, Equation (68). In order to more accurately simulate the behavior of rock in the dynamic deformation process, a reasonable method for determining the model parameters must be established. Therefore, the following will discuss in detail how to determine these model parameters.

[0221] Considering that conventional dynamic triaxial tests are usually static loads with equal confining pressure (σ 2d =σ 3d =σ3, σ3 is the static confining pressure), the first equation in equation (68) can be rewritten as:

[0222]

[0223] Among them, F d From equation (67) and let σ 2d =σ 3d =σ3, which can be expressed as:

[0224]

[0225] Therefore, according to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, it can be obtained from formula (69):

[0226]

[0227] In the formula, σ 1dc , ε 1dc They are respectively the dynamic stress and dynamic strain at the peak of the conventional rock dynamic triaxial stress-strain curve, which can be obtained from the test curve. In addition, the peak stress σ 1dc and strain ε 1dc It must also satisfy formula (69), that is:

[0228]

[0229] Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (70), we get:

[0230]

[0231] Therefore, combining equation (71) and equation (72) yields:

[0232]

[0233]

[0234] The Harris distribution model theoretical curve and the Weibull distribution model theoretical curve of the present invention are listed in the same curve graph with the experimental curve of Fang Qin et al., see Fig. 9 As shown. It can be seen that the Harris distribution model of the present invention cannot reflect the strain softening model curve of the dynamic deformation process of rock and the test curve deviates. Therefore, the simulation effect of the Weibull distribution model provided by the present invention is more consistent with the test curve.

[0235] Assume that the logarithmic Gaussian distribution method is used to describe the rock micro-element strength:

[0236]

[0237] Where F0 and S0 are Gaussian distribution parameter damage variables, which can be expressed as:

[0238]

[0239] In the formula, is the standard Gaussian distribution function. Formula (77) is the damage evolution equation established by the present invention.

[0240] The Hoek-Brown nonlinear rock dynamic yield strength criterion proposed in the present invention, that is, formula (29), is used to establish the following rock dynamic micro-element strength measurement method, which can be expressed as:

[0241] (HB criteria) (66)

[0243] In the formula, are the maximum and minimum principal stresses on the undamaged part of the rock, i.e., the maximum and minimum effective stresses; the physical meanings of other parameters or variables are as described above. Therefore, using equations (32) and (35), the dynamic micro-element strength of rock F d It is expressed as:

[0244] (HB criteria) (67)

[0246] The rock dynamic damage model and damage evolution model have been established above. Substituting equation (77) into equation (35), we can obtain the rock dynamic triaxial statistical damage constitutive model that can reflect the dynamic deformation process of rock, which can be expressed as:

[0247]

[0248] Considering that conventional dynamic triaxial tests are usually static loads with equal confining pressure (σ 2d =σ 3d=σ3, σ3 is the static confining pressure), then equation (78) can be rewritten as:

[0249]

[0250] Among them, F d From equation (67) and let σ 2d =σ 3d =σ3, which can be expressed as:

[0251]

[0252] Therefore, according to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, formula (79) can be obtained:

[0253]

[0254]

[0255] In the formula, σ 1dc , ε 1dc They are respectively the dynamic stress and dynamic strain at the peak of the experimental conventional rock dynamic triaxial stress-strain curve, which can be obtained from the experimental curve.

[0256] From formula (80) and formula (81), we can get:

[0257]

[0258] In the formula

[0259] Take the logarithm of both sides of equation (82) and sort them out:

[0260]

[0261] From formula (79), we get:

[0262]

[0263] In the formula,

[0264] For the peak point of the test curve under a certain confining pressure, a Φ value can be obtained from formula (85), and the corresponding X value can be obtained from the Gaussian distribution function table.

[0265] From equation (84) and equation (85), we can obtain the parameters F0 and S0:

[0266]

[0267] F0=XS0+lnF dc (88)

[0268] Among them, Fdc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (70), we get:

[0269]

[0270] The parameters are determined by the method proposed in the present invention, and the results are listed in Table 9.

[0271] Table 9 Constitutive model parameters under different confining pressures and strain rates (Hoek-Brown criterion)

[0272]

[0273] Substituting the above parameters into the model provided by the present invention for analysis and calculation, the theoretical curve of the model of the present invention can be obtained. The theoretical curve of the Gaussian distribution model and the theoretical curve of the Weibull distribution model of the present invention are listed in the same curve graph with the test curve. Fig.10 (a)~ Fig.10 (f) It can be seen from this that both models of the present invention can reflect the nonlinear deformation of the dynamic deformation process of rocks.

