A method for establishing a tunnel surrounding rock creep damage model based on minimum energy consumption theory

Abstract

The application discloses a tunnel surrounding rock creep damage model establishment method based on minimum energy consumption theory and relates to the technical field of geotechnical engineering. The method comprises the following steps: S1, rock sampling is carried out at the position of a tunnel roof, the sampled rock is processed, a triaxial compression creep test is carried out, and test results are obtained; S2, a yield function based on the minimum energy consumption theory is established; S3, a damage variable based on the minimum energy consumption theory is established; S4, a tunnel surrounding rock creep damage model based on the minimum energy consumption theory is established; and S5, parameter values of the tunnel surrounding rock creep damage model are determined. The yield function established in the application overcomes the defects of existing criteria. The new concept of cumulative damage variable is proposed, and the defects that existing damage variables are often dependent on an exponential or power function expression and cause single damage curve are overcome. Meanwhile, the application can more accurately describe the tunnel surrounding rock creep characteristics, and the correlation coefficient square (R 2 ) is improved by 10% compared with traditional models.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory. Background Technology

[0002] During tunnel excavation, weak surrounding rock is often encountered. Under the influence of stress, water and other factors, the surrounding rock often undergoes creep. As the deformation of the surrounding rock slowly and continuously develops, even after the tunnel is opened to traffic, the creep of the surrounding rock can cause tunnel collapse and large deformation, leading to traffic safety accidents and bringing huge social impact.

[0003] Under stress, surrounding rock develops internal microcracks, and internal damage continues to progress. When the stress level exceeds the long-term strength, the surrounding rock exhibits accelerated creep, with deformation increasing dramatically in a short period. Internal microcracks extend and connect, leading to macroscopic yield failure. Therefore, to address rock creep failure, it is necessary to select or establish a highly applicable yield function and develop an expression method that can accurately describe the damage development mechanism of surrounding rock. This is of great significance for tunnel deformation control and disaster prevention.

[0004] Existing technologies construct creep damage models to accurately predict the creep deformation behavior of tunnel surrounding rock. The key aspects of establishing a creep damage constitutive model are the yield criterion and damage representation. Firstly, regarding the yield function, three commonly used yield criteria in rock creep processes are the Mohr-Coulomb, Drucker-Prager, and Zienkiewicz-Pande criteria. However, the Mohr-Coulomb criterion does not reflect the influence of the intermediate principal stress on yielding and failure, nor does it consider the characteristics of yielding caused by hydrostatic pressure alone; the Drucker-Prager criterion does not consider the characteristics of yielding caused by hydrostatic pressure alone, nor the nonlinear characteristics of yielding and failure; and the calculation of the Zienkiewicz-Pande criterion is relatively complex. There are two main methods for establishing damage variables to represent rock creep damage. The first is based on geometric damage, defined from the effective load-bearing area of ​​the structure. However, this method cannot accurately measure the geometric damage of the rock and is difficult to quantify precisely. The second method defines damage variables based on changes in the elastic modulus. This method considers the "deterioration" of the material's elastic properties as the main factor causing material damage. The drawback of this method is that it only considers the "deterioration" of the material's elastic properties, while rock materials not only possess elasticity but also exhibit certain viscoelasticity and viscoplasticity. Therefore, defining damage variables using changes in the elastic modulus is not very convincing. Currently, the constitutive model for tunnel creep damage still suffers from technical shortcomings such as low fitting accuracy and limited applicability. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This application discloses a method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory, including:

[0008] S1. Rock samples were taken from the tunnel roof. After processing the sampled rock, a triaxial compression creep test was conducted to obtain the test results.

[0009] S2. Establish a yield function based on the minimum energy consumption theory;

[0010] S3. Establish damage variables based on the minimum energy consumption theory;

[0011] S4. Establish a creep damage model for tunnel surrounding rock based on the minimum energy consumption theory;

[0012] S5. Determine the parameter values ​​of the tunnel surrounding rock creep damage model.

[0013] Furthermore, step S2 specifically includes:

[0014] Taking the yield condition as the minimum energy dissipation constraint, the energy dissipation process of rock materials during instantaneous compressive failure is constrained by the following conditions:

[0015]

[0016] In the formula: Indicates stress in different directions. Indicates the instantaneous compressive strength of rock. Represents the yield function;

[0017] In the energy transformation during the creep process of surrounding rock, assuming that irreversible strain is the only mechanism causing energy consumption, the energy consumption rate of any micro-unit of the surrounding rock system at the instant it enters the initial yield state is considered. for:

[0018] In the formula: , This represents the irreversible creep strain rate. , For any time after the rock material enters the initial yield state;

[0019] When stresses are in different directions Equal to long-term strength At that time, the yield condition satisfied by the energy dissipation process is as follows: ;

[0020] Based on the principle of minimum energy consumption, energy consumption rate Taking the minimum value, equation (2) takes a stationary value under the condition of satisfying equation (3). Using the Lagrange multiplier algorithm, we have:

[0021] In the formula: Since there is only one constraint condition in equation (3), Represents a proportionality constant;

[0022] Substituting equation (2) into equation (4), we get:

[0023]

[0024] Integrating equation (5), we get:

[0025]

[0026] In the formula, Denotes the integral constant;

[0027] when hour, Substituting this condition into equation (6), we obtain the yield function based on the minimum energy dissipation theory:

[0028]

[0029] In the formula: when At this point, the rock enters the initial yielding state. , ,but .

