Creep characteristic analysis method and system based on soft rock nonlinear creep constitutive model

Abstract

The application provides a creep characteristic analysis method and system based on a soft rock nonlinear creep constitutive model, and relates to the technical field of geotechnical engineering.The method comprises the following steps: obtaining a soft rock sample and performing a laboratory triaxial creep test to obtain laboratory triaxial creep test results; constructing a constitutive equation of a Newton viscous pot; combining an equivalent damage stress principle to optimize a Burgers creep model; establishing a soft rock nonlinear creep constitutive model according to the optimized Burgers creep model; inputting the laboratory triaxial creep test results into the soft rock nonlinear creep constitutive model; performing calculation and analysis on the laboratory triaxial creep test results by the soft rock nonlinear creep constitutive model; and obtaining the creep characteristics of the soft rock.The soft rock nonlinear creep constitutive model of the near-field dynamics theory can comprehensively and preferably describe the three-stage creep characteristics of the soft rock, and the model has clear physical meaning and simple parameters.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geotechnical engineering, in particular, to a creep characteristic analysis method and system based on a soft rock nonlinear creep constitutive model. BACKGROUND

[0002] Soft rock is common in underground engineering, and such rock mass has obvious rheological properties and large creep deformation, which is the main reason for large deformation and damage of deep buried soft rock tunnels during operation. Under the action of constant load, the creep process of soft rock can be divided into three stages: initial creep, stable creep and accelerated creep (as shown in Figure 2 Therefore, the soft rock creep constitutive is the basis for analyzing the interaction between the surrounding rock and support of the extrusion large deformation tunnel, and it is of great engineering significance to study its constitutive model.

[0003] At present, scholars at home and abroad have proposed a relatively complete soft rock creep constitutive based on the theory of continuum mechanics, and have analyzed the time effect of the rheological rock mass tunnel surrounding rock-support interaction in actual engineering. In fact, the development process of soft rock creep involves the transformation of material from continuum to discontinuum, and the transformation of continuous problem to discontinuous problem. However, the differential form of the motion equation of the finite element method and the finite difference method based on the theory of continuum mechanics has singularity when solving discontinuous problems.

[0004] In order to overcome the limitations of traditional methods in simulating the discontinuous failure process, scholars have developed some advanced numerical methods, such as extended finite element method (XFEM), discontinuous deformation analysis (DDA), numerical manifold method (NMM) and smoothed particle hydrodynamics (SPH), and gradually applied them to the simulation of geotechnical engineering failure. Although the above methods have been successfully applied to the study of large deformation mechanism of soft rock tunnel, these numerical results are often affected by the initial mesh and block division and the form of particle discretization, and often require tedious calibration procedures to determine the calculation parameters, so it is difficult to effectively simulate the multi-scale evolution process of surrounding rock damage.

[0005] In order to more effectively solve the above problems, the peridynamics theory (Peridynamics, hereinafter referred to as PD) based on the non-local idea is proposed, which is based on the integral form of the motion equation and has no special requirements for the size of the non-local scope, so it can describe the complex mechanical behavior from continuum to discontinuum and from micro to macro. Therefore, the PD theory has also received widespread attention in the study of damage evolution of tunnel surrounding rock and lining. However, there is still a lack of soft rock nonlinear creep constitutive model under the framework of peridynamics theory, which restricts the application of peridynamics theory in the study of large deformation mechanism of deep buried soft rock tunnel.

[0006] In view of the problems in the related art, no effective solution has been proposed so far. SUMMARY

[0007] In view of this, the present invention provides a creep characteristic analysis method and system based on a nonlinear creep constitutive model of soft rock to solve the aforementioned problems.

[0008] To solve the above problems, the specific technical solution adopted by the present invention is as follows:

[0009] According to one aspect of the present invention, a creep characteristic analysis method based on a nonlinear creep constitutive model for soft rock is provided. This creep characteristic analysis method based on a nonlinear creep constitutive model for soft rock includes the following steps:

[0010] S1. Soft rock samples were obtained using in-situ technology, and the results of the indoor triaxial creep test were obtained by conducting an indoor triaxial creep test on the soft rock samples.

[0011] S2. Based on the Maxwell-Newtonian sticky pot with integrated near-field dynamic damage index, construct the constitutive equation of the Newtonian sticky pot; and optimize the Burgers creep model by combining the equivalent damage stress principle to obtain the optimized Burgers creep model. Based on the optimized Burgers creep model, establish a nonlinear creep constitutive model for soft rock.

[0012] S3. Input the results of the indoor triaxial creep test into the nonlinear creep constitutive model of soft rock, and calculate and analyze the results of the indoor triaxial creep test through the nonlinear creep constitutive model of soft rock to obtain the creep characteristics of soft rock.

[0013] Preferably, the process of obtaining soft rock samples using in-situ technology and obtaining the results of indoor triaxial creep tests on the soft rock samples includes the following steps:

[0014] S 11. Soft rock samples are taken using a waterless engineering drilling rig and wrapped with plastic wrap. The wrapped soft rock samples are then placed in a constant temperature chamber.