[0274] In addition, the present invention plots the model theoretical curve under the same confining pressure condition in the same diagram, see Fig.11 (a)~ Fig.11 (c) for intuitive comparison. By comparison, it can be found that under the same confining pressure, the deformation behavior of rock will show significant differences due to the change of strain rate. Specifically, as the strain rate increases, the strength of the rock increases accordingly, and this trend is consistent with the actual geological phenomenon. This change trend verifies the rationality of the model theoretical curve and provides strong support for the understanding of the dynamic deformation process of rock.

[0275] In summary, the Gaussian distribution model and Weibull distribution model provided by the present invention can better simulate the dynamic deformation process of rock under high confining pressure, well reflect the nonlinearity of rock deformation, fully reflect the strain softening characteristics of the dynamic deformation process of rock, and have obvious rationality and superiority.

[0276] The invention provides a method for establishing a dynamic triaxial statistical damage constitutive model for rock under high confining pressure and high strain rate. The invention aims at the nonlinear deformation mechanical characteristics of deep rock under high confining pressure and high strain rate conditions, considers the nonlinear influence of rock dynamic strain rate on rock strength based on actual engineering background, introduces nonlinear Mohr-Coulomb and Hoek-Brown strength criteria, and derives a nonlinear rock dynamic strength criterion considering strain rate effect based on the strength criterion of rock uniaxial dynamic strength and strain rate dependence of thermal activation and viscosity mechanism, so as to provide a theoretical basis for constructing a rock dynamic statistical damage constitutive relationship, establish a rock micro-element strength measurement method capable of reflecting the dynamic deformation characteristics of rock, introduce statistical damage theory into the rock dynamic constitutive model, propose a model parameter calculation method, and establish a rock dynamic triaxial statistical damage constitutive model accordingly. On this basis, through comparative analysis with corresponding rock dynamic triaxial test data, the calculated model theoretical curve can better simulate the nonlinear deformation process of rock under dynamic load, which shows the rationality of the method. The invention also analyzes that under the same confining pressure, the deformation behavior of rock will show significant differences due to the change of strain rate. Specifically, as the strain rate increases, the strength of the rock increases accordingly, and this trend is consistent with the actual geological phenomenon. This change trend verifies the rationality of the model's theoretical curve and provides strong support for the understanding of the dynamic deformation process of rocks; finally, based on the established dynamic triaxial statistical damage constitutive model, two distribution functions, Harris distribution and Gaussian distribution, are introduced to carry out sensitivity analysis of the dynamic triaxial statistical damage constitutive model of rocks. By comparing with the existing Weibull distribution model, the influence of different micro-element strength probability distribution forms on the model curve is analyzed.

[0277] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for establishing a dynamic triaxial statistical damage constitutive model of rock, characterized in that: The steps include: Step S1, introducing nonlinear Mohr-Coulomb and Hoek-Brown strength criteria, based on the rock dynamic strength and strain rate-dependent strength criteria of thermal activation and viscosity mechanisms, and establishing a nonlinear rock dynamic strength criterion considering strain rate effect; Step S2, calculating the rock dynamic yield strength parameters, and verifying the rationality of the nonlinear dynamic strength criterion in combination with the test data; Step S3, constructing a rock micro-element strength measurement method that can reflect the dynamic deformation characteristics of rock, and introducing statistical damage theory into the dynamic constitutive model of rock; Step S4, establishing a rock dynamic triaxial statistical damage constitutive model for simulating the dynamic deformation process of rock, and proposing a calculation formula for constitutive model parameters; Step S5, verifying the rationality of the rock dynamic triaxial statistical damage constitutive model by comparative analysis with rock dynamic triaxial test data; Step S6, based on the existing Weibull distribution function that describes the strength of rock micro-element, two probability density functions, Harris distribution and Gaussian distribution, are introduced, the influence of different probability density distribution function forms on the curve of the dynamic triaxial statistical damage constitutive model of rock is considered, and the sensitivity analysis of the dynamic triaxial statistical damage constitutive model of rock is carried out.

