A rock deformation prediction method based on the whole-process elastoplastic creep analysis

Abstract

The present invention discloses a method for predicting rock deformation based on full-process elastoplastic creep analysis, comprising the following steps: 1) constructing a plastic strain expression of a plastic element related to a time variable; 2) establishing an aging damage function of a rock during the creep process based on the probability density function of rock damage; 3) substituting the aging damage function into the expression in step 1) and considering the viscosity coefficient of the damaged plastic element to obtain a constitutive equation of the element stress with respect to plastic deformation; 4) constructing a rock creep stress prediction model reflecting the variation of mechanical properties with time t during the whole creep process; 5) using the rock creep stress prediction model to calculate the strain of the rock undergoing creep deformation at a specified prediction time, and predicting the deformation of the rock; The present invention can provide predictive analysis for rock deformation, and its accuracy and feasibility have been verified through the comparative analysis of the actual working condition monitoring and measuring deformation values and the model calculation values.

Description

Technical Field

[0001] The present invention relates to the field of rock creep damage judgment, and particularly relates to a rock deformation prediction method based on the whole-process elastoplastic creep analysis. Background Art

[0002] Rock creep refers to the phenomenon that rock deformation (or strain) increases with time under constant stress and temperature, also known as rock creep. Rock creep in nature is slow and not easily noticeable, but the accumulation of this slow deformation can cause serious consequences, such as landslides, cave collapses, etc. This rheological property of rocks has an important impact on the safety and long-term stability of many engineering projects.

[0003] The creep of rocks generally goes through three stages over time: ① Initial creep or transitional creep, where the strain increases with time but the rate of increase gradually slows down; ② Steady-state creep or constant creep, where the strain increases uniformly with time, and this stage is relatively long; ③ Accelerated creep, where the strain increases with time at an accelerating rate until the rupture point. The greater the stress, the shorter the total creep time; the smaller the stress, the longer the total creep time.

[0004] Obtaining the mechanical properties of rock mass from the rheological viewpoints and methods of rock mass has a high degree of agreement with the actual working conditions. Many scholars have established a series of rock creep models based on empirical formulas and combinations of creep elements, and verified them through indoor physical experiments and on-site engineering deformations. However, traditional creep constitutive models, such as the Nishihara model, the Burgers model, etc., cannot describe the accelerated stage of rock creep because the formula parameters are constant.

[0005] Rock rheology has non-linear characteristics. The non-linear characteristics of rock rheology are: plasticity, elasticity, and viscoelasticity; among them, plasticity means that if the applied stress is less than the actual result, the material will exhibit plasticity and cannot return to the initial state. That is, the deformation after yielding is permanent; elasticity means that when the stress is removed, the material returns to the state before deformation. The deformation of a linearly elastic material is proportional to the applied load, and this relationship can be expressed by a linear elastic equation; viscoelasticity means that the material not only has elasticity but also has friction. When the stress is removed, a part of the work is used for the frictional effect and is converted into heat energy, and this process can be represented by a stress-strain curve.

[0006] In view of the non-linear characteristics of rock rheology, many scholars have improved the classical models.For example, in the literature "Zhu ZY, et al. A creep model for frozen sand of qinghai-tibet based on Nishihara model[J]. Cold Regions Science and Technology, 2019, 167(Nov.): 102843.1-102843.9.", the creep parameters of the Nishihara model were improved as functions of stress and time, and a damage parameter was introduced to construct a non-linear damage creep model; another example is the literature "Wang J D, et al. A new superlinear viscoplastic shear model for accelerated rheological deformation[J]. Computers and Geotechnics, 2019, 114(Oct.): 103132.1-103132.10.", based on the Nishihara model, through granite creep tests, a non-linear granite creep model was proposed; the literature "Wang X G, et al. Moisture content effect on the creep behavior of loess for the catastrophic Baqiao landslide[J]. Catena, 2019, 187: 104371." introduced a new creep element, combined with the Burgers model to form a new non-linear model, and was verified by creep tests; the literature "Zhou H W, et al. A creep constitutive model for salt rock based on fractional derivatives[J]. International Journal of Rock Mechanics and Mining Sciences, 2011, 48(1): 116-121." improved the Nishihara model, introduced the Abel damper of fractional derivatives, and constructed a fractional derivative creep model; the literature "Yang X B, et al. Nonliear Damage Creep Model of Coal or Rock Containing Gas[J]. Applied Mechanics and Materials, 2012, 204-208." introduced a damage parameter containing time variables and established a non-linear damage model of gas-containing coal and rock based on the Kelvin model.