[0015] S1 2. Uniaxial compressive strength test was conducted on soft rock specimens by load control loading method, and the axial load graded loading condition of soft rock specimens was determined based on the uniaxial compressive strength test results to obtain the axial load of indoor triaxial creep test.

[0016] S13. The stress in the sampling area is measured using the bottom hole stress relief method to determine the maximum and minimum principal stresses in the sampling area. The upper and lower limits of the confining pressure are determined based on the maximum and minimum principal stresses. The confining pressure is then tested on the soft rock samples based on the upper and lower limits of the confining pressure to obtain the confining pressure for the indoor triaxial creep test.

[0017] S1 4. By controlling the loading method and applying axial compression tests to soft rock samples at different loading speeds until the soft rock samples fail, the axial load control rate of the indoor triaxial creep test is obtained.

[0018] S15. Based on the axial load of the indoor triaxial creep test, the confining pressure of the indoor triaxial creep test, and the axial load control rate of the indoor triaxial creep test, establish the axial creep curve, failure characteristics, and stress-strain curve respectively.

[0019] Preferably, the step of measuring the ground stress in the sampling area using the borehole bottom stress relief method to determine the maximum and minimum principal stresses in the sampling area includes the following steps:

[0020] S131. According to the preset measurement drilling depth, drill holes in the sampling area using a drill bit, and attach strain rosettes to the bottom of the holes and read the initial strain data.

[0021] S 1 32. Use a drill bit with the same diameter as the drill bit to extend the depth of the bottom of the borehole, and obtain new strain data at the bottom of the borehole after the stress field around the borehole is released.

[0022] S133. Based on the initial strain data and the new strain data, calculate the geostress value and determine the direction of the principal stress, and determine the maximum and minimum principal stresses of the sampling area.

[0023] Preferably, the optimization of the Burgers creep model based on peri-field dynamics theory and Newton's sticky pot theory, the establishment of a nonlinear creep constitutive model for soft rock based on the optimized Burgers creep model, and the input of indoor triaxial creep test results into the nonlinear creep constitutive model for soft rock, and the calculation of the three-stage creep characteristics of soft rock through the nonlinear creep constitutive model for soft rock, includes the following steps:

[0024] S2 1. Based on the peri-field dynamics theory and combined with the stochastic damage index, a nonlinear damage mechanism is introduced into the Maxwell Newton sticky pot to obtain the constitutive equation of the Newton sticky pot.

[0025] S22. Based on the principle of equivalent damage stress, the expression for Newton's sticky pot strain is established through the local damage index in the near-field dynamics theory. The Burgers creep model is then optimized based on the expression for Newton's sticky pot strain to obtain the optimized Burgers creep model.

[0026] S23. Establish the relationship between near-field dynamics and the strain density energy of the continuous medium theory to obtain the expression of the microscopic elastic modulus with respect to creep compliance, and construct the creep compliance expression through the optimized Burgers creep model.

[0027] S24. Based on the structural force function of the prototype microelastic brittle material, and combined with the expression of the microelastic modulus with respect to creep compliance and the creep compliance expression, establish a nonlinear creep constitutive model for soft rock.

[0028] Preferably, the process of establishing a Newton's sticky pot strain expression based on the principle of equivalent damage stress using local damage indices in peri-field dynamics theory, and optimizing the Burgers creep model according to the Newton's sticky pot strain expression to obtain the optimized Burgers creep model includes the following steps:

[0029] S221. Using the principle of equivalent damage stress, a relationship is established between damage variables and equivalent stress, and the damage accumulation effect of the material is described through the damage variables to obtain the Newtonian stick bottle strain expression that takes into account the degree of damage.

[0030] S222. The degree of material damage is characterized by the local damage index in the near-field dynamics theory, and the expression for Newton's stick pot strain considering the local damage index is obtained.

[0031] S223. Replace the Newton's sticky pot part in the Burgers creep model with the Newton's sticky pot strain expression that considers local damage indices to obtain the optimized Burgers creep model.

[0032] Preferably, the expression for Newton's stick pot strain considering local damage indicators is:

[0033]

[0034] In the formula, ε1(t) represents the Newtonian stick pot strain considering local damage parameters;

[0035] σ0 represents constant stress;

[0036] Indicates local damage indicators;

[0037] η M This represents the viscosity coefficient of a Newtonian body in the Maxwell model;

[0038] t represents time.

[0039] Preferably, the optimized Burgers creep model expression is:

[0040]

[0041] In the formula, ε2(t) represents the strain of the optimized Burgers creep model;

[0042] σ0 represents constant stress;

[0043] η M and η K represent the Newtonian body viscosity coefficients in the Maxwell and Kelvin models, respectively;

[0044] t represents time;

[0045] E M and E K Let represent the elastic modulus of the Hooke body in the Maxwell model and the Kelvin model, respectively;

[0046] Indicates local damage indicators.

