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

Abstract

The invention 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 creep characteristic analysis method based on the soft rock nonlinear creep constitutive model comprises the following steps that a soft rock sample is obtained and subjected to an indoor triaxial creep test, and an indoor triaxial creep test result is obtained; constructing a constitutive equation of the Newton sticky kettle; the Burgers creep model is optimized by combining an equivalent damage stress principle, and a soft rock nonlinear creep constitutive model is established according to the optimized Burgers creep model; and inputting an indoor triaxial creep test result into the soft rock nonlinear creep constitutive model, and calculating and analyzing the indoor triaxial creep test result through the soft rock nonlinear creep constitutive model to obtain the creep characteristics of the soft rock. According to the soft rock nonlinear creep constitutive model based on the near-field dynamics theory, the three-stage creep characteristics of the soft rock can be comprehensively and well described, the physical significance of the model is clear, and the parameters are simple.

Description

Technical Field

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

[0002] Soft rock is commonly found in underground engineering. This type of rock has obvious rheological characteristics and large creep deformation, which is the main reason for the large deformation and failure of deep-buried soft rock tunnels during operation. Under constant load, the creep process of soft rock can be divided into three stages: initial creep, stable creep and accelerated creep (e.g. Figure 2 Therefore, the soft rock creep constitutive model is the basis for analyzing the interaction between surrounding rock and support in large extrusion deformation tunnels, and the study of its constitutive model has important engineering significance.

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

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

[0005] In order to solve the above problems more effectively, the peridynamics theory (PD) based on the nonlocal idea was proposed. The theory is based on the integral form of the motion equation and has no special requirements on the size of the nonlocal domain, so that it can describe the complex mechanical behavior from continuous to discontinuous, microscopic to macroscopic. Therefore, the PD theory has also received extensive attention in the study of the damage evolution of tunnel surrounding rock and lining. However, there is still a lack of nonlinear creep constitutive models for soft rock under the framework of peridynamic theory, which restricts the application of peridynamic theory in the large deformation mechanism of deep buried soft rock tunnels.

[0006] Currently, no effective solution has been proposed for the problems in the related technologies. Summary of the invention

[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 above-mentioned problems.

[0008] In order to solve the above problems, the specific technical solutions adopted by the present invention are as follows:

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

[0010] S1. Obtain soft rock samples using on-site in-situ technology, and obtain indoor triaxial creep test results by performing indoor triaxial creep tests on the soft rock samples;

[0011] S2. Based on the Maxwell-Newton viscosity pot integrated with the peridynamic damage index, the constitutive equation of the Newton viscosity pot is constructed; and the Burgers creep model is optimized in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model. Based on the optimized Burgers creep model, the nonlinear creep constitutive model of soft rock is established;

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

[0013] Preferably, the method of obtaining a soft rock sample by using an on-site in-situ technology and obtaining the indoor triaxial creep test result by performing an indoor triaxial creep test on the soft rock sample comprises the following steps:

[0014] S 11. Sampling soft rock samples by using a waterless engineering drill, wrapping the soft rock samples with plastic wrap, and placing the wrapped soft rock samples in a constant temperature box;

[0015] S 1 2. Carry out uniaxial compressive strength test on soft rock specimens by load-controlled loading mode, and determine the axial load graded loading condition of soft rock specimens according to the uniaxial compressive strength test results to obtain the axial load of indoor triaxial creep test;

[0016] S13. The ground stress of the sampling area is measured by the hole bottom stress relief method to determine the maximum principal stress and the minimum principal stress of the sampling area; and the upper and lower limits of the confining pressure are determined according to the maximum principal stress and the minimum principal stress. According to the upper and lower limits of the confining pressure, a stacking confining pressure test is performed on the soft rock sample to obtain the indoor triaxial creep test confining pressure;

[0017] S 1 4. By controlling the loading mode, the axial compression test is applied to the soft rock specimen at different loading speeds until the soft rock specimen is destroyed, and the axial load control rate of the indoor triaxial creep test is obtained;

[0018] S15. According to 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, the axial creep curve, the failure characteristics and the stress-strain curve are established respectively.

