Statistical damage calculation method of rock after low-temperature freezing action

Abstract

The application discloses a kind of low-temperature frozen rock statistical damage calculation method after effect, S1: the parameter equivalent expression of frozen rock complex is constructed, and the equivalent parameter of composite microelement is obtained;S2: define statistical damage variable;S3: rock Drucker-Prager strength criterion and ice Teardrop strength criterion are converted to common stress state;S4: based on generalized Hook's law, combined with the equivalent parameter of composite microelement, composite microelement strength and statistical damage variable, the statistical damage constitutive model of frozen rock complex is established;S5: the shape parameter and scale parameter of rock statistical damage constitutive model under different freezing temperatures are solved, so as to obtain the statistical damage constitutive model for calculating the statistical damage of rock after low-temperature freezing effect.The model has higher rationality through actual test verification, can accurately reflect the deformation and failure characteristics of rock under different freezing temperatures, and has good fitting effect on the stress-strain relationship of rock sample under triaxial compression test conditions after low-temperature freezing effect.

Description

Technical Field

[0001] This invention relates to the technical field of statistical damage model calculation methods for rocks, and in particular to a method for calculating statistical damage to rocks after low-temperature freezing. Background Technology

[0002] With the further implementation of my country's Western Development Strategy, the number of tunnels and other transportation engineering projects constructed under conditions such as high altitude, extreme cold, and glacial deposits is gradually increasing. Therefore, research on the long-term stability of rock mass engineering structures in such harsh environments is becoming increasingly urgent. In practical engineering, rock mass engineering projects in cold or seasonally frozen regions are subject to long-term or intermittent low temperatures, resulting in significant differences in the strength characteristics of rocks in the frozen state compared to those at room temperature. Especially when water is present in the rock pores, this water freezes into ice under low-temperature conditions, causing stress not only to be borne by the rock itself but also by the ice. However, in actual analysis, the influence of ice in the rock pores is often overlooked, which is inconsistent with actual working conditions. Therefore, it is necessary to propose a constitutive model that conforms to the actual rock environment to provide a scientific theoretical basis for the stability assessment of rock mass engineering projects. Summary of the Invention

[0003] This invention provides a method for calculating statistical damage to rocks after low-temperature freezing, in order to overcome the technical problem that the influence of ice in rock pores is often ignored in actual analysis, which does not match the actual working conditions.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] A method for calculating statistical damage to rocks after low-temperature freezing, comprising the following steps:

[0006] S1: Construct the parameter equivalent expression of the frozen rock complex, and obtain the equivalent parameters of the composite micro-element based on the parameter equivalent expression. The frozen rock complex is a composite micro-element composed of rock and ice crystals.

[0007] S2: Define statistical damage variables and represent them as statistical functions of damage to the frozen rock complex under load;

[0008] S3: Transform the rock Drucker-Prager strength criterion and the ice Teardrop strength criterion to a common stress state to characterize the strength of the composite micro-element;

[0009] S4: Based on the generalized Hooke's law, a statistical damage constitutive model of rock after low-temperature freezing is established by combining the equivalent parameters of the composite micro-element, the strength of the composite micro-element, and the statistical damage variables. That is, the statistical damage constitutive model of the frozen rock composite.

[0010] S5: The shape and scale parameters of the statistical damage constitutive model of rocks at different freezing temperatures are obtained by using linear regression, thus obtaining the final statistical damage constitutive model of the frozen-rock complex, which is used to calculate the statistical damage of rocks after low-temperature freezing.