[0007] The above-mentioned models can better explain the non-linearity of rock creep, but the understanding of the rheological properties of the whole process of rock creep in the models is insufficient, and the rheological properties such as elasticity, viscoelasticity, and plasticity cannot be corresponding to the model parameters. Along with the increase of rock stress, its creep deformation properties also change. Most of the existing models improve a certain element in the classical parameter constant model. Although the new models formed in this way can have a better fitting for the creep test results, in terms of rock deformation prediction, the above-mentioned models do not well explain the internal reasons for creep deformation and cannot predict and analyze the whole process of rock creep. Therefore, it is necessary to construct a non-linear rheological model whose physical meaning of parameters can correspondingly explain the rheological properties of the whole process of rock creep, so as to conduct rock deformation prediction for the elastoplastic creep analysis of the whole process of rock. Summary of the Invention

[0008] The purpose of the present invention is to provide a rock deformation prediction method based on the elastoplastic creep analysis of the whole process, so as to solve the problem of poor feasibility and accuracy in the analysis of the rock creep process in the prior art.

[0009] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0010] A rock deformation prediction method based on the elastoplastic creep analysis of the whole process includes the following steps:

[0011] S1. For the plastic deformation behavior that occurs when the rock creep process exceeds the long-term strength, construct a plastic strain expression ε of the plastic element related to the time variable P ;

[0012] S2. Based on the probability density function of rock damage, establish the aging damage function D(t) of the rock during the rock creep process;

[0013] S3. Substitute the aging damage function D(t) into the plastic strain expression ε of the plastic element P and consider the viscous coefficient of the plastic element with damage to obtain the constitutive equation ε of the element stress for plastic deformation PD (t);

[0014] S4. Substitute the constitutive equation ε of the element stress PD (t) into the Burgers creep model to construct a rock creep stress prediction model ε(t) that reflects the change of mechanical properties with time t during the whole creep process;

[0015] S5. Use the rock creep stress prediction model ε(t) to calculate the strain of the rock that undergoes creep deformation at the specified prediction time, and conduct deformation prediction for the rock.

[0016] Preferably, in the step S1, the plastic element ε related to the time variable P has the following plastic strain expression:

[0017]

[0018] In the formula, ε P is the plastic strain of the plastic element, σ is the applied stress, and σ s is the long-term strength of the rock, η P represents the plastic coefficient of the plastic element, k is the strength coefficient, n is the strain hardening index, where k and n are related to material hardening, and τ is the time variable.

[0019] Preferably, in the step S2, the expression of the aging damage function D(t) of the rock during the rock creep process is:

[0020] D(t) = [1 - exp(-αt ξ )];

[0021] In the formula, α is the material proportional constant, α > 0, ξ is the material shape constant, ξ > 0, τ is the time variable, and t is the time interval.

[0022] Preferably, in the step S3, the constitutive equation ε PD (t) of the plastic deformed element stress is expressed as:

[0023]

[0024] In the formula, k is the strength coefficient, n is the strain hardening index, where k and n are related to material hardening, α is the material proportional constant, α > 0, ξ is the material shape constant, ξ > 0, t is the time interval, σ is the applied stress, and σ s is the long-term strength of the rock, η P is the plastic coefficient of the plastic element.

[0025] Preferably, in the step S4, the expression of the rock creep stress prediction model ε(t) for the full-process mechanical properties is:

[0026]

[0027] In the system of equations, σ is the applied stress, σ s is the long-term strength of the rock, E M is the elastic modulus of the Maxwell body, η M is the viscous coefficient of the Maxwell body, E K is the elastic modulus of the Kelvin body, η Kis the viscoelastic coefficient of the Kelvin body, k is the strength coefficient, n is the strain hardening index, k and n are related to material hardening, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, t is the time interval, and η P is the plastic coefficient of the plastic element.