[0047] Preferably, the creep compliance expression constructed using the optimized Burgers creep model is as follows:

[0048]

[0049] In the formula, J(t) represents creep compliance;

[0050] η M and η K represent the Newtonian body viscosity coefficients in the Maxwell and Kelvin models, respectively;

[0051] t represents time;

[0052] E M and E K Let represent the elastic modulus of the Hooke body in the Maxwell model and the Kelvin model, respectively;

[0053] Indicates local damage indicators.

[0054] Preferably, the force function expression of the nonlinear creep constitutive model for soft rock is:

[0055]

[0056] In the formula, f(η, ξ, t) represents the force function of the nonlinear creep constitutive model of soft rock;

[0057] μ represents the fracture parameter;

[0058] s represents elongation;

[0059] ξ represents the relative position of the two material points in the initial reference configuration;

[0060] η represents the relative displacement of the two material points in their current configuration;

[0061] ξ+η represents the relative positions of the two material points in the current configuration;

[0062] || represents taking the modulus of a vector;

[0063] h represents the thickness of the model;

[0064] δ represents the radius of the territory;

[0065] η M and η K represent the Newtonian body viscosity coefficients in the Maxwell and Kelvin models, respectively;

[0066] t represents time;

[0067] E M and E K These represent the elastic modulus of the Hooke body in the Maxwell model and the Kelvin model, respectively.

[0068] Indicates local damage indicators.

[0069] According to another aspect of the present invention, a creep characteristic analysis system based on a nonlinear creep constitutive model for soft rock is provided. The creep characteristic analysis system based on the nonlinear creep constitutive model for soft rock includes: a creep test result acquisition module, a model optimization module, and a creep characteristic analysis module.

[0070] The creep test result acquisition module is used to acquire soft rock samples using in-situ technology and obtain indoor triaxial creep test results by conducting indoor triaxial creep tests on the soft rock samples.

[0071] The model optimization module is used to construct the constitutive equation of the Newton's sticky pot based on the Maxwell Newton's sticky pot with the fusion of near-field dynamic damage index; and to optimize the Burgers creep model in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model. Based on the optimized Burgers creep model, a nonlinear creep constitutive model for soft rock is established.

[0072] The creep characteristic analysis module is used to input the results of indoor triaxial creep tests into the nonlinear creep constitutive model of soft rock, and to calculate and analyze the results of indoor triaxial creep tests through the nonlinear creep constitutive model of soft rock to obtain the creep characteristics of soft rock.

[0073] The beneficial effects of this invention are as follows:

[0074] 1. The nonlinear creep constitutive model of soft rock based on near-field dynamics theory proposed in this invention can comprehensively and well describe the three-stage creep characteristics of soft rock (initial creep, steady creep and accelerated creep), and the model has clear physical meaning and simple parameters.

[0075] 2. By introducing local damage indicators, this invention can achieve real-time judgment in the numerical calculation process without giving a threshold for the accelerated creep stage. It can better reflect the dynamic evolution process of surrounding rock disturbance and facilitate the accurate revelation of the large deformation evolution mechanism of soft rock tunnels. Attached Figure Description

[0076] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0077] Figure 1 This is a flowchart of a creep characteristic analysis method based on a nonlinear creep constitutive model of soft rock according to an embodiment of the present invention;

[0078] Figure 2 This is a schematic diagram of the creep curve of soft rock in the creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to an embodiment of the present invention.

[0079] Figure 3 This is a diagram of the Burgers mechanical model in the creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to an embodiment of the present invention.

[0080] Figure 4 This is an improved Burgers mechanical model diagram in the creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to an embodiment of the present invention;

[0081] Figure 5 This is a creep model diagram in the creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to an embodiment of the present invention;

[0082] Figure 6 This is a comparison of experimental and simulation results of limestone samples in the creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to an embodiment of the present invention;

[0083] Figure 7 This is a comparison of experimental and simulation results of coal and rock samples in the creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to an embodiment of the present invention;

[0084] Figure 8 This is a schematic diagram of a creep characteristic analysis system based on a nonlinear creep constitutive model of soft rock according to an embodiment of the present invention.

[0085] In the picture:

[0086] 1. Creep test result acquisition module; 2. Model optimization module; 3. Creep feature analysis module. Detailed Implementation

[0087] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0088] According to embodiments of the present invention, a method and system for creep characteristic analysis based on a nonlinear creep constitutive model for soft rock are provided.

[0089] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 1 As shown, according to an embodiment of the present invention, a creep characteristic analysis method based on a nonlinear creep constitutive model for soft rock is provided. This creep characteristic analysis method based on a nonlinear creep constitutive model for soft rock includes the following steps:

[0090] S1. Soft rock samples were obtained using in-situ technology, and the results of the indoor triaxial creep test were obtained by conducting an indoor triaxial creep test on the soft rock samples.

[0091] Specifically, it is necessary to design an indoor triaxial creep test, including determining the axial load, confining pressure, and axial load control rate for the indoor triaxial creep test.