[0019] Preferably, the method of measuring the ground stress in the sampling area by using the hole bottom stress relief method to determine the maximum principal stress and the minimum principal stress in the sampling area comprises the following steps:

[0020] S131, drilling in the sampling area by means of a drill bit according to a preset measurement drilling depth, pasting a strain rosette at the bottom of the drill hole and reading initial strain data;

[0021] S 1 32. Use a drill 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. Calculate the ground stress value and determine the principal stress direction based on the initial strain data and the new strain data, and determine the maximum principal stress and the minimum principal stress in the sampling area.

[0023] Preferably, the method of optimizing the Burgers creep model based on the peridynamics theory and the Newton viscosity pot theory, establishing a nonlinear creep constitutive model of soft rock according to the optimized Burgers creep model; and inputting the indoor triaxial creep test results into the nonlinear creep constitutive model of soft rock, and calculating the three-stage creep characteristics of soft rock through the nonlinear creep constitutive model of soft rock includes the following steps:

[0024] S2 1. Based on the peridynamic theory and combined with the random damage index, the nonlinear damage mechanism is introduced into the Maxwell-Newtonian viscosity pot, and the constitutive equation of the Newtonian viscosity pot is obtained;

[0025] S22. Based on the principle of equivalent damage stress, the Newtonian viscosity strain expression is established through the local damage index in the peridynamics theory, and the Burgers creep model is optimized according to the Newtonian viscosity strain expression to obtain the optimized Burgers creep model;

[0026] S23. Establish the relationship between the strain density energy of peridynamics and continuum theory, obtain the expression of micro elastic modulus with respect to creep compliance, and construct the creep compliance expression through the optimized Burgers creep model;

[0027] S24. Based on the constitutive force function of the prototype micro-elastic brittle material and combined with the expression of the micro elastic modulus with respect to creep compliance and the creep compliance expression, a nonlinear creep constitutive model of soft rock is established.

[0028] Preferably, the method of establishing a Newton's viscosity strain expression based on the equivalent damage stress principle by using a local damage index in the peridynamics theory, and optimizing the Burgers creep model according to the Newton's viscosity strain expression to obtain the optimized Burgers creep model comprises the following steps:

[0029] S221. Using the equivalent damage stress principle, the relationship between damage variables and equivalent stress is established, and the damage accumulation effect of the material is described by the damage variables to obtain the Newtonian viscosity strain expression considering the degree of damage;

[0030] S222. Use the local damage index in peridynamics theory to characterize the damage degree of the material and obtain the Newtonian viscosity strain expression considering the local damage index;

[0031] S223. The Newton viscosity pot strain expression considering the local damage index is used to replace the Newton viscosity pot part in the Burgers creep model to obtain the optimized Burgers creep model.

[0032] Preferably, the Newtonian viscosity strain expression considering the local damage index is:

[0033]

[0034] Where ε1(t) represents the Newtonian viscosity strain considering the local damage index;

[0035] σ0 represents constant stress;

[0036] Indicates local damage index;

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

[0038] t represents time.

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

[0040]

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

[0042] σ0 represents constant stress;

[0043] η M and η K represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model respectively;

[0044] t represents time;

[0045] E M and E K denote the Hookean elastic modulus in the Maxwell model and the Kelvin model respectively;

[0046] Indicates local damage index.

[0047] Preferably, the creep compliance expression constructed by the optimized Burgers creep model is:

[0048]

[0049] Where J(t) represents creep compliance;

[0050] η M and η K represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model respectively;

[0051] t represents time;

[0052] E M and E K denote the Hookean elastic modulus in the Maxwell model and the Kelvin model respectively;

[0053] Indicates local damage index.