[0011] Furthermore, in S1, the process of obtaining the equivalent parameters of the composite micro-element based on the constructed parametric equivalent expression of the frozen rock composite is as follows:

[0012] S11: Define the equivalent bulk modulus K of the frozen rock complex. v The equivalent shear modulus G is:

[0013]

[0014] In the formula: K s and G s These are the bulk modulus and shear modulus of the rock, respectively, K. i and G i These are the bulk modulus and shear modulus of ice, φ, respectively. s and φ i Let φ be the volume fractions of rock and ice, respectively, and satisfy the relationship: φ s +φ i =1;

[0015] S12: The relationship between the elastic modulus E and Poisson's ratio v of the frozen rock complex is defined as follows:

[0016]

[0017] S13: Combining formulas (1) and (2), we obtain the equivalent elastic modulus E and equivalent Poisson's ratio v of the frozen rock composite, expressed as:

[0018]

[0019] In the formula: E s and v s These are the elastic modulus and Poisson's ratio of the rock, respectively; E i and v i These are the elastic modulus and Poisson's ratio of ice, respectively.

[0020] Furthermore, in S2, the process of defining statistical damage variables and representing them as statistical functions of damage to the frozen rock complex under load is as follows:

[0021] S21: Assume the stress level distribution of the frozen rock complex follows a Weibull distribution function, then the probability density function P(x) is:

[0022]

[0023] In the formula: x is the random distribution variable of the intensity of the infinitesimal element with respect to the Weibull distribution function; m and k are the shape parameter and scale parameter with respect to the Weibull distribution function, respectively;

[0024] S22: Let N be the cumulative number of failures in the frozen-rock complex under a certain stress level. f (P) is:

[0025]

[0026] S23: During the loading process of rock, when the strength F of the composite micro-element exceeds a certain strength value, the damage state of the frozen rock composite is the cumulative failure number N of the composite micro-element. f The ratio of (P) to the total number of composite micro-elements N, i.e.:

[0027]

[0028] S24: Combining formulas (6) and (7), we obtain the statistical damage variable D, expressed as:

[0029]

[0030] Furthermore, in S3, the process of transforming the rock Drucker-Prager strength criterion and the ice Teardrop strength criterion to a common stress state to characterize the strength of the composite micro-element is as follows:

[0031] S31: Introducing the Drucker-Prager strength criterion for rocks to characterize the micro-element stress level F of rocks. s , is represented as:

[0032]

[0033] In the formula: The internal friction angle of the complex; I1 and J2 are the first invariant of the stress tensor and the second invariant of the stress deviator, respectively; σ * Indicates effective stress; f s Indicates the rock stress level;

[0034] The expressions for the first invariant of the stress tensor and the second invariant of the stress deviator are as follows:

[0035]

[0036] In the formula: These are the normal stresses in the x, y, and z directions, respectively, in MPa.

[0037] These are the maximum principal stress, intermediate principal stress, and minimum principal stress in the effective stress characterizing the strength of the composite micro-element, respectively, in MPa;

[0038] S32: Based on the triaxial compression test condition σ2=σ3, we can obtain:

[0039]

[0040] S33: Introducing the ice teardrop strength criterion to characterize the micro-element stress level F of ice. i , is represented as:

[0041]

[0042] in:

[0043]

[0044] In the formula, p is the mean stress; q is the deviatoric stress, which in a conventional triaxial test is q = σ1 - σ3; α = tanθ, where θ is half the tail angle of the curve; β is the equilibrium phase transition pressure of ice at a given temperature, in MPa; σ t σ is the reference tensile strength of ice at a given temperature, in MPa; i , i = 1, 2, 3, are the principal stresses in the three directions representing the nominal stress characterizing the strength of the composite micro-element;

[0045] S34: Transform the ice Teardrop strength criterion expression to a stress state common to the rock Drucker-Prager strength criterion, including:

[0046] make

[0047]

[0048] Substituting (15) and (16) into (14), we get

[0049]

[0050] S35: Based on the micro-element stress level F of the transformed ice i And the micro-element stress level F of the rock s Establish an expression characterizing the strength of a composite infinitesimal element, including:

[0051]

[0052] Substituting formulas (12) and (13) into formula (18), we obtain formula (19):

[0053]

[0054] Furthermore, in S4, based on the generalized Hooke's law, and combining the equivalent parameters of the composite micro-element, the strength of the composite micro-element, and the statistical damage variables, the process of establishing the statistical damage constitutive model of the rock after low-temperature freezing, i.e., the statistical damage constitutive model of the frozen-rock composite, is as follows:

[0055] S41: Establish the transformation relationship between nominal stress and effective stress, which characterizes the strength of a composite micro-element, expressed as:

[0056]

[0057] In the formula, [σ] is the nominal stress matrix, [σ] * [D] is the effective stress matrix, and [D] is the damage matrix;

[0058] S42: Since the effective stress of the rock satisfies the generalized Hooke's law, and its strain is equivalent in all directions, we obtain:

[0059]

[0060] In the formula: E is the equivalent elastic modulus of the frozen rock composite, v is the equivalent Poisson's ratio of the frozen rock composite, and ε i * For effective strain, ε i For nominal strain; i = 1, j = 2, k = 3;

[0061] S43: Substituting formulas (8) and (20) into formula (21), we get:

[0062]

[0063] In the formula, F is the strength of the composite element; m and k are the shape parameter and scale parameter with respect to the Weibull distribution function, respectively;

[0064] S44: Substituting formulas (3), (4), and (18) into formula (22) and rearranging, we obtain the statistical damage constitutive model of the frozen rock complex as follows:

[0065]

[0066] Furthermore, in S5, the process of obtaining the shape and scale parameters of the statistical damage constitutive model of the frozen-rock complex at different temperatures using linear regression is as follows:

[0067] S51: Based on the triaxial compression test condition σ2=σ3, for ease of calculation, equation (23) is written in the following form:

[0068]

[0069] By rearranging and transforming equation (24), we can obtain:

[0070]

[0071] Taking the logarithm of both sides of equation (25) yields:

[0072]

[0073] Taking the logarithm of both sides of equation (26) again, we get:

[0074]

[0075] in:

[0076] make

[0077] X = lnK (30)

[0078] b = lna (31)

[0079] Equation (27) can be simplified to:

[0080] Y = mX + b (32)

[0081] S52: The shape parameter m can be obtained by performing linear regression, and the scale parameter k can be obtained by using equation (33). Equation (33) is:

[0082]

[0083] Beneficial Effects: This invention proposes a method for calculating the statistical damage of rocks after cryogenic freezing. By assuming that the structural distribution of the frozen-rock complex follows a Weibull distribution function, the parameters of ice and rock are equivalentized. Furthermore, the Drucker-Prager strength criterion of rock and the Teardrop strength criterion of ice are transformed to a common stress state, constructing a constitutive model of statistical damage for the frozen-rock complex that reflects the actual stress-strain process of rocks after cryogenic freezing. This model is used to calculate the statistical damage of rocks after cryogenic freezing. Actual experimental verification shows that this model has high rationality, accurately reflects the deformation and failure characteristics of rocks at different freezing temperatures, and has a good fitting effect on the stress-strain relationship of rock samples after cryogenic freezing under triaxial compression test conditions. Attached Figure Description

[0084] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0085] Figure 1 This is a flowchart of a method for calculating statistical damage to rocks after low-temperature freezing, as described in this invention.

[0086] Figure 2 The image shows the triaxial stress-strain curve of sandstone under low-temperature freezing in an embodiment of the present invention.

[0087] Figure 3 This is a comparison chart of the experimental curve and the theoretical curve under a confining pressure of 4MPa at T=0℃ in an embodiment of the present invention.

[0088] Figure 4 This is a comparison chart of the experimental curve and the theoretical curve under a confining pressure of 4MPa at T = -10℃ in an embodiment of the present invention.

[0089] Figure 5 This is a comparison chart of the experimental curve and the theoretical curve under a confining pressure of 4MPa at T = -20℃ in an embodiment of the present invention.

[0090] Figure 6 The graph shows the variation of parameters m and k with temperature in the statistical damage constitutive model of the frozen rock complex in an embodiment of the present invention. Detailed Implementation

[0091] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0092] This embodiment provides a method for calculating statistical damage to rocks after low-temperature freezing, such as... Figure 1 As shown, the specific steps include:

[0093] S1: Construct the parameter equivalent expression of the frozen rock complex, and obtain the equivalent parameters of the composite micro-element based on the parameter equivalent expression. The frozen rock complex is a composite micro-element composed of rock and ice crystals.