[0030] Preferably, step S3 specifically includes:

[0031] Assume the surrounding rock consists of M infinitesimal elements, of which N elements are damaged and MN elements are undamaged. Assume the transformation of the damage state of each element is irreversible, and that a single damaged element cannot bear the load. The damage variable D can be expressed by the following formula:

[0032]

[0033] When the rock enters the initial yielding state, under continuous stress, damage continues to develop, and the energy dissipation rate caused by irreversible strain also accumulates continuously, resulting in accumulated energy dissipation. for:

[0034]

[0035] Assuming that cumulative energy dissipation is synchronized with the development of damaged micro-elements, the damage variable is defined by cumulative energy dissipation. The damage variable corresponding to each loading stage after the rock reaches its initial yield state is accumulated. Represented as:

[0036] In the formula, k Indicates the stress loading level. The cumulative damage variable, representing the stress loading level of 1, is calculated using the following formula: ,in This represents the stress corresponding to a stress loading level of 1. Indicates the highest level of applied stress. This indicates the maximum loading time. This represents the maximum loading time corresponding to a stress loading level of 1;

[0037] The cumulative damage variable, representing the stress loading level x, is calculated using the following formula: Where x represents a natural number greater than 1. This represents the stress corresponding to stress loading level x. This represents the stress corresponding to a stress loading level of x-1. This represents the maximum loading time corresponding to stress loading level x;

[0038] Introduce the following empirical expression for creep:

[0039]

[0040] In the formula: A、B、C、n All of these represent parameters related to rock materials. Indicates creep strain. Indicates creep strain rate;

[0041] Omit parameter A in equation (12), and then substitute it and equation (2) into the equation. and In the calculation formula, the final result is combined:

[0042] Equation (14) is the final cumulative damage variable based on the principle of minimum energy consumption.

[0043] Preferably, step S4 specifically includes:

[0044] When the stress in a rock material exceeds its long-term strength, unstable creep begins to occur. At this point, the rock enters its initial yield state and begins to accumulate irreversible strain, causing damage to develop continuously. Based on the Lemaitre equivalent strain principle, the damage evolution is performed, resulting in the Nishihara model after damage evolution, as shown in the following equation:

[0045] In the formula: Represents the total strain of the model; Represents the stress in the model; Indicates the first elastic modulus; Indicates the second elastic modulus; Indicates the first viscosity coefficient; Indicates the second viscosity coefficient;

[0046] Since the surrounding rock of the tunnel is in a three-dimensional stress space, equation (16) is extended to a three-dimensional case. Assuming that the rock material is isotropic, according to the generalized Hooke's law, we can obtain:

[0047]

[0048] In the formula: Indicates the average stress. Represents the deviatoric stress tensor. Indicates average strain. Let K denote the deviatoric strain tensor, K denote the bulk modulus, and G denote the first shear modulus.

[0049] Decompose the stress tensor and strain tensor at any point inside the rock material:

[0050]

[0051] In the formula: Represents the strain tensor. Represents the stress tensor. Represent the Kronecker tensor; combining equations (17) and (18), the instantaneous elastic strain of the Hooke body is obtained. ,for:

[0052] In the formula: Indicates the second shear modulus;

[0053] Since the spherical stress tensor mainly reflects volumetric deformation, during the viscoelastic deformation of the tunnel surrounding rock, the volumetric creep of the surrounding rock is ignored, and the viscoelastic strain is expressed as:

[0054] In the formula: This represents the viscoelastic strain of the Kelvin body. Indicates the third shear modulus; Represents the three-dimensional viscosity coefficient;

[0055] Considering the plastic flow law under three-dimensional stress, the constitutive relation of a viscoplastic body should satisfy:

[0056] In the formula: Let m represent viscoplastic strain, m represent material constants, and P represent equivalent parameters. The calculation formula is as follows: , Indicates arbitrary; express The initial reference value, when hour, ,when hour, Based on the framework of the Xiyuan model, extending equation (16) to the three-dimensional stress space yields:

[0057]

[0058] In the formula: express The corresponding deviatoric stress tensor, G1 represents the shear modulus corresponding to E1, G2 represents the shear modulus corresponding to E2, and T2 represents... The corresponding three-dimensional viscosity parameter, T3 represents The corresponding three-dimensional viscosity parameters; express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor; Q represents the plastic potential function, and using the associated flow rule, we take Q=F; Substituting equations (7) and (12) into equation (19), we get:

[0059] A triaxial compression creep test was conducted, and the following conditions existed under this stress state:

[0060]

[0061] In the formula: Indicates the maximum principal stress. Indicates the intermediate principal stress. Indicates the minimum principal stress. To represent the axial deviatoric stress tensor, in equation (25) and Seen as with Substituting equation (26) into equation (25) yields the following expression:

[0062] (27)

[0063] Equation (27) is the constitutive equation of the three-dimensional constitutive model of tunnel surrounding rock creep damage based on the minimum energy dissipation theory. s 1- s 3) S express The corresponding deviatoric stress, ( s 1- s 3) k express The corresponding deviatoric stress, ( s 1- s 3) x express The corresponding deviatoric stress, ( s 1- s 3) max express The corresponding deviatoric stress.

[0064] Preferably, step S5 specifically includes the following steps:

[0065] S51. Based on the test results of the triaxial compression creep test, obtain ( s 1- s 3) S Parameter values;

[0066] S52, obtained by fitting the creep rate curve. B , C , n The parameter values ​​are given, and the method for solving the creep rate is shown below:

[0067]

[0068] In the formula: w This indicates the number of data points in the creep test; e 1. e 2… e n Represents continuous creep data; ∆ e 1. ∆ e 2…∆ e w-1 ∆ represents the difference in continuous creep data; e for w Sum of the differences in consecutive creep data; Δ t i for w A continuous creep data point experiences creep time; v iThe creep rate;

[0069] S53. Based on the creep curve, using the formula Solve The parameter value, For instantaneous strain, the result is obtained using the generalized Hooke's law. G 1 and K The parameter values ​​are shown in the following formula:

[0070]

[0071] In the formula: m Indicates Poisson's ratio;

[0072] S54. Using a quasi-Newton algorithm combined with a general global optimization method, the rock creep test data were identified and calculated using the mathematical software 1stOpt based on equation (27). G 2. T 2. T 3 and l * The parameter value.

[0073] The beneficial effects of this invention are:

[0074] 1) This application establishes a yield function based on the minimum energy consumption theory. Starting from the premise that "any energy-consuming process will be carried out in a way that minimizes energy consumption under its corresponding constraints", it is derived from the path of minimum energy consumption and deduces the failure criterion of rock materials from the perspective of energy. It overcomes the shortcomings of the Mohr-Coulomb criterion and Drucker-Prager criterion in not considering intermediate principal stress and simple hydrostatic pressure, and also overcomes the shortcomings of the Zienkiewicz-Pande criterion in terms of complex calculation.

[0075] 2) This application proposes the new concept of cumulative damage variable, which innovatively considers the damage superposition during each loading process of surrounding rock creep, and provides a new method for establishing damage variable, overcoming the defect that existing damage variables often rely on an exponential or power function expression, resulting in a single damage curve.

[0076] 3) This application can describe the creep characteristics of tunnel surrounding rock relatively accurately, with a correlation coefficient of squared (R²). 2 It improves upon the traditional model by 10%.

[0077] 4) This application divides the model parameters into two parts. One part is the experimental parameters, which are obtained through experiments and can be manually input. The other part is calculated by programming using the mathematical software 1stOpt, which employs the quasi-Newton (BFGS) algorithm combined with the general global optimization method, thereby improving the efficiency of parameter analysis.

[0078] 5) The model established in this application innovatively constructs a yield function based on the minimum energy consumption theory and proposes a new concept - cumulative damage variable, which has strong scientific research value, is of great significance for enriching the theoretical research on rock creep mechanics, and provides an important reference for understanding the creep behavior and deformation prediction of tunnel surrounding rock. Attached Figure Description

[0079] Figure 1 This is a schematic diagram illustrating the steps of a method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory, according to an embodiment of the present invention.

[0080] Figure 2 This is a schematic diagram illustrating the calculation of cumulative damage variables in an embodiment of the present invention;

[0081] Figure 3 This is a schematic diagram of the Nishihara model according to an embodiment of the present invention;

[0082] Figure 4 This is a creep rate fitting curve according to an embodiment of the present invention;

[0083] Figure 5 Solution for embodiments of the present invention A schematic diagram;

[0084] Figure 6 This is a schematic diagram showing the comparison curve between simulated values ​​and experimental data in an embodiment of the present invention;

[0085] Figure 7 This is a schematic diagram of the tunnel surrounding rock energy consumption rate curve according to an embodiment of the present invention;

[0086] Figure 8 This is a schematic diagram of the evolution curve of cumulative damage variables in the surrounding rock of the tunnel according to an embodiment of the present invention. Detailed Implementation

[0087] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and 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.

