Method for constructing tunnel surrounding rock creep damage constitutive model based on energy conservation theorem

Abstract

The application discloses a tunnel surrounding rock creep damage constitutive model construction method based on an energy conservation theorem, relates to the technical field of geotechnical engineering, and comprises the following steps: S1, regarding the rock mass in the preset range of the tunnel surrounding rock excavation line as a closed system, sampling and processing the rock, carrying out triaxial compression creep test, and obtaining creep data and test results; S2, based on the energy conservation theorem, a constitutive equation for describing unstable creep of the tunnel surrounding rock is established, a creep constitutive basic model for the tunnel surrounding rock is determined based on a unified rheological mechanics model theory, the constitutive equation is embedded into the creep constitutive basic model, and a tunnel surrounding rock creep damage constitutive model is established; and S3, model parameters are divided into test parameters and analytical parameters, and the parameter values of the test parameters and the analytical parameters are determined respectively. The application can clearly reflect the nonlinear characteristics of tunnel surrounding rock creep, better simulate the tunnel surrounding rock creep behavior, and the correlation coefficient square is improved by 10% compared with traditional models in the simulation of unstable creep behavior.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method for constructing a constitutive model of creep damage in tunnel surrounding rock based on the law of energy conservation. Background Technology

[0002] Soft surrounding rock is a common rock type encountered in tunnel engineering. During tunnel excavation, under conditions such as groundwater infiltration and stress redistribution, soft surrounding rock often undergoes creep, with deformation increasing slowly over time. Once a certain critical point is exceeded, deformation accelerates, often resulting in large deformations of the soft rock, posing potential safety hazards to tunnel construction and operation. China's geological conditions are significantly complex, mainly manifested in the following aspects: First, the country spans multiple geological tectonic units, including stable cratons, active orogenic belts, and fault zones, such as the continuous uplift of the Qinghai-Tibet Plateau and the seismic belt along the eastern coast; second, lithological distribution is extremely uneven, ranging from the karst landforms of the southwest to the Loess Plateau of the northwest, and then to the igneous rock areas of the southeast, resulting in vastly different engineering characteristics. Given the complex and diverse rock types in China, tunnel engineering must systematically address issues such as surrounding rock deformation and prevention of geological hazards in underground engineering. Establishing a creep constitutive model with strong applicability and rapidly and accurately solving for model parameters would be of great significance for deformation prediction and stability analysis in tunnel engineering.

[0003] Existing constitutive models of rock creep mainly fall into the following categories: The first category is empirical creep models, which use polynomial expressions to fit creep curves. Empirical models are obtained by fitting logarithmic and power function expressions, but the parameters of this type of model have no physical meaning. The second category is element creep models, which are composed of Hooke bodies, Newton bodies, etc., and have clear physical meanings. However, their equations of state are linear and may not be suitable for describing the nonlinear characteristics of rock creep. Some scholars have improved them by using nonlinear elements, which has improved the simulation accuracy, but still has not solved the problem that the equations of state are linear. The third category is internal time creep models, which reflect the irreversible deformation inside the material through thermodynamic internal variables. Although this type of model has high simulation accuracy, the model structure is complex, has many parameters, and the definition of intrinsic time is controversial, making it difficult to apply systematically. The fourth category is damage and rheology coupled models, which combine damage variables with element models. The advantage of this type of model is that the physical meaning is relatively clear and the simulation effect is better. In addition, some scholars have established a fractional creep model for rocks based on fractional calculus theory. Although this type of model has good simulation effect, the physical meaning of the order of the fractional derivative is vague and the numerical solution of the equation is complicated. Other scholars have established creep models based on deep learning algorithms or neural networks, but these models can only simulate creep curves, have no physical meaning, and are controlled by the number and accuracy of samples, and need to be updated at all times. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for constructing a constitutive model of creep damage in tunnel surrounding rock based on the law of energy conservation.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This application discloses a method for constructing a constitutive model of creep damage in tunnel surrounding rock based on the law of energy conservation, including the following steps:

[0007] S1. The rock mass within the preset range of the tunnel surrounding rock excavation line is regarded as a closed system. The surrounding rock in the tunnel surrounding rock closed system includes micro-element. Let the height of the micro-element be H and the diameter be H / 2. The rock is sampled and processed at the top plate position of the tunnel surrounding rock closed system. Triaxial compression creep test is carried out on the processed rock sample to obtain creep data and test results.

