Carbon slate unsteady creep model construction method based on time-stress evolution

Abstract

The invention belongs to the technical field of rock engineering, discloses a carbonaceous slate unsteady creep model construction method based on time-stress evolution, and aims to solve the problem that creep parameters of existing carbonaceous slate cannot be accurate due to the fact that the creep parameters are regarded as constants or expressed by a nonlinear function. The unsteady creep model comprises an improved generalized Kelvin body and a Newton body with a switch, wherein the Newton body takes the stress level into consideration, and the improved generalized Kelvin body is connected with the Newton body with the switch in series. According to the method, more accurate creep parameters of the carbonaceous slate can be obtained, and a theoretical model is provided for tunnel surrounding rock creep deformation research and tunnel long-term stability analysis of a carbonaceous slate stratum tunnel penetrating through an extremely high crustal stress area.

Description

Technical Field

[0001] The present invention belongs to the technical field of rock engineering, and in particular relates to a method for constructing an unsteady creep model of carbonaceous slate based on time-stress evolution. Background Art

[0002] As tunnel construction in mountainous areas of the western plateau advances, tunnels often pass through areas of extremely high geostress and are accompanied by various adverse geological conditions, resulting in serious deformation during construction. Due to the rock creep effect, deformation gradually increases over time even after initial support is applied. Some tunnels still show slight deformation growth after six months of monitoring, leading to construction safety hazards and long-term deformation damage to the surrounding rock. The key reason for this is the lack of a rock creep constitutive model under realistic stress states to analyze the long-term stability of the surrounding rock.

[0003] Carbonaceous slate is widely found in the western plateau. It is primarily composed of quartz, plagioclase, ankerite, and clay minerals, with minor amounts of pyrite. Carbonaceous slate is influenced by the quartz and plagioclase content, exhibits irregular internal shapes, and is rich in pores, making it a relatively soft rock. After tunnel excavation, carbonaceous slate experiences long-term creep deformation due to the long-term deviatoric pressure, compromising tunnel safety. Therefore, understanding the creep properties of carbonaceous slate is crucial.

[0004] At present, a series of indoor uniaxial and triaxial creep experiments have been carried out on the creep effect of rocks, and the creep constitutive model has been obtained through empirical formula fitting (empirical model) and component combination models (such as viscous body (Maxwell body), viscoelastic body (Kelvin body), viscoplastic body (Binham body) and viscoelastic-plastic body, and their variants and combinations).

[0005] However, most current studies on carbonaceous slate creep parameters treat them as constants or use nonlinear functions to describe the creep stage. In reality, creep parameters are often affected by time and stress level. Therefore, treating carbonaceous slate creep parameters as constants or expressing them using nonlinear functions does not accurately reflect the true creep parameters of carbonaceous slate. Summary of the Invention

[0006] To address the existing problem of inaccurately obtaining carbonaceous slate creep parameters, which often arises from treating them as constants or expressing them using nonlinear functions, this paper proposes a method for constructing an unsteady creep model for carbonaceous slate based on time-stress evolution. This method can obtain more accurate carbonaceous slate creep parameters, providing a theoretical model for studying surrounding rock creep deformation and analyzing the long-term stability of tunnels traversing carbonaceous slate strata in extremely high geostress areas. Ultimately, this method provides a more scientific and accurate basis for tunnel support design, ensuring the safety of tunnel construction.

[0007] In order to solve the technical problem, the technical solution adopted by the present invention is:

[0008] A method for constructing an unsteady creep model of carbonaceous slate based on time-stress evolution includes:

[0009] (1) Drill rock from the tunnel face in the carbonaceous slate formation in the extremely high ground stress area, and prepare and obtain carbonaceous slate samples in accordance with the requirements of the specification;

[0010] (2) Perform triaxial compression tests on the obtained carbonaceous slate samples to obtain the average triaxial compression strength of the carbonaceous slate samples