[0094] In a specific embodiment, in S1, the process of obtaining the equivalent parameters of the composite micro-element based on the constructed parametric equivalent expression of the frozen rock composite is as follows:

[0095] S11: Based on the classical mixing law of composite material theory, rock particles are used as the framework and ice crystals as the filler to couple and obtain the constitutive relation of the frozen-rock composite. The equivalent bulk modulus K of the frozen-rock composite is defined. v The equivalent shear modulus G is:

[0096]

[0097] In the formula: K s and G s These are the bulk modulus and shear modulus of the rock, respectively, K. i and G i These are the bulk modulus and shear modulus of ice, φ, respectively. s and φ i Let φ be the volume fractions of rock and ice, respectively, and satisfy the relationship: φ s +φ i =1;

[0098] S12: The relationship between the elastic modulus E and Poisson's ratio v of the frozen rock complex is defined as follows:

[0099]

[0100] S13: Combining formulas (1) and (2), we obtain the equivalent elastic modulus E and equivalent Poisson's ratio v of the frozen rock composite, expressed as:

[0101]

[0102] In the formula: E s and v s These are the elastic modulus and Poisson's ratio of the rock, respectively; E i and v i These are the elastic modulus and Poisson's ratio of ice, respectively.

[0103] S2: Define statistical damage variables and represent them as statistical functions of damage to the frozen rock complex under load;

[0104] In a specific embodiment, S2, the process of defining statistical damage variables and representing them as statistical functions of damage to the frozen rock composite under load is as follows:

[0105] S21: Assume the stress level distribution of the frozen rock complex follows a Weibull distribution function, then the probability density function P(x) is:

[0106]

[0107] In the formula: x is the random distribution variable of the intensity of the infinitesimal element with respect to the Weibull distribution function; m and k are the shape parameter and scale parameter with respect to the Weibull distribution function, respectively;

[0108] S22: Let N be the cumulative number of failures in the frozen-rock complex under a certain stress level. f (P) is:

[0109]

[0110] S23: During the loading process of rock, when the strength F of the composite micro-element exceeds a certain strength value, the continuous cumulative failure of the composite micro-element will cause a decrease in the performance of the frozen rock composite and damage will occur. The damage state of the frozen rock composite is the cumulative failure number N of the composite micro-element. f The ratio of (P) to the total number of composite micro-elements N, i.e.:

[0111]

[0112] S24: Combining formulas (6) and (7), we obtain the statistical damage variable D, expressed as:

[0113]

[0114] S3: Transform the rock Drucker-Prager strength criterion and the ice Teardrop strength criterion to a common stress state to characterize the strength of the composite micro-element;

[0115] In a specific embodiment, S3, the process of converting the rock Drucker-Prager strength criterion and the ice Teardrop strength criterion to a common stress state to characterize the strength of the composite micro-element is as follows:

[0116] S31: Introducing the Drucker-Prager strength criterion for rocks to characterize the micro-element stress level F of rocks. s , is represented as:

[0117]

[0118] In the formula: The internal friction angle of the complex; I1 and J2 are the first invariant of the stress tensor and the second invariant of the stress deviator, respectively; σ * Indicates effective stress; f s Indicates the rock stress level;

[0119] The expressions for the first invariant of the stress tensor and the second invariant of the stress deviator are as follows:

[0120]

[0121] In the formula: These are the normal stresses in the x, y, and z directions, respectively, in MPa. These are the maximum principal stress, intermediate principal stress, and minimum principal stress in the effective stress characterizing the strength of the composite micro-element, respectively, in MPa;

[0122] S32: Based on the triaxial compression test condition σ2=σ3, we can obtain:

[0123]

[0124] S33: Introducing the ice teardrop strength criterion to characterize the micro-element stress level F of ice. i , is represented as:

[0125]

[0126] in:

[0127]

[0128] In the formula, p is the mean stress; q is the deviatoric stress, which in a conventional triaxial test is q = σ1 - σ3; α = tanθ, where θ is half the tail angle of the curve; β is the equilibrium phase transition pressure of ice at a given temperature, in MPa; σ t σ is the reference tensile strength of ice at a given temperature, in MPa; i , i = 1, 2, 3, are the principal stresses in the three directions representing the nominal stress characterizing the strength of the composite micro-element;

[0129] S34: Transform the ice Teardrop strength criterion expression to a stress state common to the rock Drucker-Prager strength criterion, including:

[0130] make

[0131]

[0132] Substituting (15) and (16) into (14), we get

[0133]

[0134] S35: Based on the micro-element stress level F of the transformed ice i And the micro-element stress level F of the rock s Establish an expression characterizing the strength of a composite infinitesimal element, including:

[0135]

[0136] Substituting formulas (12) and (13) into formula (18), we obtain formula (19):

[0137]

[0138] S4: Based on the generalized Hooke's law, a statistical damage constitutive model of rock after low-temperature freezing is established by combining the equivalent parameters of the composite micro-element, the strength of the composite micro-element, and the statistical damage variables. That is, the statistical damage constitutive model of the frozen rock composite.

[0139] In a specific embodiment, in S4, based on the generalized Hooke's law, and combining the equivalent parameters of the composite micro-element, the strength of the composite micro-element, and the statistical damage variables, a statistical damage constitutive model of the rock after low-temperature freezing is established. That is, the process of establishing the statistical damage constitutive model of the frozen-rock composite is as follows:

[0140] S41: Establish the transformation relationship between nominal stress and effective stress, which characterizes the strength of a composite micro-element, expressed as:

[0141]

[0142] In the formula, [σ] is the nominal stress matrix, [σ] * [D] is the effective stress matrix, and [D] is the damage matrix;

[0143] S42: Since the effective stress of the rock satisfies the generalized Hooke's law, and its strain is equivalent in all directions, we obtain:

[0144]

[0145] In the formula: E is the equivalent elastic modulus of the frozen-rock composite, and v is the equivalent Poisson's ratio of the frozen-rock composite. For effective strain, ε i For nominal response;

[0146] S43: Substituting formulas (8) and (20) into formula (21), we get:

[0147]

[0148] In the formula, F is the strength of the composite element; m and k are the shape parameter and scale parameter with respect to the Weibull distribution function, respectively;

[0149] S44: In this embodiment, to facilitate calculation, formulas (18), (3), and (4) are substituted into formula (22), and the statistical damage constitutive model of the frozen rock complex is obtained as follows:

[0150]

[0151]

[0152] S5: The shape and scale parameters of the statistical damage constitutive model of rocks at different freezing temperatures are obtained by using linear regression, thus obtaining the final statistical damage constitutive model of the frozen-rock complex, which is used to calculate the statistical damage of rocks after low-temperature freezing.

[0153] In a specific embodiment, S5, the process of obtaining the shape and scale parameters of the statistical damage constitutive model of the frozen-rock complex at different temperatures using linear regression is as follows:

[0154] S51: Based on the triaxial compression test condition σ2=σ3, for ease of calculation, equation (23) is written in the following form:

[0155]

[0156] By rearranging and transforming equation (24), we can obtain:

[0157]

[0158] Taking the logarithm of both sides of equation (25) yields:

[0159]

[0160] Taking the logarithm of both sides of equation (26) again, we get:

[0161]

[0162] in:

[0163] make

[0164] X = lnK (30)

[0165] b = lna (31)

[0166] Equation (27) can be simplified to:

[0167] Y = mX + b (32)

[0168] S52: The shape parameter m can be obtained by performing linear regression, and the scale parameter k can be obtained by using equation (33). Equation (33) is:

[0169]

[0170] Specifically, the shape and scale parameters in the statistical damage constitutive model of rocks differ at different freezing temperatures. Therefore, in practical applications, it is necessary to substitute the corresponding shape and scale parameters into the statistical damage constitutive model in the form of a Weibull function according to the specific freezing temperature, and then use it to calculate the statistical damage of rocks after low-temperature freezing and to solve for the stress-strain curve.