[0008] S2. Based on the law of conservation of energy, a constitutive equation is established to describe the unstable creep of the surrounding rock of the tunnel. Based on the unified rheological model theory, a basic constitutive model for creep of the surrounding rock of the tunnel is determined. The established constitutive equation is embedded into the basic constitutive model for creep, and a constitutive model for creep damage of the surrounding rock of the tunnel is established.

[0009] S3. Divide the model parameters into experimental parameters and analytical parameters, and determine the parameter values ​​of the experimental parameters based on the experimental results; use the nonlinear algorithm - Gauss-Newton algorithm to process the creep data, and determine the parameter values ​​of the analytical parameters using Python language.

[0010] Furthermore, establishing the constitutive equations to describe the unstable creep of the tunnel surrounding rock includes the following steps:

[0011] S201. Under triaxial stress, the surrounding rock undergoes unstable creep, wherein the unstable creep rate is... The calculation formula is: , Indicates the first strain. This represents a specific moment in unstable creep;

[0012] S202. Based on the law of conservation of energy, during the creep process of a micro-element, the load does work on it. If thermal energy is ignored, then the work done is... and kinetic energy Equal, that is Work done The calculation formula is: , Indicates the first stress. The cross-sectional area of ​​the infinitesimal element is expressed by the following formula: ;kinetic energy The calculation formula is: Where m represents the mass of the infinitesimal element, and its calculation formula is: , This represents the density of a micro-element;

[0013] S203, through formula Calculate the first strain When the first stress exceeds the long-term strength, unstable creep occurs. Referring to a Newtonian body, the first strain is calculated. The formula for viscous properties is rewritten as follows: That is, to obtain the constitutive equation used to describe the unstable creep of the surrounding rock of the tunnel, where Indicates the viscosity correction parameter. Indicates long-term strength.

[0014] Preferably, determining the creep constitutive basis model for tunnel surrounding rock includes the following steps:

[0015] S211. Rocks undergo instantaneous elastic deformation at the moment of loading, exhibiting an instantaneous mechanical form. This process is described using Hookean bodies.

[0016] After instantaneous elastic deformation, the rock enters the decay creep stage, and its creep rate begins to decrease. When the creep rate is constant, the rock enters the steady creep stage. This process is described by Newtonian bodies, which shows that the rock has viscosity.

[0017] The Kelvin description indicates that some rock creep strain is recoverable, suggesting that the rock possesses a certain degree of viscoelasticity.

[0018] When the stress exceeds the long-term strength, the rock undergoes unstable creep, exhibiting accelerated creep behavior and a sharp increase in strain. At this point, the rock exhibits significant viscoplastic characteristics, and this process is described using Bingham bodies.

[0019] Therefore, the rheological properties of the rock are viscous-viscoelastic-viscoplastic. Based on the unified rheological model theory, the basic model structure for tunnel surrounding rock is determined to be Hooke body-Kelvin body-Newton body-Bingham body.

[0020] S212, if If the Bingham body in the basic model structure fails, the state equation corresponding to the tunnel surrounding rock is: ,in Indicates the second stress. Indicates the second strain. Indicates the first elastic modulus. Indicates the first viscosity coefficient. Indicates the third stress. Indicates the third strain. This represents the second elastic modulus. This represents the second viscosity coefficient. Indicates the second stress The first derivative with respect to time t, Indicates the second strain The first derivative with respect to time t, Third strain The first derivative with respect to time t;

[0021] like Then, the Bingham body in the basic model structure comes into play, and the state equation corresponding to the tunnel surrounding rock is: ,in Indicates the fourth stress. Indicates the fourth strain. Represents the third viscosity coefficient. Indicates the fourth strain The first derivative with respect to time t;

[0022] S213. Transform the state equations corresponding to the tunnel surrounding rock into first-order linear ordinary differential equations, then calculate their general solution to obtain the one-dimensional constitutive equations of the basic model structure of the tunnel surrounding rock. ,in This represents the total strain of the model. This represents the initial stress of the model.