[0011] (3) A creep test is set up with reference to the results of the triaxial compression test in step (2). When the creep test is performed on the carbonaceous slate sample, the initial strength is the average triaxial compression strength obtained in step (2). 40-60% of the total load, and graded loading is carried out according to the proportion;

[0012] (4) collecting data every 15 seconds and every 0.005 mm change in the axial displacement of the carbonaceous slate sample, and recording the results; obtaining a creep test curve, which includes a full time-strain process curve of the carbonaceous slate and a time-strain curve obtained under different stress conditions using the Chen method;

[0013] (5) An unsteady creep model based on time-stress evolution suitable for carbonaceous slate is constructed, where the constitutive relation of the unsteady creep model is:

[0014]

[0015] In the above formula: ε ij is the strain tensor, σ m is the spherical stress tensor, S ij is the deviatoric stress tensor, σ s is the normal stress, σ ∞ is the long-term strength of carbonaceous slate, t is time, a and b are material parameters, η0 is the viscosity coefficient of the Kelvin body, K0 is the bulk modulus of the spring body alone, G0 is the shear modulus of the spring body alone, and G1 is the shear modulus of the improved Kelvin body;

[0016] (6) The LM algorithm (Levenberg-Marquardt) is used to fit the creep experimental curve and identify the parameters to obtain the model parameters of the unsteady creep model.

[0017] In some embodiments, the unsteady creep model of carbonaceous slate based on time-stress evolution includes an improved generalized Kelvin body and a Newtonian body with a switch considering the stress level, and the improved generalized Kelvin body and the Newtonian body with a switch considering the stress level are connected in series.

[0018] In some embodiments, the Newtonian body with a switch that considers stress levels includes a switch that considers the long-term strength of the material and a viscosity pot; the improved generalized Kelvin body includes two spring bodies and an unsteady viscosity pot that considers time evolution; one of the spring bodies is connected in parallel with the unsteady-length viscosity pot that considers time evolution to form an improved Kelvin body, and the other spring body is connected in series with the improved Kelvin body to form an improved generalized Kelvin body.

[0019] In other words, the present invention defines an unsteady creep model as consisting of three parts: a single spring, an improved generalized Kelvin body (another spring connected in parallel with a time-dependent variable-length viscous pot), and a Newtonian body with a switch that considers stress levels. The unsteady creep model is formed by connecting the spring in the first part, the improved generalized Kelvin body in the second part, and the Newtonian body with a switch that considers stress levels in the third part in series.

[0020] The constitutive relation of the unsteady creep model is obtained as follows:

[0021] The unsteady viscosity considering time evolution can be expressed as:

[0022] Where t is time, η0, a, and b are material parameters, and 0<a<1; η0 is the viscosity coefficient of the Kelvin body viscosity pot.

[0023] Then the constitutive relation of the unsteady creep constitutive model is established:

[0024]

[0025] Where: ε is the total strain, σ s is the normal stress, σ ∞ is the long-term strength of carbonaceous slate, E0 is the elastic modulus of a single spring body, E1 is the elastic modulus of an improved Kelvin body, η0 is the viscosity coefficient of the Kelvin body viscosity pot, η1 is the viscosity coefficient of the improved Kelvin body viscosity pot, and η2 is the viscosity coefficient of a Newtonian body with a switch considering the stress level (wherein the Newtonian body with a switch includes a switch considering the long-term strength of the material and a viscosity pot, so η2 is also the viscosity coefficient of the viscosity pot).

[0026] Then, the creep equation of the three-dimensional stress field is established, and the stress and strain equations of the three-dimensional stress state are:

[0027]

[0028] Where: σ ij is the stress tensor, S ij is the deviatoric stress tensor, σ m is the spherical stress tensor, ε ij is the strain tensor, e ij is the deviatoric strain tensor, ε m is the spherical strain tensor, σ i is the principal stress in the i direction, ε i is the principal strain in the i direction, δ ij is the Kronecker function.