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

[0055]

[0056] Where 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 two material points in the current configuration;

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

[0062] || means finding the modulus of a vector;

[0063] h represents the thickness of the model;

[0064] δ represents the field radius;

[0065] η M and η K represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model respectively;

[0066] t represents time;

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

[0068] Indicates local damage index.

[0069] According to another aspect 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 a nonlinear creep constitutive model of soft rock comprises: 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 on-site in-situ technology, and obtain indoor triaxial creep test results by performing indoor triaxial creep tests on the soft rock samples;

[0071] The model optimization module is used to construct the constitutive equation of the Newtonian viscosity pot according to the Maxwell-Newtonian viscosity pot integrated with the peridynamic damage index; and optimize the Burgers creep model in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model, and establish the nonlinear creep constitutive model of soft rock according to the optimized Burgers creep model;

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

[0073] The beneficial effects of the present invention are:

[0074] 1. The nonlinear creep constitutive model of soft rock based on the peridynamic theory proposed in the present invention can comprehensively and well 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.

[0075] 2. The present invention can realize real-time judgment in the numerical calculation process by introducing local damage indicators, without giving a threshold value for the accelerated creep stage. It can better reflect the dynamic evolution process of surrounding rock disturbance and facilitate accurate disclosure of the large deformation evolution mechanism of soft rock tunnels. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0077] Figure 1 is a flow chart 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 is a schematic diagram of a soft rock creep curve in a creep characteristic analysis method based on a nonlinear creep constitutive model of soft rock according to an embodiment of the present invention;

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

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

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

[0082] Figure 6 is a diagram comparing the test results of a limestone sample and the simulation results 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 is a diagram comparing coal and rock sample test and simulation results in a creep characteristic analysis method based on a nonlinear creep constitutive model of soft rock according to an embodiment of the present invention;

[0084] Figure 8 It is a principle block 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 figure:

[0086] 1. Creep test result acquisition module; 2. Model optimization module; 3. Creep characteristic analysis module. DETAILED DESCRIPTION

[0087] In order 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 in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of this application.

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

[0089] The present invention is further described with reference to the accompanying drawings and specific embodiments. Figure 1 As shown, according to one embodiment of the present invention, a creep characteristic analysis method based on a nonlinear creep constitutive model of soft rock is provided. The creep characteristic analysis method based on a nonlinear creep constitutive model of soft rock comprises the following steps:

[0090] S1. Obtain soft rock samples using on-site in-situ technology, and obtain indoor triaxial creep test results by performing indoor triaxial creep tests 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 of the indoor triaxial creep test.

[0092] As a preferred embodiment, the method of obtaining a soft rock sample by using an on-site in-situ technology and performing an indoor triaxial creep test on the soft rock sample to obtain the indoor triaxial creep test result includes the following steps:

[0093] S 11. Sampling soft rock samples by using a waterless engineering drill, wrapping the soft rock samples with plastic wrap, and placing the wrapped soft rock samples in a constant temperature box;

[0094] Specifically, waterless engineering drilling rigs were used for sampling to avoid softening of rock samples caused by water bodies;

[0095] The samples were wrapped with plastic wrap and placed in a constant temperature box (with the error of formation temperature within ±0.5°C) to avoid the influence of moisture content and temperature changes on their mechanical properties.

[0096] S 1 2. Carry out uniaxial compressive strength test on soft rock specimens by load-controlled loading mode, and determine the axial load graded loading condition of soft rock specimens according to the uniaxial compressive strength test results to obtain the axial load of indoor triaxial creep test;

[0097] S13. The ground stress of the sampling area is measured by the hole bottom stress relief method to determine the maximum principal stress and the minimum principal stress of the sampling area; and the upper and lower limits of the confining pressure are determined according to the maximum principal stress and the minimum principal stress. According to the upper and lower limits of the confining pressure, a stacking confining pressure test is performed on the soft rock sample to obtain the indoor triaxial creep test confining pressure;