[0092] As a preferred embodiment, the process of obtaining soft rock samples using in-situ technology and obtaining indoor triaxial creep test results by conducting indoor triaxial creep tests on the soft rock samples includes the following steps:

[0093] S 11. Soft rock samples are taken using a waterless engineering drilling rig and wrapped with plastic wrap. The wrapped soft rock samples are then placed in a constant temperature chamber.

[0094] Specifically, waterless drilling rigs are used for sampling to avoid softening of rock samples due to water.

[0095] The sample was wrapped in plastic wrap and placed in a constant temperature chamber (within ±0.5℃ of the formation temperature) to avoid the influence of moisture content and temperature changes on its mechanical properties.

[0096] S1 2. Uniaxial compressive strength test was conducted on soft rock specimens by load control loading method, and the axial load graded loading condition of soft rock specimens was determined based on the uniaxial compressive strength test results to obtain the axial load of indoor triaxial creep test.

[0097] S13. The stress in the sampling area is measured using the bottom hole stress relief method to determine the maximum and minimum principal stresses in the sampling area. The upper and lower limits of the confining pressure are determined based on the maximum and minimum principal stresses. The confining pressure is then tested on the soft rock samples based on the upper and lower limits of the confining pressure to obtain the confining pressure for the indoor triaxial creep test.

[0098] In a preferred embodiment, the step of measuring the in-situ stress in the sampling area using the borehole bottom stress relief method to determine the maximum and minimum principal stresses in the sampling area includes the following steps:

[0099] S131. According to the preset measurement drilling depth, drill holes in the sampling area using a drill bit, and attach strain rosettes to the bottom of the holes and read the initial strain data.

[0100] S 1 32. Use a drill bit with the same diameter as the drill bit to extend the depth of the bottom of the borehole, and obtain new strain data at the bottom of the borehole after the stress field around the borehole is released.

[0101] S133. Based on the initial strain data and the new strain data, calculate the geostress value and determine the direction of the principal stress, and determine the maximum and minimum principal stresses of the sampling area.

[0102] Specifically, a drill bit is used to drill a hole to measure a certain depth of the rock mass;

[0103] The strain gauge was attached to the bottom of the borehole, and the initial strain was read.

[0104] The borehole is further deepened by using a drill string of the same diameter as the drill bit to relieve the stress around the small hole;

[0105] Read the strain readings after stress relief, calculate the ground stress value, and determine the direction of the principal stress.

[0106] S1 4. By controlling the loading method and applying axial compression tests to soft rock samples at different loading speeds until the soft rock samples fail, the axial load control rate of the indoor triaxial creep test is obtained.

[0107] Specifically, the axial compression process adopts a load-controlled loading method, with an initial loading speed of 0.1 kN / s, and loading to the predetermined initial axial compression value;

[0108] The subsequent loading rate for each load level is 0.5 kN / s, and the deformation rate under each load level is less than 0.0004 mm / h before the next load level is applied, until the specimen fails.

[0109] S15. Based on the axial load of the indoor triaxial creep test, the confining pressure of the indoor triaxial creep test, and the axial load control rate of the indoor triaxial creep test, establish the axial creep curve, failure characteristics, and stress-strain curve respectively.

[0110] S2. Based on the Maxwell-Newton sticky pot with integrated near-field dynamic damage index, construct the constitutive equation of the Newton sticky pot; and optimize the Burgers creep model by combining the equivalent damage stress principle to obtain the optimized Burgers creep model. Based on the optimized Burgers creep model, establish a nonlinear creep constitutive model for soft rock.

[0111] It should be noted that element models are widely used to describe the creep behavior of soft rocks due to their simple principles and clear physical meaning of parameters. Examples include linear viscoelastic rheological constitutive models such as the Maxwell model, Kelvin model, generalized Maxwell model, generalized Kelvin model, and Burgers model. Generally, the determination of a material constitutive model should reflect the mechanical properties of the material while also being as simple and intuitive as possible. The Burgers model, using Maxwell and Kelvin elements in series, can effectively describe the elastic strain, initial creep, and stable creep stages of rocks, and can degenerate into four other models, making it the most commonly used constitutive model for soft rocks.

[0112] Classical Burgers creep model (e.g.) Figure 3 The creep equation (as shown) is:

[0113]

[0114] In the formula, ε represents creep strain, σ0 represents constant stress, t represents time, and E M E K The elastic modulus of the Hooke body in the Maxwell and Kelvin models are respectively, η. M η K These are the viscosity coefficients of Newtonian bodies in the Maxwell and Kelvin models, respectively, because the viscosity coefficient η M The constant value of φ means that the Burgers creep model cannot describe the accelerated creep process of soft rock. However, as damage accumulates during the creep process of soft rock, when a certain threshold is reached, the creep often shows an accelerated trend, that is, macroscopic cracks develop rapidly until instability and failure.