[0088] To address the shortcomings of existing yield functions and damage variables in tunnel creep processes, as well as the deficiencies of current tunnel creep damage models, this application discloses a method for establishing a tunnel surrounding rock creep damage model based on the minimum energy consumption theory. This method aims to overcome the deficiencies of existing yield functions and damage variables in creep processes, thereby establishing a tunnel surrounding rock creep damage model based on the minimum energy consumption theory. This overcomes the shortcomings of most models, such as low fitting accuracy and limited applicability, thus laying the foundation for tunnel surrounding rock creep deformation simulation and tunnel quality and safety control. The steps of the method are illustrated in the diagram below. Figure 1 As shown, it includes the following steps:

[0089] S1. Rock samples were taken from the tunnel roof. After processing the sampled rock, a triaxial compression creep test was conducted to obtain the test results.

[0090] S2. Establish a yield function based on the minimum energy consumption theory;

[0091] S3. Establish damage variables based on the minimum energy consumption theory;

[0092] S4. Establish a creep damage model for tunnel surrounding rock based on the minimum energy consumption theory;

[0093] S5. Determine the parameter values ​​of the tunnel surrounding rock creep damage model.

[0094] Specifically, the minimum energy dissipation theory states that any energy-consuming process will proceed in a manner with minimum energy dissipation under its corresponding constraints; according to the minimum energy dissipation theory, minimum energy dissipation only occurs when the rock material begins to yield.

[0095] For example, step S2 specifically includes:

[0096] Taking the yield condition as the minimum energy dissipation constraint, the energy dissipation process of rock materials during instantaneous compressive failure is constrained by the following conditions:

[0097]

[0098] In the formula: Indicates stress in different directions. Indicates the instantaneous compressive strength of rock. Represents the yield function;

[0099] When the external load just reaches the instantaneous compressive strength of the rock When the yield condition is triggered, the principle of minimum energy dissipation is satisfied. However, unlike instantaneous compression, rock compressive creep is time-dependent. This invention considers external loads exceeding long-term strength... Afterward, the rock material begins to enter the initial yield state, at which point unstable creep behavior begins to occur. Subsequently, creep damage develops under continuous loads of different loading levels, and the final loading level causes accelerated creep behavior, at which point the rock material exhibits macroscopic failure.

[0100] Some scholars have conducted rock creep tests, such as some tests with a loading level of 6. Between level 3 and level 4; some trials loaded a total of 9 levels. It falls between level 5 and level 6; some trials load a total of 5 levels. It falls between level 3 and level 4. This illustrates that different load level settings can lead to... Being between different stress loading levels indicates that during compressive creep, when > When, yield condition No longer applicable, at this time ;when When, yield condition Applicable to: Rock materials in the initial yield state undergoing unstable creep, with damage development and irreversible viscoplastic creep strain dominating;

[0101] In the energy transformation during the creep process of surrounding rock, this application assumes that irreversible strain is the only mechanism causing energy consumption, and calculates the energy consumption rate of any micro-unit of the surrounding rock system at the instant it enters the initial yield state. for:

[0102] In the formula: , This represents the irreversible creep strain rate. , For any time after the rock material enters the initial yield state;

[0103] When stresses are in different directions Equal to long-term strength At that time, the yield condition satisfied by the energy dissipation process is as follows: ;

[0104] Based on the principle of minimum energy consumption, energy consumption rate Taking the minimum value, equation (2) takes a stationary value under the condition of satisfying equation (3). Using the Lagrange multiplier algorithm, we have:

[0105] In the formula: Since there is only one constraint condition in equation (3), Represents a proportionality constant;

[0106] Substituting equation (2) into equation (4), we get:

[0107]

[0108] Integrating equation (5), we get:

[0109]

[0110] In the formula, Denotes the integral constant;

[0111] when hour, Substituting this condition into equation (6), we obtain the yield function based on the minimum energy dissipation theory:

[0112]

[0113] In the formula: when At this point, the rock enters the initial yielding state. , ,but .

[0114] Specifically, the rock itself contains a certain number of micro-defects. Over time, under long-term loading, these micro-defects continue to develop and may even connect. This process is considered damage development.

[0115] For example, step S3 specifically includes:

[0116] Assume the surrounding rock comprises M (M→∞) infinitesimal elements, of which N elements are damaged and MN elements are undamaged. Assume the transformation of the damage state of each element is irreversible, and a single damaged element cannot bear the load. The damage variable D is expressed by the following formula:

[0117]

[0118] Once the rock reaches its initial yield state, under continuous stress, damage continues to develop, and the energy dissipation rate caused by irreversible strain also accumulates. It can be regarded as being with The relevant instantaneous values ​​represent the cumulative energy consumption. for:

[0119]

[0120] Assuming that cumulative energy dissipation is synchronized with the development of damaged micro-elements, the damage variable is defined by cumulative energy dissipation. Since each loading level corresponds to a creep curve, the damage variables corresponding to each loading level after the rock reaches the initial yield state are accumulated to form the cumulative damage variable. Represented as:

[0121] In the formula, k Indicates the stress loading level. The cumulative damage variable, representing the stress loading level of 1, is calculated using the following formula: ,in This represents the stress corresponding to a stress loading level of 1. Indicates the highest level of applied stress. This indicates the maximum loading time.