2. The method according to claim 1, characterized in that In step S1, a nonlinear rock dynamic strength criterion considering the strain rate effect is established, which specifically includes: The dynamic strength-strain rate relationship criterion of rock based on thermal activation and viscosity mechanism is established and expressed as follows: Where, Y is the uniaxial dynamic strength of rock; is the uniaxial dynamic strain rate of rock; is the uniaxial limiting strain rate of rock; b is the maximum amplitude of the contribution of macro viscosity to strength growth; is the strain rate corresponding to the inflection point of the semi-logarithmic curve of rock strength-strain rate; T is the starting temperature of the rock material; C1, C2, n are material constants; The nonlinear Mohr-Coulomb criterion is introduced and expressed as follows: In the formula, σ1 and σ3 represent the maximum and minimum principal stresses of rock respectively; c is the static cohesion of rock; is the internal friction angle; σ c It represents the uniaxial compressive strength of rock; When 0≤σ3≤σ c When σ3=0, the cohesion of rock under uniaxial compression condition is expressed as follows: Substituting the uniaxial static stress σ1 in equation (4) with the uniaxial dynamic stress Y in equation (1), we can obtain the dynamic cohesion c d , expressed by the following formula: Let c = c d , substituted into formula (2), the dynamic strength criterion of rock under complex stress conditions is obtained: 1d , expressed by the following formula: Formula (6) needs to meet the rock strength standard under static conditions, and we get: Comparing equation (2) and equation (7), we get: Substituting formula (8) into formula (6), we get: Taking the temperature T as a constant and letting A1 = C2T, substituting it into equation (9), we get the nonlinear dynamic strength standard, which is expressed as follows: in: When σ3 ≥ σ c When σ3 = 0, substitute into formula (3), the cohesion of rock under uniaxial compression condition is expressed as follows: Substituting the uniaxial static stress σ1 in equation (14) with the uniaxial dynamic stress Y, we can obtain the dynamic cohesion, which is: Let c = c d , and substitute it into formula (3), we get the dynamic strength criterion of rock under complex stress conditions, namely: Formula (16) must meet the rock strength standard under static conditions, that is: σ1=σ3+C1 (17) Comparing equation (3) and equation (17), we get: Substituting formula (18) into formula (16), we get: Considering the temperature T as a constant, let A2 = C2T and substitute it into equation (19), we can obtain the nonlinear dynamic strength standard, which is expressed as follows: in: Introducing the failure criterion based on Hoek-Brown, we can obtain: In the formula, σ1 and σ3 are the maximum and minimum principal stresses of rock respectively; m and s are constants related to rock characteristics; Let σ3 = 0 and substitute it into equation (2), and we get s under uniaxial compression of rock, which is expressed as: Substituting the uniaxial static stress σ1 in equation (23) with the uniaxial dynamic stress Y, we can obtain the dynamic s d , that is: Let s = s d , and substitute it into formula (22), the dynamic strength criterion of rock under complex stress state is obtained, which is expressed as: Formula (25) must meet the rock strength standard under static conditions, that is: Comparing equation (22) and equation (26), we get: Substituting formula (27) into formula (25), we get: Considering the temperature T as a constant, let A3 = C2T and substitute it into equation (28), we can obtain the nonlinear dynamic strength standard, which is expressed as follows: α3＝m (30) 3. The method according to claim 2, characterized in that In step S2, the dynamic yield strength parameters of the rock are calculated and combined with the test data to verify the nonlinear dynamic strength criterion, which specifically includes: Combined with the test data, the yield strength of rock under different confining pressure conditions is determined. The static yield strength index of rock is calculated by nonlinear fitting of static stress-strain curve. The dynamic yield stress of rock is obtained by studying the dynamic stress-strain curve of rock under different confining pressures and loading rates. The dynamic yield strength of rock under different confining pressures is fitted by using equations (10), (20) and (29), and the dynamic yield strength parameters of rock under different strength standards are obtained. The static and dynamic yield strength parameters are substituted into equations (10), (20) and (29) to construct the dynamic strength curves of rock under different confining pressures and different strength criteria, and verify the rationality of the nonlinear dynamic strength criterion.

4. The method according to claim 3, characterized in that Step S3 specifically includes: On the basis of Lemaitre strain equivalence hypothesis, the rock under dynamic loading is regarded as two parts: damaged and undamaged. It is further assumed that the rock no longer has bearing capacity after being damaged, and all loads are borne by the undamaged rock. The dynamic damage model of rock is constructed, which is expressed by the following formula: 0≤σ3≤σ c s id =σ′ id (1-D d ),i=1.2or3 (32) In the formula, σ id is the dynamic macroscopic nominal stress of rock, σ id is the dynamic effective stress of rock, D d is the rock dynamic damage variable or damage factor; Due to σ id is the stress on the undamaged part of the rock. Assuming that the undamaged part of the rock obeys the generalized Hooke's law, then: In the formula, E d and μ d are the dynamic elastic modulus and dynamic Poisson’s ratio of rock, respectively; is the microscopic strain of the undamaged part of the material; i, j, k = 1, 2, 3 or 2, 3, 1 or 3, 2, 1; Since damaged and undamaged materials are closely intermixed, their deformation is considered to be a synergistic relationship, namely: In the formula, ε i is the dynamic macroscopic strain of rock. Substituting equations (32) and (34) into equation (33), we get: s id =E d e i (1-D d )+μ d (s jd +s kd ) (35) Assuming that the rock micro-element strength or rock micro-element failure obeys Weibull distribution, its probability density function is expressed as: P(F)=m / F0(F / F0) m-1 exp[-(F d / F0) m ] (36) Where, F is the distribution variable of the infinitesimal destruction Weibull distribution, m and F0 are the Weibull distribution parameters; The damage variable is: The dynamic statistical damage evolution model of rock is expressed as: The rock dynamic micro-element strength measurement method is established by equations (10), (20) and (29), which is expressed as: In the formula, σ` 1d ,σ` 3d are the maximum and minimum principal stresses of the undamaged part of the rock, respectively; the dynamic micro-element strength F of the rock is converted into d It is expressed as:

5. The method according to claim 4, characterized in that Step S4 specifically includes: Based on the rock dynamic damage model and damage evolution model, equation (38) is substituted into equation (35) to obtain the rock dynamic triaxial statistical damage constitutive model describing the dynamic deformation of rock, which is expressed as follows: The dynamic triaxial statistical damage constitutive model of rock contains multiple parameters for simulating the dynamic deformation process of rock. The parameters are determined by the following method: Constitutive model based on nonlinear Mohr-Coulomb criterion: When 0≤σ3≤σ c When the conventional dynamic triaxial test is usually performed with constant confining pressure, that is, σ 2d =σ 3d =σ3, σ3 is the static confining pressure, the first formula in equation (45) is rewritten as: s 1d =E d e i exp[-(F d / F0) m ]+2m d p3 (46) Among them, F d From equation (42) and let σ 2d =σ 3d =σ3, which is expressed by the following formula: According to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, formula (47) yields: In the formula, σ 1dc , ε 1dc They are respectively the dynamic stress and dynamic strain at the peak of the conventional rock dynamic triaxial stress-strain curve measured by the test curve; In addition, the peak stress σ 1dc and strain ε 1dc Satisfies formula (46), that is: s 1dc =E d e 1dc exp[-(F dc / F0) m ]+2m d p3 (49) Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (47), we get: Combining equation (48) and equation (49), we get: When σ3 ≥ σ c When the conventional dynamic triaxial test is usually performed with constant confining pressure, that is, σ 2d =σ 3d =σ3, σ3 is the static confining pressure, the first formula in equation (45) is rewritten as: s 1d =E d e i exp[-(F d / F0) m ]+2m d p3 (46) Among them, F d From equation (43) and let σ 2d =σ 3d =σ3, which is expressed by the following formula: According to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, formula (46) gives: In the formula, σ 1dc , ε 1dc They are respectively the dynamic stress and dynamic strain at the peak of the conventional rock dynamic triaxial stress-strain curve measured by the test curve; In addition, the peak stress σ 1dc and strain ε 1dc Satisfies formula (46), that is: s 1dc =E d e 1dc exp[-(F dc / F0) m ]+2m d p3 (49) Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (53), we get: Combining equation (48) and equation (49), we get: Constitutive model based on nonlinear Hoek-Brown criterion: Since conventional dynamic triaxial tests are usually conducted with constant confining pressure, i.e., σ 2d =σ 3d =σ3, σ3 is the static confining pressure, the first formula in equation (45) is rewritten as: s 1d =E d e i exp[-(F d / F0) m ]+2m d p3 (46) Among them, F d From equation (43) and let σ 2d =σ 3d =σ3, which is expressed by the following formula: According to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, formula (46) gives: In the formula, σ 1dc , ε 1dc They are respectively the dynamic stress and dynamic strain corresponding to the peak point of the conventional rock dynamic triaxial stress-strain curve, obtained from the test curve; In addition, the peak stress σ 1dc and strain ε 1dc Satisfies formula (46), that is: s 1dc =E d e 1dc exp[-(F dc / F0) m ]+2m d p3 (49) Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (57), we get: Combining equation (48) and equation (49), we get: Among them, D d σ 1d =σ 1dc and ε i =ε 1dc Substitute into equation (35) and let σ 2d =σ 3d =σ3, which is expressed as follows: Formula (51) and (52), formula (55) and (56), formula (59) and (60) are the methods for determining parameters m and F0; Through conventional rock dynamic triaxial test, the peak stress σ` of the rock dynamic triaxial dynamic stress-strain curve is obtained. 1dc , strain ε` 1dc ,but: s 1dc =s` 1dc +σ3 (62) e 1dc =e` 1dc +e c (63) In the formula, ε c The rock specimen is subjected to hydrostatic pressure σ3, that is, the axial stress σ 1d Initial strain generated by loading to confining pressure σ3; σ` 1dc , ε` 1dc It is directly obtained from the stress and strain at the peak point of the test curve; Assuming that the rock is not damaged under hydrostatic pressure, according to the second formula in equation (45), σ 1d =σ 2d =σ 3d =σ3 to obtain the method for determining the initial strain, namely: e c =(1-2m d )σ3 / E d (64).