[0098] As a preferred embodiment, the method of measuring the ground stress in the sampling area by using the hole bottom stress relief method to determine the maximum principal stress and the minimum principal stress in the sampling area includes the following steps:

[0099] S131, drilling in the sampling area by means of a drill bit according to a preset measurement drilling depth, pasting a strain rosette at the bottom of the drill hole and reading initial strain data;

[0100] S 1 32. Use a drill 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. Calculate the ground stress value and determine the principal stress direction based on the initial strain data and the new strain data, and determine the maximum principal stress and the minimum principal stress in the sampling area.

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

[0103] Glue the strain gauge rosette to the bottom of the drilled hole and read the initial strain;

[0104] Use a drill with the same diameter as the drill bit to further deepen the hole and relieve stress around the small hole;

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

[0106] S 1 4. By controlling the loading mode, the axial compression test is applied to the soft rock specimen at different loading speeds until the soft rock specimen is destroyed, and the axial load control rate of the indoor triaxial creep test is obtained;

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

[0108] The subsequent loading speed of each level of load is 0.5 kN / s, and the deformation rate under each level of load is less than 0.0004 mm / h before the next level of loading is carried out until the specimen is damaged;

[0109] S15. According to 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, the axial creep curve, the failure characteristics and the stress-strain curve are established respectively.

[0110] S2. Based on the Maxwell-Newton viscosity pot integrated with the peridynamic damage index, the constitutive equation of the Newton viscosity pot is constructed; and the Burgers creep model is optimized in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model. Based on the optimized Burgers creep model, the nonlinear creep constitutive model of soft rock is established.

[0111] It should be noted that the component model is widely used to describe the creep behavior of soft rock due to its simple principle and clear physical meaning of parameters, such as the Maxwell model, Kelvin model, generalized Maxwell model, generalized Kelvin model and Burgers model, etc. Linear viscoelastic rheological constitutive models. Generally speaking, the determination of the material constitutive model should not only reflect the mechanical properties of the material, but also be as simple and intuitive as possible. The Burgers model can better describe the elastic strain, initial creep and stable creep stages of rocks by connecting Maxwell units and Kelvin units in series, and can be degenerated into the other four models. It is currently the most commonly used soft rock constitutive model.

[0112] The classic Burgers creep model (e.g. Figure 3 The creep equation is:

[0113]

[0114] In the formula, ε represents creep strain, σ0 represents constant stress, t represents time, and E M 、E K are the Hookean elastic modulus in the Maxwell model and the Kelvin model, η M , η K are the Newtonian viscosity coefficients in the Maxwell model and the Kelvin model respectively. M is a constant, which makes the Burgers creep model unable to describe the accelerated creep process of soft rock. However, as the damage continues to accumulate during the creep process of soft rock, when a certain threshold is reached, its creep often shows an accelerating trend, that is, macro cracks develop rapidly until instability and failure.

[0115] As a preferred implementation, the constitutive equation of the Newtonian viscosity pot is constructed according to the Maxwell-Newtonian viscosity pot integrated with the peridynamic damage index; and the Burgers creep model is optimized in combination with the equivalent damage stress principle to obtain an optimized Burgers creep model. The nonlinear creep constitutive model of soft rock is established according to the optimized Burgers creep model, including the following steps:

[0116] S2 1. Based on the peridynamic theory and combined with the random damage index, the nonlinear damage mechanism is introduced into the Maxwell-Newtonian viscosity pot, and the constitutive equation of the Newtonian viscosity pot is obtained;

[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, the present invention proposes a one-dimensional nonlinear Newtonian viscosity considering random damage based on the Maxwell Newtonian viscosity and the peridynamic damage index, so as to realize the description of the accelerated creep stage of soft rock.