[0023] Preferably, establishing a constitutive model for creep damage in the surrounding rock of a tunnel includes the following steps:

[0024] S221. The constitutive equations used to describe the unstable creep of tunnel surrounding rock are embedded into the basic model of tunnel surrounding rock and improved to obtain a one-dimensional constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation. The constitutive equations are as follows: ;

[0025] S222. Assuming the rock material is isotropic, according to the generalized Hooke's law, we get... ;in Indicates average stress. Represents the deviatoric stress tensor. Indicates average strain. Let K represent the deviatoric strain tensor, K represent the bulk modulus, and G represent the shear modulus.

[0026] S223, Stress tensor at any point inside the rock material and strain tensor Decompose: ;in Represents the Kronecker tensor;

[0027] S224. In the tunnel surrounding rock sealing system, neglecting the volumetric creep of the surrounding rock, and using the yield function F to reflect the yield state of the rock material, the constitutive equation in step S221 is extended to three-dimensional stress space, then we have: ;in Indicates long-term strength The corresponding deviatoric stress tensor; G 1 represents E The shear modulus corresponding to 1, G 2 indicates E The corresponding shear modulus of 2 T 1 represents η The corresponding three-dimensional viscosity parameter is 1. T 2 indicates η The corresponding three-dimensional viscosity parameters are 2. Q Given the plastic potential function, the associated flow rule is used to make... ; This represents the initial reference value of the yield function F;

[0028] S225. Conduct a triaxial compression creep test. Under this stress state, what are the... , Representing the axial deviatoric stress tensor, we substitute it into the three-dimensional stress space equation in step S224 to obtain the constitutive equation of the tunnel surrounding rock creep damage constitutive model based on the energy conservation theorem. ;in Indicates long-term strength The corresponding deviatoric stress, This represents the axial strain tensor.

[0029] Preferably, dividing the model parameters into experimental parameters and analytical parameters includes: ρ , H and Divide into experimental parameters, T 1. T 2. G 1. K , G 2 and It is divided into parsed parameters.

[0030] Preferably, the determination of experimental parameters includes: obtaining the experimental results... The parameter values ​​are determined based on the International System of Units (SI). ρ The parameter values ​​for H.

[0031] Preferably, the determination of the analytical parameters includes the following steps:

[0032] S31. Based on the generalized Hooke's law, through the formula calculate G 1 and K The parameter values, where μ Represents Poisson's ratio, and a creep curve is constructed based on creep data. Solve ,in Indicates instantaneous strain;

[0033] S32, respectively using a , b , c and d Indicates parameters T 1. T 2. G 2 and , will the known G 1. K, ρ , H and The parameter values ​​are substituted into the constitutive equation of the tunnel surrounding rock creep damage constitutive model, and Gaussian noise is added to it. ,Right now Gaussian noise Gaussian distribution is 0 represents the expectation of the Gaussian distribution. Let be the variance of the Gaussian distribution;

[0034] S33. Assume that the constitutive equations in step S32 have N equations relating to t and The data points are transformed into the following least squares problem: ;

[0035] S34. Generating t and t based on the constitutive model of creep damage in tunnel surrounding rock in Python. The true value is obtained by adding Gaussian noise to the true value and fitting the data from the noisy data using the Gauss-Newton method. When, fitting error for: ,in express The truth value of;

[0036] Therefore, the derivatives of a, b, c, and d with respect to the state variables are: Obtain the Jacobian matrix. , Where T denotes matrix transpose; the incremental equation of Gauss-Newton's method is , where i represents the iteration number. Indicates the time step.

[0037] The beneficial effects of this invention are:

[0038] 1) The simulation effect is significantly improved. The constitutive model of tunnel surrounding rock creep based on the law of energy conservation established in this application can clearly reflect the nonlinear characteristics of tunnel surrounding rock creep and simulate the mechanical behavior of tunnel surrounding rock creep better. For the simulation of unstable creep behavior, compared with the traditional model, the correlation coefficient squared (R²) of this application is significantly improved. 2 Increase by 10%.