[0028] Preferably, in step S2, the method for obtaining the aging damage function D(t) of the rock during the rock creep process specifically includes the following steps:

[0029] S2.1. Based on the probability density function of rock damage, obtain the total amount of rock damage M within the time interval where the time variable τ is in [0, t]. D It is:

[0030]

[0031] In the formula, M D (τ) is the function of the total amount of rock damage and the time variable τ, M V is the rock volume element, P(τ) is the probability density function with the time variable τ as the random variable that the damage of the rock volume element M V follows, τ is the time variable, and τ ∈ [0, t];

[0032] The probability density function of the rock damage is:

[0033]

[0034] In the formula, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, and τ is the time variable;

[0035] S2.2. Define the aging damage function D(t) of the rock as the ratio of the total amount of rock damage M D (τ) to the rock volume element M V , and the expression can be obtained:

[0036]

[0037] In the formula, M D (τ) is the function of the total amount of rock damage and the time variable τ, M V is the rock volume element, P(τ) is the probability density function with the time variable τ as the random variable that the damage of the rock volume element M V follows, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, τ is the time variable, and τ ∈ [0, t].

[0038] Preferably, in step S3, the method for determining the constitutive equation of the element stress of plastic deformation ε PD (τ) specifically includes the following steps:

[0039] S3.1. Determine the plastic coefficient η of the plastic element considering the time-dependent damage of the rock according to the damage mechanics theory PD It is determined as follows:

[0040] η PD = η P (1 - D(t));

[0041] In the formula, η PD is the plastic coefficient of the plastic element considering the time-dependent damage of the rock, η P is the plastic coefficient of the plastic element, and D(t) is the time-dependent damage function of the rock;

[0042] S3.2. Substitute the plastic coefficient η of the damaged plastic element PD to replace the plastic coefficient η of the plastic element in step S1 P and substitute it into the plastic element expression in step S1. At the same time, substitute the expression of the time-dependent damage function D(t) of the rock into the plastic element expression in step S1 to obtain the constitutive expression of the plastic element based on the statistical distribution of microcracks:

[0043]

[0044] In the formula, k is the strength coefficient, n is the strain hardening index, k and n are related to material hardening, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, t is the time interval, σ is the applied stress, σ s is the long-term strength of the rock, and η P is the plastic coefficient of the plastic element.

[0045] Preferably, the method for improving the Burgers model in step S4 specifically includes the following steps:

[0046] S4.1. The constitutive equation of the original Burgers model is:

[0047]

[0048] In the formula, ε B is the deformation of the material, σ is the applied stress, E M is the elastic modulus of the Maxwell body, η M is the viscous coefficient of the Maxwell body, E K is the elastic modulus of the Kelvin body, η K is the viscoelastic coefficient of the Kelvin body, and t is the time interval;

[0049] S4.2. Substitute the constitutive expression ε of the plastic element obtained in step S3 PD(t) is introduced into the original Burgers model constitutive equation in step S4.1 to obtain a group of rock creep stress prediction models ε(t) related to time.

[0050] Preferably, the Maxwell refers to the Maxwell model, which is a constitutive model obtained by connecting an elastic element and a viscoelastic element in series.

[0051] Preferably, the Kelvin refers to the Kelvin model, which is a constitutive model obtained by connecting an elastic element and a viscoelastic element in parallel.

[0052] The present invention has the following beneficial effects:

[0053] Based on the Ramberg-Osgood plastic equation, the present invention constructs a plastic strain expression of a plastic element related to a time variable. At the same time, based on the probability density function of rock damage, an aging damage function of the rock during the creep process is established. Furthermore, a constitutive equation of the element stress of plastic deformation is obtained and introduced into the Burgers creep model to construct a rock creep stress prediction model that reflects the variation of mechanical properties with time t during the entire creep process. This rock creep stress prediction model can explain the entire process of rock creep, and the creep failure state can be determined through the long-term strength of the rock. Furthermore, it can provide prediction and analysis for rock deformation, and its accuracy and feasibility have been verified through the comparative analysis of the actual working condition monitoring deformation value and the model calculation value. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to make the objectives, technical solutions, and advantages of the invention clearer, the present invention will be further described in detail below with reference to the drawings, where:

[0055] Figure 1 is a schematic diagram of the entire creep process of the present invention.