[0118] Among them, the constitutive equation of Newton's clay pot is:

[0119]

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

[0121] S22. Based on the principle of equivalent damage stress, the Newtonian viscosity strain expression is established through the local damage index in the peridynamics theory, and the Burgers creep model is optimized according to the Newtonian viscosity strain expression to obtain the optimized Burgers creep model;

[0122] As a preferred implementation, based on the equivalent damage stress principle, a Newton viscosity strain expression is established through a local damage index in the peridynamics theory, and the Burgers creep model is optimized according to the Newton viscosity strain expression to obtain the optimized Burgers creep model, which includes the following steps:

[0123] S221. Using the equivalent damage stress principle, the relationship between damage variables and equivalent stress is established, and the damage accumulation effect of the material is described by the damage variables to obtain the Newtonian viscosity strain expression considering the degree of damage;

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

[0125]

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

[0127] Among them, according to the relationship between the equivalent stress and the damage variable, as well as the constitutive equation of the Newton's viscosity, the strain expression of the Newton's viscosity considering the degree of damage can be obtained.

[0128] Specifically, the strain expression of Newton's clay pot considering the degree of damage is:

[0129]

[0130] Where ε represents the strain of the Newtonian viscosity considering the degree of damage, σ0 represents the constant stress, t represents the time, D represents the damage variable, and η M represents the viscosity coefficient of the Newtonian body in the Maxwell model.

[0131] S222. Use the local damage index in peridynamics theory to characterize the damage degree of the material and obtain the Newtonian viscosity strain expression considering the local damage index;

[0132] It should be noted that the damage variable D is defined in the damage mechanics theory as the physical quantity of the degree of damage to the standard material caused by external forces or external environment. In the peridynamics theory, the local damage index is the ratio of the number of broken bonds to the number of initially intact bonds, which has the same definition as the damage variable D and also characterizes the degree of material damage. Substituting it into the strain expression of Newton's viscosity considering the degree of damage, the strain expression of Newton's viscosity considering the local damage index is obtained.

[0133] As a preferred embodiment, the Newtonian strain expression considering the local damage index is:

[0134]

[0135] Where ε1(t) represents the Newtonian viscosity strain considering the local damage index; σ0 represents the constant stress; Represents the local damage index; η M represents the viscosity coefficient of the Newtonian body in the Maxwell model; t represents time.

[0136] From the Newtonian strain expression considering the local damage index, it can be seen that when the rock is in the stable creep stage, its damage degree is small, that is, Close to 0, the Newtonian viscosity strain considering the degree of damage increases approximately linearly with time; as the creep time increases, the degree of material damage continues to increase, and its strain gradually shows a nonlinear growth; when the material is close to complete destruction, that is, Its strain tends to infinity.

[0137] S223. The Newton viscosity pot strain expression considering the local damage index is used to replace the Newton viscosity pot part in the Burgers creep model to obtain the optimized Burgers creep model.

[0138] Specifically, the Newton's viscosity strain expression that takes local damage indicators into consideration replaces the Newton's viscosity part in the Burgers creep model, and an improved damage-related Burgers creep model, namely the optimized Burgers creep model, can be obtained.

[0139] As a preferred implementation, the optimized Burgers creep model expression is:

[0140]

[0141] Where ε2(t) represents the optimized Burgers creep model strain; σ0 represents the constant stress; η M and η K Respectively represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model; t represents time, E M and E K denote the Hookean elastic modulus in the Maxwell model and the Kelvin model respectively; Indicates local damage index.

[0142] S23. Establish the relationship between the strain density energy of peridynamics and continuum theory, obtain the expression of micro 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 of peridynamics and classical continuum theory equal, the expression of the micro elastic modulus with respect to creep compliance can be obtained;

[0144]

[0145] Where c represents the micro elastic modulus, h represents the thickness of the model, δ represents the domain radius, and J represents the creep compliance.