[0029] In plastic mechanics, since elastic bodies obey Hooke's law:

[0030] Where G is the shear modulus, K is the bulk modulus, and σ m is the spherical stress tensor, e ij is the deviatoric strain tensor, ε m is the spherical strain tensor.

[0031] After decomposing formula (4) and substituting it into formula (3), and then substituting it together with formula (1) into formula (2), the constitutive relation of this unsteady creep model can be obtained:

[0032]

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The proposed method for constructing an unsteady creep model for carbonaceous slate based on time-stress evolution can obtain more accurate creep parameters and determine the long-term strength of carbonaceous slate. It also provides a theoretical model for studying the creep deformation of surrounding rock and analyzing the long-term stability of tunnels traversing carbonaceous slate strata in extremely high geostress areas. Ultimately, it provides a more scientific and accurate basis for tunnel support design, ensuring the safety of tunnel construction.

[0035] The unsteady creep model constructed in this paper also incorporates a switched Newtonian body. The long-term creep of rock is affected by its long-term strength. When the deviatoric stress exceeds the long-term strength, creep occurs. When the deviatoric stress is less than the long-term strength, creep essentially stops. Therefore, the introduction of a switched Newtonian body is more consistent with the actual conditions of carbonaceous slate and enables the generation of more accurate creep parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a schematic diagram of the full time-strain process curve of carbonaceous slate obtained during the creep experiment of the present invention;

[0037] Figure 2 Schematic diagram of the time-strain curves of carbonaceous slate under different stress conditions obtained during the creep experiment of the present invention;

[0038] Figure 3 Schematic diagram of the unsteady creep model of the present invention;

[0039] Figure 4 A schematic diagram of an existing Kelvin body;

[0040] Figure 5 Schematic diagram of the fitting results of the creep experimental curve using the LM algorithm at a stress level of 16.9 MPa;

[0041] Figure 6 Schematic diagram of the fitting results of the creep experimental curve using the LM algorithm at a stress level of 20.28 MPa;

[0042] Figure 7 Schematic diagram of the fitting results of the creep experimental curve using the LM algorithm at a stress level of 23.66 MPa;

[0043] Figure 8 Schematic diagram of the fitting results of the creep experimental curve using the LM algorithm at a stress level of 27.04 MPa;

[0044] Figure 9 Schematic diagram of the fitting results of the creep experimental curve using the LM algorithm at a stress level of 30.42 MPa. DETAILED DESCRIPTION

[0045] The present invention will be further described below with reference to the embodiments. The embodiments described are only a part of the embodiments of the present invention and are not all embodiments. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative work are all within the scope of protection of the present invention.

[0046] In the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or components referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention; the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance; in addition, unless otherwise expressly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection or an indirect connection through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0047] In conjunction with the accompanying drawings, the method for constructing an unsteady creep model of carbonaceous slate based on time-stress evolution of the present invention includes:

[0048] (1) Drill rock from the tunnel face in the carbonaceous slate formation in the extremely high ground stress area, and prepare and obtain carbonaceous slate samples in accordance with the requirements of the specifications.

[0049] (2) Perform triaxial compression tests on the obtained carbonaceous slate samples to obtain the average triaxial compression strength of the carbonaceous slate samples

[0050] (3) A creep test is set up with reference to the results of the triaxial compression test in step (2). When the creep test is performed on the carbonaceous slate sample, the initial strength is the average triaxial compression strength obtained in step (2). 40-60% of the total load, and graded loading is performed in proportion. Among them, graded loading is clear and understandable to those skilled in the art, and will not be described in detail here. The present invention introduces the average triaxial compressive strength The creep test of carbonaceous slate was carried out by adopting graded loading method, which can more accurately reflect the actual stress creep of carbonaceous slate in extremely high ground stress area. Because the structural characteristics of carbonaceous slate itself make the actual stress direction of carbonaceous slate in the formation not uniform and regular, therefore, the average triaxial compressive strength is introduced. It can more realistically reflect the actual situation of carbonaceous slate, thus laying the foundation for obtaining more accurate and realistic creep parameters in the later stage.