[0122] The cumulative damage variable, representing the stress loading level x, is calculated using the following formula: Where x represents a natural number greater than 1. This represents the stress corresponding to stress loading level x. This represents the stress corresponding to a stress loading level of x-1. This represents the maximum loading time corresponding to stress loading level x; a schematic diagram of the cumulative damage variable calculation is shown below. Figure 2 As shown, where This represents the maximum loading time corresponding to a stress loading level of 1. This represents the maximum loading time corresponding to a stress loading level of 2; This represents the highest level of loading stress corresponding to a stress loading level of 1. The cumulative damage variable represents the stress loading level as 2.

[0123] Introduce the following empirical expression for creep:

[0124]

[0125] In the formula: A、B、C、n All of these represent parameters related to rock materials. Indicates creep strain. Indicates creep strain rate;

[0126] Equation (12) has been proven to fit the creep curve morphology of different rocks well. When the rock enters the initial yield state, irreversible viscoplastic strain dominates. Therefore, Equation (12) is approximated as the viscoplastic strain fitting formula in this paper. Since parameter A in Equation (12) mainly reflects instantaneous strain, and the damage calculation is mainly for creep damage, it is omitted in the calculation process. Then, it and Equation (2) are substituted into the equation. and In the calculation formula, the final result is combined:

[0127] Equation (14) is the final cumulative damage variable based on the principle of minimum energy consumption.

[0128] For example, this application improves upon the Nishihara model, as shown in the schematic diagram of the Nishihara model. Figure 3 As shown, the constitutive equation of the Nishihara model is:

[0129] Damage mechanics theory suggests that there exists a certain stress threshold that causes materials to begin to develop damage, while rheology theory suggests that when the stress exceeds the long-term strength, the material undergoes unstable creep.

[0130] Specifically, step S4 includes:

[0131] When the stress in a rock material exceeds its long-term strength, unstable creep begins to occur. At this point, the rock enters its initial yield state and begins to accumulate irreversible strain, causing damage to develop continuously. Based on the Lemaitre equivalent strain principle, the damage evolution is performed, resulting in the Nishihara model after damage evolution, as shown in the following equation:

[0132] In the formula: Represents the total strain of the model; Represents the stress in the model; This represents the first elastic modulus (the elastic modulus of the elastic body in the Nishihara model). This represents the second elastic modulus (the Kelvin elastic modulus in the Nishihara model). This represents the first viscosity coefficient (the viscosity coefficient in Kelvin in the Nishihara model). This represents the second viscosity coefficient (the viscosity coefficient of viscoplastic bodies in the Nishihara model).

[0133] Since the surrounding rock of the tunnel is in a three-dimensional stress space, and there are few one-dimensional cases, we extend equation (16) to a three-dimensional case. Assuming that the rock material is isotropic, according to the generalized Hooke's law, we can obtain:

[0134]

[0135] In the formula: Indicates the average stress. Represents the deviatoric stress tensor. Indicates average strain. Let K denote the deviatoric strain tensor, K denote the bulk modulus, and G denote the first shear modulus.

[0136] Decompose the stress tensor and strain tensor at any point inside the rock material:

[0137]

[0138] In the formula: Represents the strain tensor. Represents the stress tensor. Represent the Kronecker tensor; combining equations (17) and (18), the instantaneous elastic strain of the Hooke body is obtained. ,for:

[0139] In the formula: Indicates the second shear modulus;

[0140] Since the spherical stress tensor mainly reflects volumetric deformation, during the viscoelastic deformation of the tunnel surrounding rock, the volumetric creep of the surrounding rock is ignored, and the viscoelastic strain is expressed as:

[0141] In the formula: This represents the viscoelastic strain of the Kelvin body. Indicates the second shear modulus; Represents the three-dimensional viscosity coefficient;

[0142] Considering the plastic flow law under three-dimensional stress, the constitutive relation of a viscoplastic body should satisfy:

[0143] In the formula: The strain represents viscoplastic strain, m represents the material constant (usually m=1), and P represents the equivalent parameter, which is calculated using the following formula: , Indicates arbitrary; express The initial reference value is usually 1. hour, ,when hour, Based on the framework of the Xiyuan model, extending equation (16) to the three-dimensional stress space yields:

[0144]

[0145] In the formula: express The corresponding deviatoric stress tensor, G1 represents the shear modulus corresponding to E1, G2 represents the shear modulus corresponding to E2, and T2 represents... The corresponding three-dimensional viscosity parameter, T3 represents The corresponding three-dimensional viscosity parameters; express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor; Q represents the plastic potential function, and using the associated flow rule, we take Q=F; Substituting equations (7) and (12) into equation (19), we get:

[0146] A triaxial compression creep test was conducted, and the following conditions existed under this stress state:

[0147]

[0148] In the formula: Indicates the maximum principal stress. Indicates the intermediate principal stress. Indicates the minimum principal stress. To represent the axial deviatoric stress tensor, in equation (25) and Seen as with Substituting equation (26) into equation (25) yields the following expression:

[0149] (27)

[0150] Equation (27) is the constitutive equation of the three-dimensional constitutive model of tunnel surrounding rock creep damage based on the minimum energy dissipation theory. s 1- s 3) S express The corresponding deviatoric stress, ( s 1- s 3) k express The corresponding deviatoric stress, ( s 1- s 3) x express The corresponding deviatoric stress, ( s 1- s 3) max express The corresponding deviatoric stress.