[0039] 2) The parameter analysis is more accurate. This invention 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 based on the Python language and uses the nonlinear algorithm - Gauss-Newton algorithm to process the creep data and achieve automatic analysis.

[0040] 3) The physical meaning is clearer. The model established in this application has 9 model parameters, each of which has a clear physical meaning. Many scholars' improved models inevitably have fitting parameters or integral constants that have no physical meaning. Therefore, the model established in this application has strong application value. Attached Figure Description

[0041] Figure 1 This is a schematic diagram illustrating the steps of the method for constructing a constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation, according to an embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram of the micro-unit composition of the tunnel enclosure system according to an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of the basic model structure for tunnel surrounding rock according to an embodiment of the present invention;

[0044] Figure 4 Solution for embodiments of the present invention A schematic diagram of the creep curve;

[0045] Figure 5 This is a schematic diagram showing the comparison curve between simulated values ​​and experimental data in an embodiment of the present invention. Detailed Implementation

[0046] 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.

[0047] This application discloses a method for constructing a constitutive model of creep damage in tunnel surrounding rock based on the law of energy conservation. Addressing the shortcomings of current tunnel surrounding rock creep constitutive models, such as low simulation accuracy, complex and difficult-to-calculate parameters, and unclear physical meaning, this method constructs a creep constitutive model of tunnel surrounding rock from the perspective of energy conservation. It creates a new method to accurately solve for the model parameters, improving simulation accuracy, simplifying model parameters and accurately calculating them, and clarifying their physical meaning. This provides an important reference for understanding, predicting, and controlling creep phenomena in tunnel engineering, enhancing the risk management capabilities of tunnel construction projects, and ultimately improving the overall efficiency and economic benefits of tunnel construction. A schematic diagram of the steps of the method is shown below. Figure 1 As shown; including the following steps:

[0048] S1. The rock mass within the preset range of the tunnel surrounding rock excavation line is regarded as a closed system. The surrounding rock in the tunnel surrounding rock closed system includes micro-element. Let the height of the micro-element be H and the diameter be H / 2. The rock is sampled and processed at the top plate position of the tunnel surrounding rock closed system. Triaxial compression creep test is carried out on the processed rock sample to obtain creep data and test results.

[0049] For example, the law of conservation of energy presupposes a closed system; in an open system, the total amount of energy changes. After tunnel excavation, the surrounding rock should be in a triaxial stress state. Therefore, it is proposed to consider the rock mass within the predetermined excavation line as a closed system. Assume that the surrounding rock in this closed system is composed of countless cylindrical micro-elements, each with a height of H and a diameter of H / 2, where H is infinitesimally small relative to the surrounding rock boundary. A schematic diagram of the micro-unit composition of the tunnel closed system is shown below. Figure 2 As shown, rock samples were taken from the tunnel roof for triaxial compression creep testing.

[0050] S2. Based on the law of conservation of energy, a constitutive equation is established to describe the unstable creep of the surrounding rock of the tunnel. Based on the unified rheological model theory, a basic constitutive model for creep of the surrounding rock of the tunnel is determined. The established constitutive equation is embedded into the basic constitutive model for creep, and a constitutive model for creep damage of the surrounding rock of the tunnel is established.

[0051] Specifically, taking the cylindrical micro-element of the tunnel roof as an example, and considering the stress conditions of the surrounding rock of the tunnel roof, and taking into account that the deformation of unstable creep accounts for a large proportion of the creep development process and takes a relatively short time, the focus is on the development of unstable creep deformation. Based on the law of conservation of energy, the constitutive model of creep damage in the tunnel surrounding rock is established. The constitutive equation for describing the unstable creep of the tunnel surrounding rock includes the following steps:

[0052] S201. Under triaxial stress, the surrounding rock undergoes unstable creep, wherein the unstable creep rate is... The calculation formula is: , Indicates the first strain. This represents a specific moment in unstable creep;