[0146] Specifically, creep compliance is the ratio of strain to stress at any time during the creep process of the material. The creep compliance expression constructed by the optimized Burgers creep model is:

[0147]

[0148] Where J(t) represents creep compliance; η M and η K Respectively represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model; t represents time; E M and E K denote the Hookean elastic modulus in the Maxwell model and the Kelvin model respectively; Indicates local damage index.

[0149] S24. According to the constitutive force function of the prototype micro-elastic brittle material, and in combination with the expression of micro elastic modulus on creep compliance and the creep compliance expression, a nonlinear creep constitutive model of soft rock is established;

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

[0151]

[0152] Where 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 the modulus of the vector.

[0153] As a preferred implementation, the force function expression of the nonlinear creep constitutive model of soft rock is:

[0154]

[0155] Where f(η, ξ, t) represents the force function of the nonlinear creep constitutive model of 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 the material points in the initial state, etc.); η represents the relative displacement of the two material points in the current configuration (referring to the spatial distribution of the material points in the current deformation state, etc.); 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 field radius; η M and η K Respectively represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model; t represents time; E M and E K represent the elastic modulus of the Hooke body in the Maxwell model and the Kelvin model respectively; Indicates local damage index.

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

[0157] It should be noted that the creep characteristics of soft rock include 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, and the creep characteristic analysis system based on a nonlinear creep constitutive model of soft rock comprises: 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 by using on-site in-situ technology, and obtain indoor triaxial creep test results by performing indoor triaxial creep tests on the soft rock samples;

[0160] The model optimization module 2 is used to construct the constitutive equation of the Newtonian viscosity pot according to the Maxwell-Newtonian viscosity pot integrated with the peridynamic damage index; and optimize the Burgers creep model in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model, and establish the nonlinear creep constitutive model of soft rock according to the optimized Burgers creep model;

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

[0162] In order to facilitate understanding of the above technical solution of the present invention, the creep characteristic analysis method and system based on the nonlinear creep constitutive model of soft rock proposed in the present invention are verified according to the creep test results of limestone and coal rock.

[0163] according to Figure 4 The elastic strain, initial creep tangent slope, intersection of the stable creep reverse extension line and other parameter values ​​shown in the curve are combined with the test curve to obtain the creep model calculation parameters, as shown in Table 1. Figure 5 This is a creep model diagram, in which the material point spacing (Δx) is 1.0 mm, the field radius δ=3Δx, and the critical elongation (s) is approximately 0.007 (limestone) and 0.002 (coal rock).

[0164] Table 1 Calculation parameters of creep model

[0165]

[0166] like Figure 6 As shown in Figure 2, the limestone sample only produces initial creep and stable creep under uniaxial compression loads at stress levels of 16.3 and 27.1 MPa, and no accelerated creep process occurs. The nonlinear creep constitutive model proposed in the invention can better simulate the limestone creep test curve. For coal rock samples (such as Figure 7 As shown in the figure, when the loading stress level is 3.0MPa, its initial creep and stable creep characteristics can also be effectively reproduced; when the loading stress level is 12.0MPa, the nonlinear creep constitutive model proposed by the invention can better predict its creep characteristics, which is consistent with the experimental data. The difference is that at the moment of loading, the test results of the specimens all show instantaneous elastic deformation (strain is not 0). Although the simulation results can reproduce its elastic deformation process, the strain gradually increases from 0. The above phenomenon is mainly related to the integration process of the near-field dynamics equation of motion. At the time step t=0, its initial acceleration, velocity, and displacement are all 0, and as the time step increases, its displacement continues to accumulate and gradually increase. On the whole, the model can comprehensively and well describe the three-stage creep characteristics of rock, and the model has clear physical meaning and simple parameters.

[0167] In summary, with the help of the above technical solution of the present invention, the nonlinear creep constitutive model of soft rock based on the peridynamic theory proposed in the present invention can comprehensively and well 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. The present invention can realize real-time judgment in the numerical calculation process by introducing local damage indicators, without giving a threshold value of the accelerated creep stage, and can well reflect the dynamic evolution process of surrounding rock disturbance, which is convenient for accurately revealing the large deformation evolution mechanism of soft rock tunnels.