[0151] Specifically, step S5 includes the following steps:

[0152] S51. Based on the test results of the triaxial compression creep test, obtain ( s 1- s 3) S The parameter values ​​must be entered manually.

[0153] S52, obtained by fitting the creep rate curve. B , C , n The parameter values ​​are given, and the method for solving the creep rate is shown below:

[0154]

[0155] In the formula: w This indicates the number of data points in the creep test; e 1. e 2… e n Represents continuous creep data; ∆ e 1. ∆ e 2…∆ e w-1 ∆ represents the difference in continuous creep data; e for w Sum of the differences in consecutive creep data; Δ t i for w A continuous creep data point experiences creep time; v i For the creep rate, we fit it using equation (12), that is... The parameters are shown in Table 1, and the creep rate fitting curve is shown in Table 1. Figure 4 As shown;

[0156] Table 1: Fitting parameters

[0157]

[0158] S53. Based on the creep curve, using the formula Solve Solve for the parameter values. The schematic diagram is as follows Figure 5 As shown, For instantaneous strain, the result is obtained using the generalized Hooke's law. G 1 and K The parameter values ​​are shown in the following formula:

[0159]

[0160] In the formula: m To express Poisson's ratio, simply enter it manually.

[0161] S54. Using the quasi-Newton (BFGS) algorithm combined with the general global optimization method, the rock creep test data were identified and calculated using the mathematical software 1stOpt based on equation (27). G 2. T 2. T 3 and l * The parameter value.

[0162] For example, for ease of calculation, the parameters are... G 2. T 2. l * and T Let 3 be a, b, c, and d. Calculate this in the mathematical software 1stOpt. The calculation code is shown below:

[0163] 1) Title: "New Creep Model";

[0164] 2) Parameters a, b, c, d;

[0165] 3)Function y=50.91*0.33 / 2056+0.33*50.91*(1-exp(-a*x / b)) / a+(50.91+24) / (9*3269)+((x)*(x)*(50.91-42.66)*(0.000548 / (x+1)+3.857*(9.78E-10)*(x^2.857))*(0.000548 / (x+1)+3.857*(9.78E-10)*(x^2.857))) / ((3*c*c*d)*(1-(2*2.11*(0.000548*LN(87.428+1)+(9.78E-10)*(87.428^3.857))) / (3*7.25*(0.000548*LN(87.428+1)+(9.78E-10)*(87.428^3.857)))-(2*5.14*(0.000548*LN(x+1)+(9.78E-10)*(x^3.857))) / (3*7.25*(0.000548*LN(42+1)+(9.78E-10)*(42^3.857)))));

[0166] 4)data; 5) 6)0 0.010632942 7)0.381515542 0.0108 8)2.6 0.0111 9)5.331515542 0.01139 10)8.770778042 0.01165 11)13.25151554 0.01199 12)18.60567795 0.012342034 13)20.18151554 0.01241 14)24.14151554 0.012680407 15)31.07151554 0.0131 16)37.72909956 0.0135 17)41.38869303 0.01387 18)41.4 0.014 19)41.6 0.014063626 20)41.88 0.014463626 21)42 0.015263626

[0184] Using the above method, the creep model parameters of the surrounding rock-sandstone of a certain tunnel are shown in Table 2:

[0185] Table 2: Creep Model Parameters of Surrounding Rock-Sandstone in a Tunnel

[0186]

[0187] As shown in Table 2, when hour, l * and T 3 has a range of values, when hour, l * and T 3 does not exist, therefore it has no value; substituting the parameter values ​​in Table 2 into equation (27), we obtain the comparison curve between the simulated value and the experimental data, the schematic diagram of which is shown below. Figure 6 As shown, by Figure 6 The superiority of this invention is evident; it exhibits better identification performance and can effectively identify the nonlinear characteristics of surrounding rock creep, with a correlation coefficient of R². 2 The accuracy reaches over 0.99, which is 10% higher than the traditional model.