[0053] S202. Based on the law of conservation of energy, during the creep process of a micro-element, the load does work on it. If thermal energy is ignored, then the work done is... and kinetic energy Equal, that is Work done The calculation formula is: , Indicates the first stress. The cross-sectional area of ​​the infinitesimal element is expressed by the following formula: ;kinetic energy The calculation formula is: Where m represents the mass of the infinitesimal element, and its calculation formula is: , This represents the density of a micro-element;

[0054] S203, through formula Calculate the first strain When the first stress exceeds the long-term strength, unstable creep occurs. Referring to a Newtonian body, the first strain is calculated. The formula for viscous properties is rewritten as follows: That is, to obtain the constitutive equation used to describe the unstable creep of the surrounding rock of the tunnel, where Indicates the viscosity correction parameter. Indicates long-term strength.

[0055] Specifically, determining the creep constitutive basis model for tunnel surrounding rock includes the following steps:

[0056] S211. Rocks undergo instantaneous elastic deformation at the moment of loading, exhibiting an instantaneous mechanical form. This process is described using Hookean bodies.

[0057] After instantaneous elastic deformation, the rock enters the decay creep stage, and its creep rate begins to decrease. When the creep rate is constant, the rock enters the steady creep stage. This process is described by Newtonian bodies, which shows that the rock has viscosity.

[0058] The Kelvin description indicates that some rock creep strain is recoverable, suggesting that the rock possesses a certain degree of viscoelasticity.

[0059] When the stress exceeds the long-term strength, the rock undergoes unstable creep, exhibiting accelerated creep behavior and a sharp increase in strain. At this point, the rock exhibits significant viscoplastic characteristics, and this process is described using Bingham bodies.

[0060] Therefore, the rheological properties of the rock are viscous-viscoelastic-viscoplastic. Based on the unified rheological model theory, the basic model structure for tunnel surrounding rock is determined to be Hooke-Kelvin-Newtonian-Bingham body. A schematic diagram of the basic model structure for tunnel surrounding rock is shown below. Figure 3 As shown; Indicates the long-term strength of the mountain range in the village;

[0061] S212, if If the Bingham body in the basic model structure fails, the state equation corresponding to the tunnel surrounding rock is: ,in Indicates the second stress. Indicates the second strain. Indicates the first elastic modulus. Indicates the first viscosity coefficient. Indicates the third stress. Indicates the third strain. This represents the second elastic modulus. This represents the second viscosity coefficient. Indicates the second stress The first derivative with respect to time t, Indicates the second strain The first derivative with respect to time t, Third strain The first derivative with respect to time t;

[0062] like Then, the Bingham body in the basic model structure comes into play, and the state equation corresponding to the tunnel surrounding rock is: ,in Indicates the fourth stress. Indicates the fourth strain. Represents the third viscosity coefficient. Indicates the fourth strain The first derivative with respect to time t;

[0063] S213. Transform the state equation corresponding to the tunnel surrounding rock into a first-order linear ordinary differential equation. Taking the state equation at time as an example, it can be transformed into Then, the general solution was calculated to obtain the one-dimensional constitutive equation of the basic model structure of the tunnel surrounding rock. ,in This represents the total strain of the model. This represents the initial stress of the model.

[0064] Specifically, establishing a constitutive model for creep damage in tunnel surrounding rock includes the following steps:

[0065] S221. The constitutive equations used to describe the unstable creep of tunnel surrounding rock are embedded into the basic model of tunnel surrounding rock and improved to obtain a one-dimensional constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation. The constitutive equations are as follows: ;

[0066] S222. Because the tunnel surrounding rock is in a three-dimensional stress space, and rarely in a one-dimensional case, the constitutive equation of the one-dimensional constitutive model of tunnel surrounding rock creep damage in step S221 needs to be extended to a three-dimensional case; assuming the rock material is isotropic, according to the generalized Hooke's law, we get... ;in Indicates average stress. Represents the deviatoric stress tensor. Indicates average strain. Let K represent the deviatoric strain tensor, K represent the bulk modulus, and G represent the shear modulus.