[0115] As a preferred embodiment, the step of constructing the constitutive equation of the Newtonian sticky pot based on the Maxwell-Newtonian sticky pot with the fusion of near-field dynamic damage index; and optimizing the Burgers creep model by combining the equivalent damage stress principle to obtain the optimized Burgers creep model, and establishing a nonlinear creep constitutive model for soft rock based on the optimized Burgers creep model includes the following steps:

[0116] S2 1. Based on the peri-field dynamics theory and combined with the stochastic damage index, a nonlinear damage mechanism is introduced into the Maxwell Newton sticky pot to obtain the constitutive equation of the Newton sticky pot.

[0117] It should be noted that, in order to describe the accelerated creep process of soft rock that is related to the degree of damage, this invention proposes a one-dimensional nonlinear Newtonian sticky pot that considers random damage, based on the Maxwell Newton sticky pot and combined with the peri-field dynamic damage index, so as to describe the accelerated creep stage of soft rock.

[0118] The constitutive equation for Newton's sticky pot is:

[0119]

[0120] In the formula, σ represents stress, ε represents creep strain, t represents time, and η represents stress. M This represents the viscosity coefficient of Newtonian volumes in the Maxwell model.

[0121] S22. Based on the principle of equivalent damage stress, the expression for Newton's sticky pot strain is established through the local damage index in the near-field dynamics theory. The Burgers creep model is then optimized based on the expression for Newton's sticky pot strain to obtain the optimized Burgers creep model.

[0122] As a preferred embodiment, the step of establishing a Newtonian stickpot strain expression based on the principle of equivalent damage stress using local damage indices in near-field dynamics theory, and optimizing the Burgers creep model according to the Newtonian stickpot strain expression to obtain the optimized Burgers creep model includes the following steps:

[0123] S221. Using the principle of equivalent damage stress, a relationship is established between damage variables and equivalent stress, and the damage accumulation effect of the material is described through the damage variables to obtain the Newtonian stick bottle strain expression that takes into account the degree of damage.

[0124] It should be noted that, according to the equivalent damage stress principle (Lemaitre strain equivalence principle), the equivalent stress and damage variable satisfy the following relationship:

[0125]

[0126] In the formula, Let σ represent the equivalent stress, D represent the damage variable, and σ represent the stress.

[0127] Based on the relationship between equivalent stress and damage variable, and the constitutive equation of Newton's sticky pot, the strain expression of Newton's sticky pot considering the degree of damage can be obtained.

[0128] Specifically, the strain expression for a Newton's sticky pot, considering the degree of damage, is as follows:

[0129]

[0130] In the formula, ε represents the strain of the Newton's mud pot considering the degree of damage, σ0 represents constant stress, t represents time, D represents the damage variable, and η M This represents the viscosity coefficient of Newtonian volumes in the Maxwell model.

[0131] S222. The degree of material damage is characterized by the local damage index in the near-field dynamics theory, and the expression for Newton's stick pot strain considering the local damage index is obtained.

[0132] It should be noted that in damage mechanics theory, the damage variable D is defined as a physical quantity representing the degree of damage to a standard material under the influence of external forces or the external environment. In peri-field dynamics theory, the local damage index... The ratio of the number of broken bonds to the number of initially intact bonds is the same as the damage variable D, and it also characterizes the degree of material damage. Therefore, the local damage index... Substituting these values ​​into the strain expression for a Newton's sticky pot that considers the degree of damage, we obtain the strain expression for a Newton's sticky pot that considers local damage indices.

[0133] In a preferred embodiment, the expression for Newton's stick pot strain considering local damage indicators is:

[0134]

[0135] In the formula, ε1(t) represents the Newtonian stick bottle strain considering local damage parameters; σ0 represents constant stress; Indicates a local damage index; η M represents the viscosity coefficient of a Newtonian volume in the Maxwell model; t represents time.

[0136] From the Newtonian stick pot strain expression considering local damage indices, it can be seen that when the rock is in a stable creep stage, its damage degree is relatively small, i.e. Approximately zero, the Newtonian strain in a stick pot, considering the degree of damage, increases linearly with time; as creep time increases, the degree of material damage continuously increases, and its strain gradually exhibits a non-linear growth; when the material approaches complete failure, i.e. Its adaptability tends to be infinite.

[0137] S223. Replace the Newton's sticky pot part in the Burgers creep model with the Newton's sticky pot strain expression that considers local damage indices to obtain the optimized Burgers creep model.

[0138] Specifically, by replacing the Newton's sticky pot part in the Burgers creep model with the Newton's sticky pot strain expression that considers local damage indices, we can obtain an improved damage-related Burgers creep model, i.e., the optimized Burgers creep model.

[0139] As a preferred embodiment, the optimized Burgers creep model expression is as follows:

[0140]

[0141] In the formula, ε2(t) represents the strain of the optimized Burgers creep model; σ0 represents constant stress; η M and η K E represents the viscosity coefficient of Newtonian volume in the Maxwell and Kelvin models, respectively; t represents time, and E represents the viscosity coefficient of Newtonian volume. M and E K Let represent the elastic modulus of the Hooke body in the Maxwell model and the Kelvin model, respectively; Indicates local damage indicators.