[0188] For example, a schematic diagram of the energy consumption rate curve of the surrounding rock of the tunnel is shown below. Figure 7 As shown, Figure 7 This reflects the changes in the energy dissipation rate and creep rate of the tunnel surrounding rock. The energy dissipation rate curve and the creep rate curve have basically the same shape, and the energy dissipation rate reaches its peak at the end of the accelerated creep stage. t max2 Corresponding maximum value f ( t e ) max , f ( t e ) max The confining pressure increases with increasing confining pressure. In this embodiment, the confining pressure... s 3 = 8 MPa f ( t e ) max =0.397h -1 MPa This represents the first level of deviatoric stress after entering the initial yield state. This indicates the second-order deviatoric stress after entering the initial yield state.

[0189] For example, a schematic diagram of the evolution curve of cumulative damage variables in tunnel surrounding rock is shown below. Figure 8As shown, this reflects the changes in cumulative damage variables of the tunnel surrounding rock. The damage variable construction process in this application provides a new approach and method for damage evolution.

[0190] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory, characterized in that, include: S1. Rock samples were taken from the tunnel roof. After processing the sampled rock, a triaxial compression creep test was conducted to obtain the test results. S2. Establish a yield function based on the minimum energy consumption theory. In the energy transformation of the surrounding rock creep process, it is assumed that irreversible strain is the only mechanism causing energy consumption. Based on the principle of minimum energy consumption, the energy consumption rate of any micro-unit of the surrounding rock system at the moment of entering the initial yield state is taken as the minimum value. The yield condition is taken as the minimum energy consumption constraint of the rock material in the instantaneous compression failure process. The yield function based on the minimum energy consumption theory is derived by the Lagrange multiplier method. The yield condition includes stress in different directions equal to long-term strength. S3. Establish damage variables based on the minimum energy dissipation theory. Assume the surrounding rock consists of M micro-elements, of which N micro-elements are damaged and MN micro-elements are undamaged. Assume the transformation process of the damage state of the micro-elements is irreversible, and a single damaged element cannot bear the load. When the rock enters the initial yield state, under the action of continuous stress, the damage continues to develop, and the energy dissipation rate caused by irreversible strain also accumulates continuously, forming cumulative energy dissipation. Assume that the cumulative energy dissipation is synchronous with the development of the damaged micro-elements. Define the damage variable through the cumulative energy dissipation. Accumulate the damage step by step according to the stress loading level to obtain the cumulative damage variable under each loading level. Based on the creep empirical expression, obtain the damage variable based on the minimum energy dissipation theory. S4. Establish a creep damage model for tunnel surrounding rock based on the minimum energy dissipation theory. When the stress of the rock material exceeds its long-term strength, unstable creep begins to occur. At this time, the rock enters the initial yield state and begins to accumulate irreversible strain. Damage continues to develop. Based on the Lemaitre equivalent strain principle, damage evolution is carried out to obtain the Nishihara model after damage evolution. Considering the plastic flow law, the Nishihara model after damage evolution is extended to a three-dimensional case. Under the stress state corresponding to the triaxial compression creep test, the constitutive equation of the three-dimensional constitutive model of tunnel surrounding rock creep damage based on the minimum energy dissipation theory is established. S5. Determine the parameter values ​​of the tunnel surrounding rock creep damage model.

2. The method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory according to claim 1, characterized in that, Step S2 specifically includes: Taking the yield condition as the minimum energy dissipation constraint, the energy dissipation process of rock materials during instantaneous compressive failure is constrained by the following conditions: In the formula: Indicates stress in different directions. Indicates the instantaneous compressive strength of rock. Represents the yield function; Energy dissipation rate of any micro-unit of the surrounding rock system just as it enters the initial yield state for: In the formula: , This represents the irreversible creep strain rate. , For any time after the rock material enters the initial yield state; When stresses are in different directions Equal to long-term strength At that time, the yield condition satisfied by the energy dissipation process is as follows: ; Based on the principle of minimum energy consumption, energy consumption rate Taking the minimum value, equation (2) takes a stationary value under the condition of satisfying equation (3). Using the Lagrange multiplier algorithm, we have: In the formula: Since there is only one constraint condition in equation (3), Represents a proportionality constant; Substituting equation (2) into equation (4), we get: Integrating equation (5), we get: In the formula, U represents the integration constant; when hour, Substituting this condition into equation (6), we obtain the yield function based on the minimum energy dissipation theory: In the formula: when At this point, the rock enters the initial yielding state. , ,but .

3. The method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory according to claim 2, characterized in that, Step S3 specifically includes: The damage variable D is expressed by the following formula: When the rock enters the initial yielding state, under continuous stress, damage continues to develop, and the energy dissipation rate caused by irreversible strain also accumulates continuously, resulting in accumulated energy dissipation. for: Assuming that the cumulative energy dissipation is synchronized with the development of the damaged micro-elements, the damage variable is defined by the cumulative energy dissipation. The damage variable corresponding to each loading level after the rock enters the initial yielding state is accumulated, and the cumulative damage variable is expressed as: In the formula, k Indicates the stress loading level. The cumulative damage variable, representing the stress loading level of 1, is calculated using the following formula: ,in This represents the stress corresponding to a stress loading level of 1. Indicates the highest level of applied stress. This indicates the maximum loading time. This represents the maximum loading time corresponding to a stress loading level of 1; The cumulative damage variable, representing the stress loading level x, is calculated using the following formula: Where x represents a natural number greater than 1. This represents the stress corresponding to stress loading level x. This represents the stress corresponding to the stress loading level x-1. This represents the maximum loading time corresponding to stress loading level x; Introduce the following empirical expression for creep: In the formula: A, B, C, n All of these represent parameters related to rock materials. Indicates creep strain. Indicates creep strain rate; Omit parameter A in equation (12), and then substitute it and equation (2) into the equation. and In the calculation formula, the final result is combined: Equation (14) is the final cumulative damage variable obtained based on the principle of minimum energy consumption.