[0171] In this embodiment, the rationality of the statistical damage constitutive model of the final frozen-rock composite is verified by conducting a low-temperature freezing triaxial compression test. The specific steps are as follows:

[0172] a. Determination of basic parameters: Measure the porosity and water content of the rock sample;

[0173] b. Moisture content setting: Place the rock sample in a vacuum saturator and perform vacuuming for 2 hours and saturation for 24 hours to bring the rock sample to the saturated moisture content state. Then place the saturated standard rock sample in an oven to dry to the set moisture content.

[0174] c. Low-temperature treatment: The standard rock sample is frozen at a low temperature T and held for several hours;

[0175] d queries the mechanical parameters E of ice at freezing temperature T. i G i v i ; Calculate the volume fraction φ of rock and ice. s and φ i The stress-strain curves and mechanical parameters of rock samples were measured at a freezing temperature T; the mechanical parameters included the internal friction angle of the rock sample. Initiation stress-strain (σ) ci , ε ci ) and peak stress-strain (σ c , ε c );

[0176] e. Substitute the mechanical parameters of rock and ice from step d into the final statistical damage constitutive model of the frozen-rock complex to verify the rationality of the final statistical damage constitutive model of the frozen-rock complex.

[0177] Specifically, in this embodiment, under the same confining pressure, rock performance tests were conducted at temperatures set to 0℃, -10℃, and -20℃, and the test results were plotted as curves. Simultaneously, the measured data parameters were substituted into the established statistical damage constitutive model of the frozen rock complex to obtain the frozen rock performance curve obtained through the model. The curve plotted based on the experimental results was compared with the performance curve obtained through the statistical damage constitutive model of the frozen rock complex, thereby verifying the rationality of the established model.

[0178] Specifically, in the triaxial compression test of the rock under low-temperature freezing, the rock temperature was set to 0℃, -10℃, and -20℃ respectively to obtain the rock's performance under different temperature conditions. The external load was set to 4MPa, and the calculated model parameters are shown in the table below:

[0179] 0 5435 407 0.201 0.023 31.04 0.712 44.45 4 -10 5932 559 0.219 0.035 31.04 1.088 63.75 4 -20 6059 1319 0.227 0.041 31.04 1.552 72.05 4

[0180] The stress-strain model calculation curves were obtained based on the statistical damage constitutive model of the frozen rock complex, and compared with the experimental curves, such as... Figure 3 , Figure 4 and Figure 5 As shown in the figure, the theoretical values ​​calculated by the statistical damage constitutive model of the frozen rock complex constructed in this invention are not significantly different from the experimental values, fully reflecting the trend in the post-peak stage.

[0181] In constructing the statistical damage constitutive model, all parameters were obtained from macroscopic rock mechanical test data, and each parameter has a certain physical meaning. To study the influence of freezing temperature on the Weibull distribution parameters, the data in the table above were analyzed, yielding the curves showing the variation of the Weibull distribution function parameters m and k in the constitutive equation with temperature and cycle number, as shown below. Figure 6 As shown, it can be seen that the values ​​of m and k both increase with increasing temperature and number of cycles. However, for the strength of rock micro-elements following a Weibull distribution, the physical meaning of parameter m is an indicator of the rock's brittleness, according to... Figure 3 , Figure 4 and Figure 5 Verification shows that the larger the value of m, the stronger the brittleness. The physical meaning of the parameter k can be understood as an indicator of the macroscopic strength of the rock. As the temperature decreases, the peak strength of the rock increases, such as... Figure 2 As shown, the value of k also shows an increasing trend at this time. Meanwhile, according to... Figure 6 The increasing trend of the m value indicates that the low temperature effect leads to a gradual increase in the brittleness and macroscopic strength of the sandstone, which is consistent with the actual deformation and failure characteristics observed in the experiment.