[0067] S223, Stress tensor at any point inside the rock material and strain tensor Decompose: ;in Represents the Kronecker tensor;

[0068] S224. In the tunnel surrounding rock sealing system, neglecting the volumetric creep of the surrounding rock, and using the yield function F to reflect the yield state of the rock material, the constitutive equation in step S221 is extended to three-dimensional stress space, then we have: ;in Indicates long-term strength The corresponding deviatoric stress tensor; G 1 represents E The shear modulus corresponding to 1, G 2 indicates E The corresponding shear modulus of 2 T 1 represents η The corresponding three-dimensional viscosity parameter is 1. T 2 indicates η The corresponding three-dimensional viscosity parameters are 2. Q Given the plastic potential function, the associated flow rule is used to make... ; This represents the initial reference value of the yield function F, which is usually taken as 1;

[0069] S225. Conduct a triaxial compression creep test. Under this stress state, what are the... , Representing the axial deviatoric stress tensor, we substitute it into the three-dimensional stress space equation in step S224 to obtain the constitutive equation of the tunnel surrounding rock creep damage constitutive model based on the energy conservation theorem. ;in Indicates long-term strength The corresponding deviatoric stress, This represents the axial strain tensor.

[0070] S3. Divide the model parameters into experimental parameters and analytical parameters, and determine the parameter values ​​of the experimental parameters based on the experimental results; use the nonlinear algorithm - Gauss-Newton algorithm to process the creep data, and determine the parameter values ​​of the analytical parameters using Python language.

[0071] Specifically, the model parameters are divided into experimental parameters and analytical parameters, including: ρ , H and Divide into experimental parameters, T 1. T 2. G 1. K , G 2 and It is divided into parsed parameters.

[0072] Specifically, the determination of experimental parameters includes: obtaining the parameters based on the experimental results. The parameter values ​​can be entered manually; they are determined based on the International System of Units (SI). ρ The parameter values ​​for H.

[0073] For example, in this application, H is 0.1m. ρ Take 2.48 g / cm 3 During calculation ρ Use 2480 kg / m² (SI) 3 .

[0074] Specifically, determining the parsing parameters includes the following steps:

[0075] S31. Based on the generalized Hooke's law, through the formula calculate G 1 and K The parameter values, where μ This represents Poisson's ratio, an experimental parameter that can be manually entered. A creep curve is constructed based on the creep data, and the solution is obtained. A schematic diagram of the creep curve is shown below. Figure 4 As shown, for Solve ,in Indicates instantaneous strain;

[0076] S32, respectively using a , b , c and d Indicates parameters T 1. T 2. G 2 and , will the knownG 1. K, ρ , H and The parameter values ​​are substituted into the constitutive equation of the tunnel surrounding rock creep damage constitutive model, and Gaussian noise is added to it. ,Right now Gaussian noise Gaussian distribution is 0 represents the expectation of the Gaussian distribution. Let be the variance of the Gaussian distribution;

[0077] S33. Assume that the constitutive equations in step S32 have N equations relating to t and The data points are transformed into the following least squares problem: ;

[0078] S34. Generating t and t based on the constitutive model of creep damage in tunnel surrounding rock in Python. The true value is obtained by adding Gaussian noise to the true value and fitting the data from the noisy data using the Gauss-Newton method. When, fitting error for: ,in express The truth value of;

[0079] Therefore, the derivatives of a, b, c, and d with respect to the state variables are: Obtain the Jacobian matrix. , Where T denotes matrix transpose; the incremental equation of Gauss-Newton's method is , where i represents the iteration number. Indicates the time step.

[0080] For example, experiments were conducted using the creep model parameters given in Table 1, when hour, Only then will there be relevant values, if ,but The parameters of the creep model given in Table 1 are not present. Substituting them into the constitutive equation of the tunnel surrounding rock creep damage constitutive model based on the law of energy conservation obtained in this application, a comparison curve between the simulated values ​​and experimental data is obtained, as shown in the schematic diagram. Figure 5 As shown; it can be seen that the simulation effect of this application is good, especially for the nonlinear characteristics of tunnel surrounding rock creep, which can be clearly reflected, and the correlation coefficient squared (R 2 The accuracy reaches over 0.99, which is 10% higher than traditional models for simulating unstable creep behavior.