4. The method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory according to claim 3, characterized in that, Step S4 specifically includes: The Nishihara model after damage evolution is shown in the following equation: In the formula: Represents the total strain of the model; Represents the stress in the model; Indicates the first elastic modulus; Indicates the second elastic modulus; Indicates the first viscosity coefficient; Indicates the second viscosity coefficient; Since the surrounding rock of the tunnel is in a three-dimensional stress space, equation (16) is extended to a three-dimensional case. Assuming that the rock material is isotropic, according to the generalized Hooke's law, we can obtain: In the formula: Indicates the average stress. Represents the deviatoric stress tensor. Indicates average strain. Let K denote the deviatoric strain tensor, K denote the bulk modulus, and G denote the first shear modulus. Decompose the stress tensor and strain tensor at any point inside the rock material: In the formula: Represents the strain tensor. Represents the stress tensor. Represent the Kronecker tensor; combining equations (17) and (18), the instantaneous elastic strain of the Hooke body is obtained. ,for: In the formula: Indicates the second shear modulus; Since the spherical stress tensor mainly reflects volumetric deformation, during the viscoelastic deformation of the tunnel surrounding rock, the volumetric creep of the surrounding rock is ignored, and the viscoelastic strain is expressed as: In the formula: This represents the viscoelastic strain of the Kelvin body. Indicates the third shear modulus; Represents the three-dimensional viscosity coefficient; Considering the plastic flow law under three-dimensional stress, the constitutive relation of a viscoplastic body should satisfy: In the formula: Let m represent viscoplastic strain, m represent material constants, and P represent equivalent parameters. The calculation formula is as follows: , Indicates arbitrary; express The initial reference value, when hour, ,when hour, Based on the framework of the Xiyuan model, extending equation (16) to the three-dimensional stress space yields: In the formula: express The corresponding deviatoric stress tensor, G1 represents the shear modulus corresponding to E1, G2 represents the shear modulus corresponding to E2, and T2 represents... The corresponding three-dimensional viscosity parameter, T3 represents The corresponding three-dimensional viscosity parameters; express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor, express The corresponding deviatoric stress tensor; Q represents the plastic potential function, and using the associated flow rule, we take Q=F; Substituting equations (7) and (12) into equation (19), we get: A triaxial compression creep test was conducted, and the following conditions existed under this stress state: In the formula: Indicates the maximum principal stress. Indicates the intermediate principal stress. Indicates the minimum principal stress. To represent the axial deviatoric stress tensor, in equation (25) and Seen as with Substituting equation (26) into equation (25) yields the following expression: （27） Equation (27) is the constitutive equation of the three-dimensional constitutive model of tunnel surrounding rock creep damage based on the minimum energy dissipation theory. σ 1- σ 3) S express The corresponding deviatoric stress, ( σ 1- σ 3) k express The corresponding deviatoric stress, ( σ 1- σ 3) x express The corresponding deviatoric stress, ( σ 1- σ 3) max express The corresponding deviatoric stress.

5. The method for establishing a creep damage model of tunnel surrounding rock based on the minimum energy consumption theory according to claim 4, characterized in that, Step S5 specifically includes the following steps: S51. Based on the test results of the triaxial compression creep test, obtain ( σ 1- σ 3) S Parameter values; S52, obtained by fitting the creep rate curve B , C , n The parameter values ​​are given, and the method for solving the creep rate is shown below: In the formula: w This indicates the number of data points in the creep test; ε 1. ε 2… ε n Represents continuous creep data; ∆ ε 1. ∆ ε 2…∆ ε w-1 ∆ represents the difference in continuous creep data; ε for w Sum of the differences in consecutive creep data; Δ t i for w A continuous creep data point experiences creep time; v i The creep rate; S53. Based on the creep curve, using the formula Solve The parameter value, For instantaneous strain, the result is obtained using the generalized Hooke's law. G 1 and K The parameter values ​​are shown in the following formula: In the formula: μ Indicates Poisson's ratio; S54. Using a quasi-Newton algorithm combined with a general global optimization method, the rock creep test data were identified and calculated using the mathematical software 1stOpt based on equation (27). G 2. T 2. T 3 and λ * The parameter value.

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