[0142] S23. Establish the relationship between near-field dynamics and the strain density energy of the continuous medium theory to obtain the expression of the microscopic elastic modulus with respect to creep compliance, and construct the creep compliance expression through the optimized Burgers creep model.

[0143] Specifically, by making the strain density energy equal to that of the near-field dynamics and the classical continuum theory, we can obtain the expression of the microscopic elastic modulus with respect to creep compliance.

[0144]

[0145] In the formula, c represents the microelastic modulus, h represents the thickness of the model, δ represents the radius of the domain, and J represents the creep compliance.

[0146] Specifically, creep compliance is the ratio of strain to stress at any moment during the creep process of a material. The creep compliance expression is constructed using the optimized Burgers creep model as follows:

[0147]

[0148] In the formula, J(t) represents creep compliance; η M and η K Represent the Newtonian viscosity coefficients in the Maxwell and Kelvin models, respectively; t represents time; E M and E K Let represent the elastic modulus of the Hooke body in the Maxwell model and the Kelvin model, respectively; Indicates local damage indicators.

[0149] S24. Based on the structural force function of the prototype microelastic brittle material, and combined with the expression of the microelastic modulus with respect to creep compliance and the creep compliance expression, establish a nonlinear creep constitutive model for soft rock.

[0150] Specifically, for the prototype microelastic-brittle material, its constitutive force function f(η, ξ, t) is:

[0151]

[0152] In the formula, μ represents the fracture parameter, s represents the elongation, ξ represents the relative position of the two material points in the initial reference configuration, η represents the relative displacement of the two material points in the current configuration, ξ+η represents the relative position of the two material points in the current configuration, and || represents taking the modulus of the vector.

[0153] In a preferred embodiment, the force function expression of the nonlinear creep constitutive model for soft rock is as follows:

[0154]

[0155] In the formula, f(η, ξ, t) represents the force function of the nonlinear creep constitutive model for soft rock; μ represents the fracture parameter; s represents the elongation; ξ represents the relative position of the two material points in the initial reference configuration (referring to the spatial distribution of material points in the initial state); η represents the relative displacement of the two material points in the current configuration (referring to the spatial distribution of material points in the current deformation state); ξ+η represents the relative position of the two material points in the current configuration; || represents the modulus of the vector; h represents the thickness of the model; δ represents the radius of the neighborhood; η M and η K Represent the Newtonian viscosity coefficients in the Maxwell and Kelvin models, respectively; t represents time; E M and E K These represent the elastic modulus of the Hooke body in the Maxwell model and the Kelvin model, respectively. Indicates local damage indicators.

[0156] S3. Input the results of the indoor triaxial creep test into the nonlinear creep constitutive model of soft rock, and calculate and analyze the results of the indoor triaxial creep test through the nonlinear creep constitutive model of soft rock to obtain the creep characteristics of soft rock.

[0157] It should be noted that the creep characteristics of soft rock include the three-stage creep characteristics of soft rock (initial creep, stable creep, and accelerated creep).

[0158] like Figure 8 As shown, according to another embodiment of the present invention, a creep characteristic analysis system based on a nonlinear creep constitutive model of soft rock is provided. The creep characteristic analysis system based on the nonlinear creep constitutive model of soft rock includes: a creep test result acquisition module 1, a model optimization module 2, and a creep characteristic analysis module 3.

[0159] The creep test result acquisition module 1 is used to acquire soft rock samples using in-situ technology and obtain indoor triaxial creep test results by conducting indoor triaxial creep tests on the soft rock samples.

[0160] The model optimization module 2 is used to construct the constitutive equation of the Newton's sticky pot based on the Maxwell Newton's sticky pot with the fusion of near-field dynamic damage index; and to optimize the Burgers creep model in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model. Based on the optimized Burgers creep model, a nonlinear creep constitutive model for soft rock is established.

[0161] The creep characteristic analysis module 3 is used to input the indoor triaxial creep test results into the soft rock nonlinear creep constitutive model, and to calculate and analyze the indoor triaxial creep test results through the soft rock nonlinear creep constitutive model to obtain the creep characteristics of the soft rock.

[0162] To facilitate understanding of the above technical solutions of the present invention, the creep characteristic analysis method and system based on the nonlinear creep constitutive model of soft rock proposed in this invention are verified below based on the creep test results of limestone and coal.

[0163] according to Figure 4 The parameters such as elastic strain, initial creep tangent slope, and intersection of the reverse extension of stable creep shown in the curves are combined with the experimental curves to obtain the creep model calculation parameters, as shown in Table 1. Figure 5 The diagram shows a creep model with a point spacing (Δx) of 1.0 mm, a domain radius of δ = 3Δx, and a critical elongation (s) of approximately 0.007 (limestone) and 0.002 (coalstone).