6. The method according to claim 5, characterized in that In step S5, the rationality of the dynamic triaxial statistical damage constitutive model of rock is verified, which specifically includes: Combined with the test data and test curves, the parameter values ​​under different confining pressure conditions and strain rate conditions are calculated according to the test data and theoretical formulas. The theoretical curve of the dynamic triaxial statistical damage constitutive model of rock is obtained according to the parameter values. The curve is compared and analyzed with the test curve to verify the rationality of the dynamic triaxial statistical damage constitutive model of rock, and the calculated parameter values ​​are analyzed.

7. The method according to claim 6, characterized in that In step S6, two probability density functions, Harris distribution and Gaussian distribution, are introduced to consider the influence of different probability density distribution function forms on the dynamic triaxial statistical damage constitutive model curve of rock, including: Assuming that the rock micro-element strength obeys the improved Harris probability density distribution, the rock statistical damage softening model is obtained, which is expressed by the following formula: Where D is the rock damage variable, F is the random distribution variable of micro-element strength, and a and b are model parameters greater than 0; Based on the Hoek-Brown nonlinear rock dynamic yield strength criterion, equation (43) is used to establish the following rock dynamic micro-element strength measurement method, which is expressed as follows: In the formula, σ′ 1d ,σ′ 3d are the maximum and minimum principal stresses on the undamaged part of the rock, respectively; the dynamic micro-element strength F of the rock is converted into d It is expressed as: Substituting equation (65) into equation (34), we obtain the dynamic triaxial statistical damage constitutive model of rock that can describe the dynamic deformation of rock, namely:

8. The method according to claim 7, characterized in that The parameters in the dynamic triaxial statistical damage constitutive model of rock are determined by the following method: Considering that conventional dynamic triaxial tests are usually static loads with equal confining pressure, that is, σ 2d =σ 3d =σ3, σ3 is the static confining pressure, the first formula in equation (68) can be rewritten as: Among them, F d From equation (67) and let σ 2d =σ 3d =σ3, which is expressed by the following formula: According to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, it can be obtained from formula (69): In the formula, σ 1dc , ε 1dc are the dynamic stress and dynamic strain at the peak of the conventional rock dynamic triaxial stress-strain curve, obtained from the test curve; in addition, the peak stress σ 1dc and strain ε 1dc Satisfies formula (69), that is: Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (70), we get: Combining equation (71) and equation (72), we get: Assume that the logarithmic Gaussian distribution method is used to describe the rock micro-element strength: In the formula, F0 and S0 are Gaussian distribution parameter damage variables, which are expressed as follows: In the formula, is the standard Gaussian distribution function, which is the established damage evolution equation; The following rock dynamic micro-element strength measurement method is established based on the Hoek-Brown nonlinear rock dynamic yield strength criterion, that is, formula (29), which is expressed as follows: Using equations (32) and (35), the rock dynamic micro-element strength F d It is expressed as: Substituting equation (77) into equation (35), the dynamic triaxial statistical damage constitutive model of rock that can reflect the dynamic deformation process of rock is obtained, which is expressed as follows: Considering that conventional dynamic triaxial tests are usually static loads with equal confining pressure, that is, σ 2d =σ 3d =σ3, σ3 is the static confining pressure, then formula (78) can be rewritten as: Among them, F d From equation (67) and let σ 2d =σ 3d =σ3, which is expressed by the following formula: According to the extreme value characteristics of the conventional rock dynamic triaxial stress-strain curve, formula (79) yields: From formula (80) and formula (81), we can get: In the formula Taking the logarithm of both sides of equation (82) and sorting them, we get: From formula (79), we get: In the formula, For the peak point of the test curve under a certain confining pressure, a Φ value is obtained by equation (85), and the corresponding X value is obtained by the Gaussian distribution function table; The parameters F0 and S0 are obtained from equations (84) and (85): F0=XS0+lnF dc (88) Among them, F dc σ 1d =σ 1dc and ε i =ε 1dc Substituting into formula (70), we get:

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