[0051] (4) Collect data every 15 seconds and every 0.005mm change in the axial displacement of the carbonaceous slate sample, and record the results; obtain a creep test curve, which includes a full time-strain process curve of the carbonaceous slate and a time-strain curve obtained under different stress conditions using the Chen method. In the specific implementation process, the full time-strain process curve of the carbonaceous slate obtained in one embodiment of the present invention is as shown in the attached figure. Figure 1 In one embodiment of the present invention, the time-strain curves of carbonaceous slate under different stress conditions are shown in FIG. Figure 2 shown.

[0052] (5) An unsteady creep model based on time-stress evolution suitable for carbonaceous slate is constructed, where the constitutive relation of the unsteady creep model is:

[0053]

[0054] In the above formula: ε ij is the strain tensor, σ m is the spherical stress tensor, S ij is the deviatoric stress tensor, σ s is the normal stress, σ ∞ is the long-term strength of carbonaceous slate, t is time, a and b are material parameters, η0 is the viscosity coefficient of the Kelvin body, K0 is the bulk modulus of the individual spring body, G0 is the shear modulus of the individual spring body, and G1 is the shear modulus of the improved Kelvin body.

[0055] (6) The LM algorithm (Levenberg-Marquardt) is used to fit the creep experimental curve and identify parameters to obtain the model parameters of the unsteady creep model. In other words, the model parameters of the unsteady creep model are obtained by inverting the creep experimental curve. Specifically: by fitting the creep experimental curve, the values of a and b can be identified, and then the bulk modulus K is calculated according to the bulk modulus calculation formula, and the shear modulus G is calculated according to the shear modulus calculation formula; finally, the model parameters are obtained by inverting the creep experimental curve.

[0056] The bulk modulus K (bulk modulus K represents the force per unit area and is used to describe incompressibility) is calculated as follows: K = E / (3×(1-2×v)), where E is the elastic modulus and v is the Poisson's ratio.

[0057] The calculation formula of the shear modulus G is: G = E / (2(1+v), where E is the elastic modulus and v is the Poisson's ratio.

[0058] The calculation of the bulk modulus K and the shear modulus K is well understood by those skilled in the art and will not be described in detail here.

[0059] In some embodiments, the present invention uses the LM algorithm (Levenberg-Marquardt) to fit the creep test curve and perform parameter identification. The parameters of each stage obtained are shown in the following table:

[0060]

[0061] The fitting results show that when the axial pressure reaches 23.66 MPa, the carbonaceous slate undergoes long-term creep, that is, the long-term strength of the carbonaceous slate σ ∞ It is 23.66MPa.

[0062] Combined with the above table and attached Figure 5 , Attachment Figure 6 , Attachment Figure 7 , Attachment Figure 8 and attached Figure 9 The unsteady creep model constructed (established) shows excellent fitting results for the creep curve, with a high degree of agreement with the experimental data. Therefore, the unsteady creep model constructed in this invention accurately reflects the creep process of carbonaceous slate, and the creep parameters obtained are also more accurate. The creep parameters obtained by inversion using the constructed unsteady creep model are relatively close, because the time effect of the creep parameters is considered in the relationship, which better reflects the changes in the creep parameters of carbonaceous slate.

[0063] Combined with attachment Figure 3 The unsteady creep model of carbonaceous slate based on time-stress evolution of the present invention includes an improved generalized Kelvin body and a Newtonian body with a switch that considers the stress level. The improved generalized Kelvin body and the Newtonian body with a switch that considers the stress level are connected in series. The long-term creep of rock is affected by the long-term strength of rock. When the deviatoric stress level exceeds the long-term strength of rock, rock creep occurs. When the deviatoric stress is less than the long-term strength of rock, basically no creep occurs. Therefore, the introduction of a Newtonian body with a switch that considers the stress level can make the creep parameters more accurate. When the stress level exceeds the long-term strength σ ∞ After that, the creep model enters the stable creep stage. s ≤σ ∞ When , Newtonian bodies do not work.