[0164] Table 1 Calculation parameters for the creep model

[0165]

[0166] like Figure 6 As shown, the limestone samples under uniaxial compressive loads of 16.3 and 27.1 MPa only exhibited initial and steady creep, without accelerated creep. The proposed nonlinear creep constitutive model can better simulate the creep test curve of limestone. For coal and rock samples (such as...), the model can also be used to simulate the creep test curve of limestone. Figure 7 As shown, when the loading stress level is 3.0 MPa, it can effectively reproduce the initial creep and stable creep characteristics. When the loading stress level is 12.0 MPa, the proposed nonlinear creep constitutive model can predict its creep characteristics well, and it matches the experimental data well. The difference is that at the instant of loading, the test results of the specimens all show instantaneous elastic deformation (strain is not zero). Although the simulation results can reproduce the elastic deformation process, the strain gradually increases from 0. The above phenomenon is mainly related to the integration process of the near-field dynamic equation of motion. At time step t = 0, its initial acceleration, velocity, and displacement are all 0, and as the time step increases, its displacement also accumulates and gradually increases. Overall, the model can comprehensively and well describe the three-stage creep characteristics of rocks, and the model has clear physical meaning and simple parameters.

[0167] In summary, by utilizing the above-mentioned technical solutions of this invention, the nonlinear creep constitutive model for soft rock based on near-field dynamics theory proposed in this invention can comprehensively and effectively describe the three-stage creep characteristics of soft rock (initial creep, stable creep, and accelerated creep), and the model has clear physical meaning and simple parameters. This invention, by introducing a local damage index, enables real-time judgment during numerical calculations, eliminating the need for a given threshold for the accelerated creep stage. It can better reflect the dynamic evolution process of surrounding rock disturbance, facilitating accurate revelation of the large deformation evolution mechanism of soft rock tunnels.

[0168] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.

[0169] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing creep characteristics based on a soft rock nonlinear creep constitutive model, characterized in that, The creep characteristic analysis method based on the soft rock nonlinear creep constitutive model comprises the following steps: S1, obtaining soft rock samples by using in-situ technology, and obtaining indoor triaxial creep test results by performing indoor triaxial creep tests on the soft rock samples; S2, constructing a constitutive equation of the Newtonian dashpot according to a Maxwell Newtonian dashpot fused with a near-field dynamic damage index; and optimizing a Burgers creep model in combination with an equivalent damage stress principle to obtain an optimized Burgers creep model, and establishing a soft rock nonlinear creep constitutive model according to the optimized Burgers creep model; S3, inputting the indoor triaxial creep test results into the soft rock nonlinear creep constitutive model, and performing calculation and analysis on the indoor triaxial creep test results by the soft rock nonlinear creep constitutive model to obtain the creep characteristics of the soft rock; The step of constructing the constitutive equation of the Newtonian dashpot according to the Maxwell Newtonian dashpot fused with the near-field dynamic damage index, and optimizing the Burgers creep model in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model, and establishing the soft rock nonlinear creep constitutive model according to the optimized Burgers creep model comprises the following steps: S21, introducing a nonlinear damage mechanism into the Maxwell Newtonian dashpot according to the near-field dynamic theory and in combination with a random damage index to obtain the constitutive equation of the Newtonian dashpot; S22, establishing a Newtonian dashpot strain expression based on the equivalent damage stress principle and by using a local damage index in the near-field dynamic theory, and optimizing the Burgers creep model according to the Newtonian dashpot strain expression to obtain the optimized Burgers creep model; S23, establishing a relationship that the strain density energy of the near-field dynamics is equal to that of the continuous medium theory to obtain an expression of a micro elastic modulus with respect to a creep compliance, and constructing a creep compliance expression by using the optimized Burgers creep model; S24, establishing the soft rock nonlinear creep constitutive model according to a constitutive function of a prototype micro elastic brittle material and in combination with the expression of the micro elastic modulus with respect to the creep compliance and the creep compliance expression; The step of establishing the Newtonian dashpot strain expression based on the equivalent damage stress principle and by using the local damage index in the near-field dynamic theory, and optimizing the Burgers creep model according to the Newtonian dashpot strain expression to obtain the optimized Burgers creep model comprises the following steps: S221, establishing a relationship between a damage variable and an equivalent stress by using the equivalent damage stress principle, and describing damage accumulation effects of a material by using the damage variable to obtain a Newtonian dashpot strain expression considering damage degrees; S222, using a local damage index in the near-field dynamic theory to represent damage degrees of the material to obtain a Newtonian dashpot strain expression considering the local damage index; S223, replacing a Newtonian dashpot part in the Burgers creep model with the Newtonian dashpot strain expression considering the local damage index to obtain the optimized Burgers creep model; The expression of the optimized Burgers creep model is as follows: ； In the formula, ε 2 (t) represents a strain of the optimized Burgers creep model; σ 0 represents a constant stress; η M and η K represent the Newtonian viscosity of the Maxwell and Kelvin models, respectively. t represents time; E M and E K E and E represent the Hookian elastic modulus in the Maxwell and Kelvin models, respectively; represents a local damage indicator.