[0056] Figure 2 is a diagram of a new plastic element proposed by the present invention.

[0057] Figure 3 is a schematic diagram of the original Burgers creep model of the present invention.

[0058] Figure 4 is a schematic diagram of the Maxwell model of the present invention.

[0059] Figure 5 is a schematic diagram of the Kelvin model of the present invention.

[0060] Figure 6 is a schematic diagram of the improved Burgers creep model of the present invention.

[0061] Figure 7Schematic diagram of the specimen loading device for Embodiment 1 of the present invention.

[0062] Figure 8 Process diagram of the creep test for Embodiment 1 of the present invention.

[0063] Figure 9 Comparison diagram of the experimental values, calculated values of the improved Burgers model, and calculated values of the original Burgers model for Embodiment 1 of the present invention.

[0064] Figure 10 Schematic diagram of the tunnel section monitoring points for Embodiment 2 of the present invention.

[0065] Figure 11 Comparison diagram of the measured displacement of the tunnel measurement points and the calculated values of the improved Burgers model for Embodiment 2 of the present invention. Detailed implementation manners

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0067] It should be noted that similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the present invention is usually placed during use. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as a limitation to the present invention. In addition, the terms "first", "second", "third", etc. are only used for descriptive distinction and should not be construed as indicating or implying relative importance. In addition, terms such as "horizontal" and "vertical" do not mean that the components are required to be absolutely horizontal or hanging, but can be slightly inclined. For example, "horizontal" only means that its direction is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but can be slightly inclined. In the description of the present invention, it should also be noted that unless otherwise clearly specified and limited, the terms "set", "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 mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal communication of two components. 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 situations.

[0068] The technical problems to be solved by the present invention are as follows: In the prior art, most improvements are made to a certain component in the classical parameter constant model, and the existing non-linear models of rock creep do not fully understand the rheological characteristics of the whole process of rock creep.

[0069] As Figures 1 to 6 shown, based on the above technical problems to be solved, the present invention discloses a rock deformation prediction method based on the whole-process elastoplastic creep analysis, including:

[0070] S1. For the plastic deformation behavior that occurs during the rock creep process when exceeding the long-term strength, construct a plastic strain expression ε of the plastic component related to the time variable P ;

[0071] S2. Based on the probability density function of rock damage, establish the aging damage function D(t) of the rock during the rock creep process;

[0072] S3. Substitute the aging damage function D(t) into the plastic strain expression of the plastic component ε P , and consider the viscosity coefficient of the plastic component with damage, to obtain the constitutive equation of the component stress regarding plastic deformation ε PD (t);

[0073] S4. Substitute the constitutive equation of the component stress ε PD (t) into the Burgers creep model, and construct a rock creep stress prediction model ε(t) that reflects the variation of mechanical properties with time t during the whole creep process;

[0074] S5. Use the rock creep stress prediction model ε(t) to calculate the strain of the rock that undergoes creep deformation at the specified prediction time, and conduct deformation prediction on the rock.

[0075] In step S1, the plastic strain expression ε of the plastic component can be constructed based on the Ramberg-Osgood equation P .