[0081] Table 1: Creep Model Parameters

[0082]

[0083] 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 constructing a constitutive model of creep damage in tunnel surrounding rock based on the law of energy conservation, characterized in that, Includes the following steps: S1. The rock mass within the preset range of the tunnel surrounding rock excavation line is regarded as a closed system. The surrounding rock in the tunnel surrounding rock closed system includes micro-element. Let the height of the micro-element be H and the diameter be H / 2. The rock is sampled and processed at the top plate position of the tunnel surrounding rock closed system. Triaxial compression creep test is carried out on the processed rock sample to obtain creep data and test results. S2. Based on the law of conservation of energy, a constitutive equation is established to describe the unstable creep of the surrounding rock of the tunnel. Based on the unified rheological model theory, a basic constitutive model for creep of the surrounding rock of the tunnel is determined. The established constitutive equation is embedded into the basic constitutive model for creep, and a constitutive model for creep damage of the surrounding rock of the tunnel is established. S3. Divide the model parameters into experimental parameters and analytical parameters, and determine the parameter values ​​of the experimental parameters based on the experimental results; use the nonlinear algorithm - Gauss-Newton algorithm to process the creep data, and determine the parameter values ​​of the analytical parameters using Python language; The steps in step S2 to establish the constitutive model of creep damage in the surrounding rock of the tunnel include the following steps: S221. The constitutive equations used to describe the unstable creep of tunnel surrounding rock are embedded into the basic model of tunnel surrounding rock and improved to obtain a one-dimensional constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation. The constitutive equations are as follows: ;in Indicates the first stress. Indicates long-term strength. Indicates the viscosity correction parameter. The density of the infinitesimal element is represented by its density. Indicates the first elastic modulus. Indicates the first viscosity coefficient. This represents the second elastic modulus. This represents the second viscosity coefficient, and t represents time. Represents the total strain of the model; S222. Assuming the rock material is isotropic, according to the generalized Hooke's law, we get... ;in Indicates average stress. Represents the deviatoric stress tensor. Indicates average strain. Let K represent the deviatoric strain tensor, K represent the bulk modulus, and G represent the shear modulus. S223, Stress tensor at any point inside the rock material and strain tensor Decompose: ;in Represents the Kronecker tensor; S224. In the tunnel surrounding rock sealing system, neglecting the volumetric creep of the surrounding rock, and using the yield function F to reflect the yield state of the rock material, the constitutive equation in step S221 is extended to three-dimensional stress space, then we have: ;in Indicates long-term strength The corresponding deviatoric stress tensor; G 1 represents E The shear modulus corresponding to 1, G 2 indicates E The corresponding shear modulus of 2 T 1 represents η The corresponding three-dimensional viscosity parameter is 1. T 2 indicates η The corresponding three-dimensional viscosity parameters are 2. Q Given the plastic potential function, the associated flow rule is used to make... , This represents the initial reference value of the yield function F; S225. Conduct a triaxial compression creep test. Under this stress state, what are the... , This represents the axial deviatoric stress tensor. Indicates the second stress. Indicates the third stress. Representing the fourth stress, we substitute it into the three-dimensional stress space equation in step S224 to obtain the constitutive equation of the tunnel surrounding rock creep damage constitutive model based on the energy conservation theorem. ;in Indicates long-term strength The corresponding deviatoric stress, This represents the axial strain tensor.

2. The method for constructing a constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation as described in claim 1, characterized in that, Establishing constitutive equations to describe the unstable creep of tunnel surrounding rock includes the following steps: S201. Under triaxial stress, the surrounding rock undergoes unstable creep, wherein the unstable creep rate is... The calculation formula is: , Indicates the first strain. This represents a specific moment in unstable creep; S202. Based on the law of conservation of energy, during the creep process of a micro-element, the load does work on it. If thermal energy is ignored, then the work done is... and kinetic energy Equal, that is Work done The calculation formula is: , The cross-sectional area of ​​the infinitesimal element is expressed by the following formula: ;kinetic energy The calculation formula is: Where m represents the mass of the infinitesimal element, and its calculation formula is: ; S203, through formula Calculate the first strain When the first stress exceeds the long-term strength, unstable creep occurs. Referring to a Newtonian body, the first strain is calculated. The formula for viscous properties is rewritten as follows: This yields the constitutive equations used to describe the unstable creep of the surrounding rock in tunnels.