[0182] The beneficial effects of this invention are as follows:

[0183] 1. The ice-rock coupling effect during the rock loading process under low temperature was considered, and the solution process for equivalence of ice and rock parameters was established;

[0184] 2. Assuming that the strength of the composite micro-element subjected to low-temperature freezing follows the Weibull distribution, a statistical damage constitutive model of rock under the common stress state was established using the Drucker-Prager strength criterion and the Teardrop strength criterion.

[0185] 3. The theoretical values ​​calculated by the constructed statistical damage constitutive model are not much different from the experimental values, which fully reflects the trend in the post-peak stage and can better reflect the stress-strain relationship of rocks after different freezing temperatures.

[0186] In summary, this invention reveals the stress-strain relationship of rock after low-temperature treatment by constructing a statistical damage constitutive model of frozen rock complex, providing a scientific basis for stability evaluation of geotechnical engineering in cold regions.

[0187] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating statistical damage to rocks after low-temperature freezing, characterized in that, The specific steps include: S1: Construct the parameter equivalent expression of the frozen rock complex, and obtain the equivalent parameters of the composite micro-element based on the parameter equivalent expression. The frozen rock complex is a composite micro-element composed of rock and ice crystals. S2: Define statistical damage variables and represent them as statistical functions of damage to the frozen rock complex under load; S3: Transform the rock Drucker-Prager strength criterion and the ice Teardrop strength criterion to a common stress state to characterize the strength of the composite micro-element; In S3, the process of transforming the rock Drucker-Prager strength criterion and the ice Teardrop strength criterion to a common stress state to characterize the strength of the composite micro-element is as follows: S31: Introducing the Drucker-Prager strength criterion for rocks to characterize the micro-element stress level of rocks. , represented as: (9) In the formula: , The internal friction angle of the complex; , These are the first invariant of the stress tensor and the second invariant of the stress deviator, respectively; Indicates effective stress; Indicates the rock stress level; The expressions for the first invariant of the stress tensor and the second invariant of the stress deviator are as follows: (10) (11) In the formula: , , These are the normal stresses in the x, y, and z directions, respectively, in MPa. These are the maximum principal stress, intermediate principal stress, and minimum principal stress in the effective stress characterizing the strength of the composite micro-element, respectively, in MPa; S32: According to the triaxial compression test conditions = ,get: (12) (13) In the formula: E This is the equivalent elastic modulus of the frozen rock complex. v It is the equivalent Poisson's ratio; For nominal response; S33: Introducing the ice teardrop strength criterion to characterize the micro-element stress level of ice. , represented as: (14) in: ; ； In the formula, The average stress; For deviatoric stress, in conventional triaxial tests, ; , It is half the tail angle of the curve; It is the equilibrium phase transition pressure of ice at a given temperature, and its unit is MPa; The reference tensile strength of ice at a given temperature, in MPa; These are the principal stresses in three directions representing the nominal stress that characterizes the strength of the composite micro-element; S34: Transform the ice Teardrop strength criterion expression to a stress state common to the rock Drucker-Prager strength criterion, including: make (15) (16) Substituting (15) and (16) into (14), we get (17) S35: Micro-element stress level based on the transformed ice and the micro-element stress level of the rock Establish an expression characterizing the strength of a composite infinitesimal element, including: (18) Substituting formulas (12) and (13) into formula (18), we obtain formula (19): (19) S4: Based on the generalized Hooke's law, a statistical damage constitutive model of rock after low-temperature freezing is established by combining the equivalent parameters of the composite micro-element, the strength of the composite micro-element, and the statistical damage variables. That is, the statistical damage constitutive model of the frozen rock composite. S5: The shape and scale parameters of the statistical damage constitutive model of rocks at different freezing temperatures are obtained by using linear regression, thus obtaining the final statistical damage constitutive model of the frozen-rock complex, which is used to calculate the statistical damage of rocks after low-temperature freezing.