[0168] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented 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 objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is 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 in the scope of protection of the present invention.

Claims

1. A creep characteristic analysis method based on a nonlinear creep constitutive model of soft rock, characterized in that: The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock includes the following steps: S1. Obtain soft rock samples using on-site in-situ technology, and obtain indoor triaxial creep test results by performing indoor triaxial creep tests on the soft rock samples; S2. Based on the Maxwell-Newton viscosity pot integrated with the peridynamic damage index, the constitutive equation of the Newton viscosity pot is constructed; and the Burgers creep model is optimized in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model. Based on the optimized Burgers creep model, the nonlinear creep constitutive model of soft rock is established; S3. Input the indoor triaxial creep test results into the nonlinear creep constitutive model of soft rock, calculate and analyze the indoor triaxial creep test results through the nonlinear creep constitutive model of soft rock, and obtain the creep characteristics of soft rock.

2. The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to claim 1 is characterized in that: The method of obtaining a soft rock sample by using an on-site in-situ technology and performing an indoor triaxial creep test on the soft rock sample to obtain the indoor triaxial creep test result comprises the following steps: S11. Sampling soft rock samples by using a waterless engineering drill, wrapping the soft rock samples with plastic wrap, and placing the wrapped soft rock samples in a constant temperature box; S1 2. Perform uniaxial compressive strength test on soft rock specimens by load-controlled loading method, and determine the axial load graded loading condition of soft rock specimens according to the uniaxial compressive strength test results to obtain the axial load of indoor triaxial creep test; S13. The ground stress of the sampling area is measured by the hole bottom stress relief method to determine the maximum principal stress and the minimum principal stress of the sampling area; and the upper and lower limits of the confining pressure are determined according to the maximum principal stress and the minimum principal stress. According to the upper and lower limits of the confining pressure, a stacking confining pressure test is performed on the soft rock sample to obtain the indoor triaxial creep test confining pressure; S1 4. By load-controlled loading mode, axial compression test is applied to soft rock specimens at different loading speeds until the soft rock specimens are damaged, and the axial load control rate of indoor triaxial creep test is obtained; S15. According to 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, the axial creep curve, the failure characteristics and the stress-strain curve are established respectively.

3. The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to claim 2 is characterized in that: The method of measuring the ground stress in the sampling area by using the hole bottom stress relief method to determine the maximum principal stress and the minimum principal stress in the sampling area comprises the following steps: S131, drilling in the sampling area by means of a drill bit according to a preset measurement drilling depth, pasting a strain rosette at the bottom of the drill hole and reading initial strain data; S1 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; S133. Calculate the ground stress value and determine the principal stress direction based on the initial strain data and the new strain data, and determine the maximum principal stress and the minimum principal stress in the sampling area.

4. The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to claim 1 is characterized in that: The constitutive equation of the Newtonian viscosity pot is constructed according to the Maxwell-Newtonian viscosity pot integrated with the peridynamic damage index; and the Burgers creep model is optimized in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model. The nonlinear creep constitutive model of soft rock is established according to the optimized Burgers creep model, which includes the following steps: S2 1. Based on the peridynamic theory and combined with the random damage index, the nonlinear damage mechanism is introduced into the Maxwell-Newtonian viscosity pot, and the constitutive equation of the Newtonian viscosity pot is obtained; S22. Based on the principle of equivalent damage stress, the Newtonian viscosity strain expression is established through the local damage index in the peridynamics theory, and the Burgers creep model is optimized according to the Newtonian viscosity strain expression to obtain the optimized Burgers creep model; S23. Establish the relationship between the strain density energy of peridynamics and continuum theory, obtain the expression of micro elastic modulus with respect to creep compliance, and construct the creep compliance expression through the optimized Burgers creep model; S24. Based on the constitutive force function of the prototype micro-elastic brittle material and combined with the expression of the micro elastic modulus with respect to creep compliance and the creep compliance expression, a nonlinear creep constitutive model of soft rock is established.