3. The method for constructing a constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation as described in claim 2, characterized in that, Determining the basic creep constitutive model for tunnel surrounding rock includes the following steps: S211. Rocks undergo instantaneous elastic deformation at the moment of loading, exhibiting an instantaneous mechanical form. This process is described using Hookean bodies. After instantaneous elastic deformation, the rock enters the decay creep stage, and its creep rate begins to decrease. When the creep rate is constant, the rock enters the steady creep stage. This process is described by Newtonian bodies, which shows that the rock has viscosity. The Kelvin description indicates that some rock creep strain is recoverable, suggesting that the rock possesses a certain degree of viscoelasticity. When the stress exceeds the long-term strength, the rock undergoes unstable creep, exhibiting accelerated creep behavior and a sharp increase in strain. At this point, the rock exhibits significant viscoplastic characteristics, and this process is described using Bingham bodies. Therefore, the rheological properties of the rock are viscous-viscoelastic-viscoplastic. Based on the unified rheological model theory, the basic model structure for tunnel surrounding rock is determined to be Hooke body-Kelvin body-Newton body-Bingham body. S212, if If the Bingham body in the basic model structure fails, the state equation corresponding to the tunnel surrounding rock is: ,in Indicates the second strain. Indicates the third strain. Indicates the second stress The first derivative with respect to time t, Indicates the second strain The first derivative with respect to time t, Third strain The first derivative with respect to time t; like Then, the Bingham body in the basic model structure comes into play, and the state equation corresponding to the tunnel surrounding rock is: ,in Indicates the fourth strain. Represents the third viscosity coefficient. Indicates the fourth strain The first derivative with respect to time t; S213. Transform the state equations corresponding to the tunnel surrounding rock into first-order linear ordinary differential equations, then calculate their general solution to obtain the one-dimensional constitutive equations of the basic model structure of the tunnel surrounding rock. ,in This represents the initial stress of the model.

4. The method for constructing a constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation as described in claim 3, characterized in that, Model parameters are divided into experimental parameters and analytical parameters, including: ρ , H and Divide into experimental parameters, T 1. T 2. G 1. K , G 2 and It is divided into parsed parameters.

5. The method for constructing a constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation as described in claim 4, characterized in that, The determination of experimental parameters includes: obtaining them based on the experimental results. The parameter values ​​are determined based on the International System of Units (SI). ρ And the parameter values ​​of H.

6. The method for constructing a constitutive model of tunnel surrounding rock creep damage based on the law of energy conservation as described in claim 5, characterized in that, Determining the parsing parameters includes the following steps: S31. Based on the generalized Hooke's law, through the formula calculate G 1 and K The parameter values, where μ Represents Poisson's ratio, and a creep curve is constructed based on creep data. Solve ,in Indicates instantaneous strain; S32, respectively using a , b , c and d Indicates parameters T 1. T 2. G 2 and , will the known G 1. K, ρ , H and The parameter values ​​are substituted into the constitutive equation of the tunnel surrounding rock creep damage constitutive model, and Gaussian noise is added to it. ,Right now Gaussian noise Gaussian distribution is 0 represents the expectation of the Gaussian distribution. Let be the variance of the Gaussian distribution; S33. Assume that the constitutive equations in step S32 have N equations relating to t and The data points are transformed into the following least squares problem: ; S34. Generating t and t based on the constitutive model of creep damage in tunnel surrounding rock in Python. The true value is obtained by adding Gaussian noise to the true value and fitting the data from the noisy data using the Gauss-Newton method. When, fitting error for: ,in express The truth value of; Therefore, the derivatives of a, b, c, and d with respect to the state variables are: Obtain the Jacobian matrix. , Where T denotes matrix transpose; the incremental equation of Gauss-Newton's method is , where i represents the iteration number. Indicates the time step.

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