2. The method for calculating statistical damage to rocks after low-temperature freezing according to claim 1, characterized in that, In S1, the process of obtaining the equivalent parameters of the composite micro-element based on the constructed parametric equivalent expression of the frozen rock composite is as follows: S11: Define the equivalent bulk modulus of the frozen rock complex. and equivalent shear modulus G for: (1) In the formula: and These are the bulk modulus and shear modulus of the rock, respectively. and These are the bulk modulus and shear modulus of ice, respectively. and Let be the volume fractions of rock and ice, respectively, and satisfy the following relationship: ; S12: Set the elastic modulus of the frozen rock complex E Compared to Poisson The relationship between them is: (2) S13: Combining formulas (1) and (2), the equivalent elastic modulus of the frozen rock composite is obtained. E and equivalent Poisson ratio v The expression is: (3) (4) In the formula: and These are the elastic modulus and Poisson's ratio of the rock, respectively. and These are the elastic modulus and Poisson's ratio of ice, respectively.

3. The method for calculating statistical damage to rocks after low-temperature freezing according to claim 2, characterized in that, In S2, the process of defining statistical damage variables and representing them as statistical functions of damage to the frozen rock composite under load is as follows: S21: Assume the horizontal stress distribution of the frozen rock complex follows a Weibull distribution function, then the probability density function is... for: (5) In the formula: x Let the intensity of the infinitesimal element be a random distribution variable with respect to the Weibull distribution function; m and k These are the shape and scale parameters of the Weibull distribution function, respectively. S22: Define the cumulative number of failures in the frozen-rock complex under a certain stress level. for: (6) S23: During the loading process of rock, when the strength of the composite micro-element... When a certain strength value is exceeded, the damage state of the frozen rock composite is the cumulative number of failures of the composite micro-elements. Total number of composite micro-elements N The ratio, that is: (7) S24: By combining formulas (6) and (7), the statistical damage variable is obtained. D , represented as: (8)。 4. The method for calculating statistical damage to rocks after low-temperature freezing according to claim 3, characterized in that, In S4, based on the generalized Hooke's law, and combining the equivalent parameters of the composite micro-element, the strength of the composite micro-element, and the statistical damage variables, a statistical damage constitutive model of the rock after low-temperature freezing is established. That is, the process of establishing the statistical damage constitutive model of the frozen-rock composite is as follows: S41: Establish the transformation relationship between nominal stress and effective stress, which characterizes the strength of a composite micro-element, expressed as: (20) In the formula, The nominal stress matrix, For the effective stress matrix, The damage matrix; S42: Since the effective stress of the rock satisfies the generalized Hooke's law, and its strain is equivalent in all directions, we obtain: (21) In the formula: E This is the equivalent elastic modulus of the frozen rock complex. The equivalent Poisson's ratio for the frozen rock complex. In order to respond effectively, For nominal response; ; S43: Substituting formulas (8) and (20) into formula (21), we get: (22) In the formula, F Strength of composite micro-element; m and k These are the shape and scale parameters of the Weibull distribution function, respectively. S44: Substituting formulas (3), (4), and (18) into formula (22) and rearranging, we obtain the statistical damage constitutive model of the frozen rock complex as follows: (23)。 5. The method for calculating statistical damage to rocks after low-temperature freezing according to claim 4, characterized in that, In S5, the process of obtaining the shape and scale parameters of the statistical damage constitutive model of the frozen-rock complex at different temperatures using linear regression is as follows: S51: According to the triaxial compression test conditions = For ease of calculation, equation (23) is written in the following form: (24) Rearranging equation (24) yields: (25) Taking the logarithm of both sides of equation (25) yields: (26) Taking the logarithm of both sides of equation (26) again, we get: (27) in: (28) make (29) (30) (31) Equation (27) is transformed into: (32) S52: Perform linear regression to obtain the shape parameters. m Then, the scale parameter is obtained using equation (33). k Equation (33) is: (33)。

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