5. The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to claim 4 is characterized in that: The method of establishing a Newton's viscosity strain expression based on the equivalent damage stress principle by using the local damage index in the peridynamics theory, and optimizing the Burgers creep model according to the Newton's viscosity strain expression to obtain the optimized Burgers creep model includes the following steps: S221. Using the equivalent damage stress principle, the relationship between damage variables and equivalent stress is established, and the damage accumulation effect of the material is described by the damage variables to obtain the Newtonian viscosity strain expression considering the degree of damage; S222. Use the local damage index in peridynamics theory to characterize the damage degree of the material and obtain the Newtonian viscosity strain expression considering the local damage index; S223. The Newton viscosity pot strain expression considering the local damage index is used to replace the Newton viscosity pot part in the Burgers creep model to obtain the optimized Burgers creep model.

6. The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to claim 5 is characterized in that: The Newtonian viscosity strain expression considering the local damage index is: Where ε1(t) represents the Newtonian viscosity strain considering the local damage index; σ0 represents constant stress; Indicates local damage index; η M represents the viscosity coefficient of Newtonian body in Maxwell model; t represents time.

7. The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to claim 5 is characterized in that: The optimized Burgers creep model expression is: Where, ε2(t) represents the optimized Burgers creep model strain; σ0 represents constant stress; η M and η K represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model respectively; t represents time; E M and E K denote the Hookean elastic modulus in the Maxwell model and the Kelvin model respectively; Indicates local damage index.

8. The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to claim 5 is characterized in that: The creep compliance expression constructed by the optimized Burgers creep model is: Where J(t) represents creep compliance; η M and η K represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model respectively; t represents time; E M and E K denote the Hookean elastic modulus in the Maxwell model and the Kelvin model respectively; Indicates local damage index.

9. The creep characteristic analysis method based on the nonlinear creep constitutive model of soft rock according to claim 5 is characterized in that: The force function expression of the nonlinear creep constitutive model of soft rock is: Where f(η, ξ, t) represents the force function of the nonlinear creep constitutive model of soft rock; μ represents the fracture parameter; s represents elongation; ξ represents the relative position of the 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 the two material points in the current configuration; || means finding the modulus of a vector; h represents the thickness of the model; δ represents the field radius; η M and η K represent the viscosity coefficient of Newtonian body in Maxwell model and Kelvin model respectively; t represents time; E M and E K represent the elastic modulus of the Hooke body in the Maxwell model and the Kelvin model respectively; Indicates local damage index.

10. A creep characteristic analysis system based on a nonlinear creep constitutive model of soft rock, used to implement the creep characteristic analysis method based on a nonlinear creep constitutive model of soft rock as claimed in any one of claims 1 to 9, characterized in that: The creep characteristic analysis system based on the nonlinear creep constitutive model of soft rock includes: a creep test result acquisition module, a model optimization module and a creep characteristic analysis module; The creep test result acquisition module is used to acquire soft rock samples using on-site in-situ technology, and obtain indoor triaxial creep test results by performing indoor triaxial creep tests on the soft rock samples; The model optimization module is used to construct the constitutive equation of the Newtonian viscosity pot according to the Maxwell-Newtonian viscosity pot integrated with the peridynamic damage index; and optimize the Burgers creep model in combination with the equivalent damage stress principle to obtain the optimized Burgers creep model, and establish the nonlinear creep constitutive model of soft rock according to the optimized Burgers creep model; The creep characteristic analysis module is used to input the indoor triaxial creep test results into the nonlinear creep constitutive model of soft rock, and calculate and analyze the indoor triaxial creep test results through the nonlinear creep constitutive model of soft rock to obtain the creep characteristics of soft rock.

Images