[0064] Combined with attachment Figure 3 In some embodiments, the improved generalized Kelvin body includes two spring bodies and an unsteady viscosity pot that considers time evolution; one of the spring bodies is connected in parallel with the unsteady viscosity pot that considers time evolution to form an improved Kelvin body, and the other spring body is connected in series with the improved Kelvin body to form an improved generalized Kelvin body.

[0065] Combined with attachment Figure 3The present invention defines an unsteady creep model as consisting of three parts: a single spring, an improved Kelvin body (another spring connected in parallel with a time-stress-constant-length viscous pot), and a Newtonian body with a switch that considers stress levels. The unsteady creep model is formed by connecting the spring, the improved Kelvin body, and the Newtonian body with a switch that considers stress levels in series.

[0066] The constitutive relation of the unsteady creep model is obtained as follows:

[0067] Among them, the unsteady viscosity considering time evolution is expressed as:

[0068] Where t is time, η0, a, and b are material parameters, with 0 < a < 1. η0 is a constant (i.e., the viscosity coefficient of the Kelvin viscosity pot), whose value can be obtained by fitting the creep experimental curve. η1 is the viscosity coefficient of the improved Kelvin viscosity pot; by introducing a and b, it can be linked to time t. a and b are obtained by fitting the creep experimental curve.

[0069] Then the constitutive relation of the unsteady creep constitutive model is established:

[0070]

[0071] Where: ε is the total strain, σ s is the normal stress, σ ∞ is the long-term strength of carbonaceous slate, E0 is the elastic modulus of a single spring body, E1 is the elastic modulus of an improved Kelvin body, η0 is the viscosity coefficient of a Kelvin body viscosity pot, η1 is the viscosity coefficient of an improved Kelvin body viscosity pot, and η2 is the viscosity coefficient of a Newtonian body with a switch.

[0072] Then, the creep equation of the three-dimensional stress field is established, and the stress and strain equations of the three-dimensional stress state are:

[0073]

[0074] Where: σ ij is the stress tensor, S ij is the deviatoric stress tensor, σ m is the spherical stress tensor, ε ij is the strain tensor, e ij is the deviatoric strain tensor, ε m is the spherical strain tensor, σ i is the principal stress in the i direction, ε i is the principal strain in the i direction, δ ij is the Kronecker function. iand ε i The i direction represents the principal stress in three directions (in creep experiments, the three directions are the X-axis, Y-axis and Z-axis, which are perpendicular to each other. Therefore, the i direction here is the X-axis, Y-axis and Z-axis, and the X-axis, Y-axis and Z-axis directions can be replaced by the values 1, 2 and 3. For those skilled in the art, they can understand and appreciate it, so they will not be repeated here).

[0075] Under three-dimensional stress state, the stress tensor σ of rock ij Can be decomposed into the deviatoric stress tensor S ij and the spherical stress tensor σ m , the corresponding strain tensor ε ij It can also be decomposed into the deviatoric strain tensor e ij and the spherical strain tensor ε m It is usually considered that deviatoric stress causes creep deformation, while spherical stress only causes elastic deformation.

[0076] In plastic mechanics, since the elastic element satisfies

[0077] Where G is the shear modulus, K is the bulk modulus, and σ m is the spherical stress tensor, e ij is the deviatoric strain tensor, ε m is the spherical strain tensor.