[0076] The Ramberg-Osgood equation is a classical theoretical model in solid mechanics for describing the stress-strain relationship (stress-strain curve) of materials near their yield points. The Ramberg-Osgood equation has a simple form and can well simulate the plastic deformation behavior of materials. It is the most widely used in engineering, and its original expression is shown in formula (1):

[0077]

[0078] In the formula, ε represents the total strain, that is, including elastic and plastic strains, ε e is the elastic strain, and ε pwhere ε is the plastic strain, σ is the applied stress, E is the Young's modulus of the material; the first term on the right side of Equation (1) is the elastic strain expression, that is In the formula, ε e is the elastic strain, σ is the applied stress, E is the Young's modulus of the material, and the elastic strain satisfies Hooke's law; the second term on the right side of Equation (1) is the plastic strain expression, that is In the formula, ε p is the plastic strain, σ is the applied stress; E is the Young's modulus of the material; k is the strength coefficient, n is the strain hardening index (i.e., the strength characterizing the hardening of the material during plastic deformation), and k and n are related to material hardening. The value of n has a very significant impact on the degree of deformation uniformity, the size of the deformation limit, and whether cracks will occur, etc. A high value of n indicates a high degree of strain hardening of the material. The Young's modulus E is a measure of the stiffness of a solid under load or its resistance to elastic deformation. The basic principle is that the material undergoes elastic deformation when compressed or stretched and returns to its original shape after the load is removed. A low value of the Young's modulus indicates that the solid is elastic, and a high value of the Young's modulus indicates that the solid is inelastic or hard.

[0079] Reference Figure 1 , the creep process can be divided into three stages: OA - the attenuation creep stage, AB - the steady creep stage, BC - the accelerating creep stage. Microcracks always exist in the rock, damage accumulates continuously, and plastic deformation always exists. When the external load exceeds the yield strength of the rock, the damage develops rapidly, microcracks grow rapidly, and finally failure occurs. The Ramberg - Osgood plastic equation explains the plastic failure of the rock.

[0080] As Figure 2 shown, according to the above, the present invention defines a new plastic element to replace the plastic strain expression in Equation (1), introducing the time variable τ, the long - term strength σ s of the rock, and the plastic coefficient η P , and obtaining the expression of the plastic element as shown in Equation (2):

[0081]

[0082] In the formula, ε P is the plastic strain of the plastic element, σ is the applied stress, σ s is the long - term strength of the rock, η P characterizes the plastic coefficient of the plastic element, k is the strength coefficient, n is the strain hardening index (used to characterize the strength of material hardening during plastic deformation), k and n are related to material hardening, and τ is the time variable.

[0083] The long - term strength σ sIt refers to that each material has a minimum stress value. When the stress is lower than this value, it will not break no matter how long the time is, or in other words, the creep time is infinitely long. This stress value is called the long-term strength of the material.

[0084] The plasticity coefficient η of the plastic element P It refers to the ratio of the total work consumed before the plastic element breaks to the elastic deformation work before breaking. The larger the value of the plasticity coefficient, the greater the plasticity of the plastic element.

[0085] In step S2, the method for obtaining the aging damage function D(t) of the rock during the creep process of the rock specifically includes the following steps:

[0086] S2.1. The damage of the rock volume unit M V follows the Weibull distribution and is related to time, following the following probability density function, that is, the statistical distribution function of microcracks:

[0087]

[0088] In the formula, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, and τ is the time variable.

[0089] The Weibull distribution, also known as the Weibull distribution or the Weibull distribution, is the theoretical basis for reliability analysis and life testing. From the perspective of probability theory and statistics, the Weibull distribution is a continuous probability distribution.

[0090] Then, based on formula (3), it is possible to obtain that within the time interval where the time variable τ is in [0, t], the total damage M of the rock D is:

[0091]

[0092] In the formula, M D (τ) is the function of the total damage of the rock and the time variable τ, M V is the rock volume unit, P(τ) is the probability density function with the time variable τ as the random variable that the damage of the rock volume unit M V follows, τ is the time variable, and τ ∈ [0, t].

[0093] S2.2. Define the aging damage function D(t) of the rock as the ratio of the total damage M of the rock D (τ) to the rock volume unit M V , and the expression is as shown in formula (5):

[0094]

[0095] Wherein, M D (τ) is a function of the total damage of the rock and the time variable τ, and M V is the rock volume unit, and P(τ) is the probability density function with the time variable τ as a random variable that the damage of the rock volume unit M V follows. α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, τ is the time variable, and τ ∈ [0, t].