2. The creep characteristic analysis method based on the soft rock nonlinear creep constitutive model according to claim 1, characterized in that, The indoor triaxial creep test result obtained by the in-situ technique and the indoor triaxial creep test of the soft rock sample includes the following steps: S11, the soft rock sample is sampled by the waterless engineering drilling machine, and the soft rock sample is wrapped with the preservative film, and the wrapped soft rock sample is placed in the thermostat; S12, the uniaxial compressive strength test of the soft rock sample is carried out by the load control loading mode, and the axial load grading loading condition of the soft rock sample is determined according to the uniaxial compressive strength test result, and the indoor triaxial creep test axial load is obtained; S13, the hole bottom stress relief method is used to measure the ground stress of the sampling area, and the maximum principal stress and the minimum principal stress of the sampling area are determined; and the upper and lower limit values of the confining pressure are determined according to the maximum principal stress and the minimum principal stress, and the soft rock sample is subjected to the confining pressure test according to the upper and lower limit values of the confining pressure, and the indoor triaxial creep test confining pressure is obtained; S14, the axial test is carried out on the soft rock sample by the load control loading mode and at different loading speeds until the soft rock sample is damaged, and the indoor triaxial creep test axial load control rate is obtained; S15, the axial creep curve, the failure characteristics and the stress-strain curve are respectively established according to the indoor triaxial creep test axial load, the indoor triaxial creep test confining pressure and the indoor triaxial creep test axial load control rate.

3. The creep characteristic analysis method based on the soft rock nonlinear creep constitutive model according to claim 2, characterized in that, The hole bottom stress relief method is used to measure the ground stress of the sampling area, and the maximum principal stress and the minimum principal stress of the sampling area are determined, including the following steps: S131, according to the pre-set measurement drilling depth, the drill bit is drilled in the sampling area, and the strain rosette is pasted at the bottom of the drill hole and the initial strain data is read; S132, the bottom of the drill hole is extended in depth by using a sleeve drill with the same diameter as the drill bit, and after the stress field around the drill hole is relieved, the new strain data of the bottom of the drill hole is obtained; S133, according to the initial strain data and the new strain data, the ground stress value is calculated and the principal stress direction is judged, and the maximum principal stress and the minimum principal stress of the sampling area are determined.

4. The creep characteristic analysis method based on the soft rock nonlinear creep constitutive model according to claim 1, characterized in that, The Newtonian viscous pot strain expression considering the local damage index is: ； In the formula, ε1(t) represents the Newtonian viscous pot strain considering the local damage index; σ0 represents the constant stress; represents a local damage indicator; η M represents the Newtonian bulk viscosity coefficient in the Maxwell model; t represents time.

5. The creep characteristic analysis method based on the soft rock nonlinear creep constitutive model according to claim 1, characterized in that, The creep flexibility expression constructed by the optimized Burgers creep model is: ； In the formula, J(t) represents the creep flexibility; η M and η K represent the Newtonian viscosity of the Maxwell and Kelvin models, respectively. t represents time; E M and E K E and E represent the Hookian elastic modulus in the Maxwell and Kelvin models, respectively; represents a local damage indicator.

6. The method according to claim 1, wherein, The force function expression of the soft rock nonlinear creep constitutive model is: ； In the formula, f(η,ξ,t) represents the force function of the soft rock nonlinear creep constitutive model; μ represents the fracture parameter; s represents elongation; ξ represents the relative position of two material points in the initial reference configuration; η represents the relative displacement of two material points in the current configuration; ξ+η represents the relative position of two material points in the current configuration; || represents the modulus of the vector; h represents the thickness of the model; δ represents the domain radius; η M and η K represent the Newtonian viscosity of the Maxwell and Kelvin models, respectively. t represents time; E M and E K E and E represent the Hookean elastic modulus in the Maxwell and Kelvin models, respectively; represents a local damage indicator.

7. A creep characteristic analysis system based on the soft rock nonlinear creep constitutive model, for implementing the creep characteristic analysis method based on the soft rock nonlinear creep constitutive model according to any one of claims 1-6, characterized in that, The creep characteristic analysis system based on the soft rock nonlinear creep constitutive model comprises a creep test result acquisition module, a model optimization module and a creep characteristic analysis module. The creep test result acquisition module is configured to acquire a soft rock sample by using an in-situ technique, and obtain a triaxial creep test result by performing a triaxial creep test on the soft rock sample in a laboratory; The model optimization module is configured to construct a constitutive equation of the Newtonian dashpot according to a Maxwell-Newtonian dashpot fused with a near-field dynamic damage index; and optimize a Burgers creep model according to an equivalent damage stress principle to obtain an optimized Burgers creep model, and establish a soft rock nonlinear creep constitutive model according to the optimized Burgers creep model; The creep characteristic analysis module is configured to input the triaxial creep test result into the soft rock nonlinear creep constitutive model, and perform calculation and analysis on the triaxial creep test result by using the soft rock nonlinear creep constitutive model to obtain a creep characteristic of the soft rock.

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