[0078] After decomposing formula (4) and substituting it into formula (3), and then substituting it together with formula (1) into formula (2), the constitutive relation of this unsteady creep model can be obtained:

[0079]

Claims

1. A method for constructing an unsteady creep model of carbonaceous slate based on time-stress evolution, characterized in that: include: (1) Drill rock from the tunnel face in the carbonaceous slate formation in the extremely high ground stress area, and prepare and obtain carbonaceous slate samples in accordance with the requirements of the specification; (2) Perform triaxial compression tests on the obtained carbonaceous slate samples to obtain the average triaxial compression strength of the carbonaceous slate samples (3) A creep test is set up with reference to the results of the triaxial compression test in step (2). When the creep test is performed on the carbonaceous slate sample, the initial strength is the average triaxial compression strength obtained in step (2). 40-60% of the total load, and graded loading is carried out according to the proportion; (4) collecting data every 15 seconds and every 0.005 mm change in the axial displacement of the carbonaceous slate sample, and recording the results; obtaining a creep test curve, which includes a full time-strain process curve of the carbonaceous slate and a time-strain curve obtained under different stress conditions using the Chen method; (5) An unsteady creep model based on time-stress evolution suitable for carbonaceous slate is constructed, where the constitutive relation of the unsteady creep model is: In the above formula: ε ij is the strain tensor, σ m is the spherical stress tensor, S ij is the deviatoric stress tensor, σ s is the normal stress, σ ∞ is the long-term strength of carbonaceous slate, t is time, a and b are material parameters, η0 is the viscosity coefficient of the Kelvin body, K0 is the bulk modulus of the spring body alone, G0 is the shear modulus of the spring body alone, and G1 is the shear modulus of the improved Kelvin body; (6) The LM algorithm is used to fit the creep experimental curve and identify the parameters to obtain the model parameters of the unsteady creep model.

2. The method for constructing an unsteady creep model of carbonaceous slate based on time-stress evolution according to claim 1 is characterized in that: The unsteady creep model includes an improved generalized Kelvin body and a Newtonian body with a switch that considers stress levels. The improved generalized Kelvin body and the Newtonian body with a switch that considers stress levels are connected in series.

3. The method for constructing an unsteady creep model of carbonaceous slate based on time-stress evolution according to claim 2, characterized in that: The Newtonian body with a switch that considers stress levels includes a switch that considers the long-term strength of the material and a viscosity pot; the improved generalized Kelvin body includes two spring bodies and an unsteady viscosity pot that considers time evolution; one of the spring bodies is connected in parallel with the unsteady length viscosity pot that considers time evolution to form an improved Kelvin body, and the other spring body is connected in series with the improved Kelvin body to form an improved generalized Kelvin body.

4. The method for constructing an unsteady creep model of carbonaceous slate based on time-stress evolution according to claim 3 is characterized in that: The establishment of the constitutive relation of the unsteady creep model specifically includes the following steps: (1) The unsteady viscosity considering time evolution can be expressed as: Where t is time, a and b are material parameters, and 0<a<1, η0 is the viscosity coefficient of the Kelvin body viscosity pot; (2) Establish the constitutive relationship of the unsteady creep constitutive model: Where: ε is the total strain, σ s is the normal stress, σ ∞ is the long-term strength of carbonaceous slate, E0 is the elastic modulus of a single spring body, E1 is the elastic modulus of an improved Kelvin body, η0 is the viscosity coefficient of a Kelvin body viscosity pot, η1 is the viscosity coefficient of an improved Kelvin body viscosity pot, and η2 is the viscosity coefficient of a Newtonian body with a switch; (3) Establish the creep equation of the three-dimensional stress field. The stress and strain equations of the three-dimensional stress state are: Where: σ ij is the stress tensor, S ij is the deviatoric stress tensor, σ m is the spherical stress tensor, ε ij is the strain tensor, e ij is the deviatoric strain tensor, ε m is the spherical strain tensor, σ i is the principal stress in the i direction, ε i is the principal strain in the i direction, δ ij is the Kronecker function; (4) Under three-dimensional stress conditions, the elastic body satisfies the generalized Hooke's law: Where G is the shear modulus, K is the bulk modulus, and σ m is the spherical stress tensor, e ij is the deviatoric strain tensor, ε m is the spherical strain tensor; (5) After decomposing formula (4) and substituting it into formula (3), and then substituting it together with formula (1) into formula (2), the constitutive relationship of the unsteady creep model of the present invention can be obtained:

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