[0096] The method for determining the constitutive equation ε PD (τ) of the element stress in the plastic deformation in step S3 specifically includes the following steps:

[0097] S3.1. According to the damage mechanics theory, the plastic coefficient η PD of the plastic element considering the aging damage of the rock is determined as:

[0098] η PD = η P (1 - D(t)) (6);

[0099] Wherein, η PD is the plastic coefficient of the plastic element considering the aging damage of the rock, η P is the plastic coefficient of the plastic element, and D(t) is the aging damage function of the rock.

[0100] S3.2. Substitute the plastic coefficient η PD of the damaged plastic element for the plastic coefficient η P in step S1 and substitute it into the plastic element expression in step S1, that is, formula (2). At the same time, substitute the expression of the aging damage function D(t) of the rock into the plastic element expression in step S1, that is, formula (2), to obtain the constitutive expression of the plastic element based on the statistical distribution of microcracks:

[0101]

[0102] Wherein, k is the strength coefficient, n is the strain hardening index (used to characterize the strength of material hardening in plastic deformation), k and n are related to material hardening, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, t is the time interval, σ is the applied stress, σ s is the long-term strength of the rock, and η P is the plastic coefficient of the plastic element.

[0103] The non-linear element expressed by formula (7) can be used to describe the three stages of the creep process. The material constants (k, n, α, ξ) involved in formula (7) vary with the differences in material properties and are obtained from creep tests.

[0104] The method for improving the Burgers model in step S4 specifically includes the following steps:

[0105] As a creep model widely used to describe the deformation behavior of materials, the Burgers model can well explain the first and second stages of creep. However, due to the lack of a nonlinear element, it cannot describe the last stage of creep. Based on this, the above-mentioned nonlinear plastic element is combined with the original Burgers model to construct an improved Burgers model that can reflect the mechanical properties of the three stages of creep:

[0106] S4.1. The constitutive equation of the original Burgers model is:

[0107]

[0108] In the formula, ε B is the deformation of the material, σ is the applied stress, E M is the elastic modulus of the Maxwell body, η M is the viscosity coefficient of the Maxwell body, E K is the elastic modulus of the Kelvin body, η K is the viscoelastic coefficient of the Kelvin body, and t is the time interval.

[0109] As Figure 4 shown, the Maxwell refers to the Maxwell model, which is a constitutive model obtained by connecting an elastic element and a viscoelastic element in series. When the Maxwell model is subjected to stress, its deformation and the force on the viscoelastic element are as shown in formula (9):

[0110]

[0111] In the formula, σ is the applied stress; ε is the strain; E M is the elastic modulus of the Maxwell body, ε1 is the deformation of the elastic element, η M is the viscosity coefficient of the Maxwell body, and ε2 is the deformation of the viscoelastic element.

[0112] As Figure 5 shown, the Kelvin refers to the Kelvin model, which is a constitutive model obtained by connecting an elastic element and a viscoelastic element in parallel. When the Kelvin model is subjected to stress, its total deformation and the force on the viscoelastic element are as shown in formula (10):

[0113]

[0114] In the formula, σ is the applied stress, σ1 is the stress of the elastic element, σ2 is the stress of the viscoelastic element, E Kis the elastic modulus of the Kelvin body, η K is the viscoelastic coefficient of the Kelvin body, and ε3 is the deformation of the component.

[0115] S4.2. Introduce the constitutive expression of the plastic element ε PD (t) obtained in step S3 into formula (8) in step S4.1, and considering the factor that the stress exceeds the long-term strength of the rock σ s enters the plastic stage, and obtain a set of rock creep stress prediction models related to time ε(t):

[0116]

[0117] In the system of equations, σ is the applied stress, σ s is the long-term strength of the rock, E M is the elastic modulus of the Maxwell body, η M is the viscous coefficient of the Maxwell body, E K is the elastic modulus of the Kelvin body, η K is the viscoelastic coefficient of the Kelvin body, k is the strength coefficient, n is the strain hardening index (i.e., the strength of material hardening in plastic deformation), k and n are related to material hardening, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, t is the time interval, η P is the plastic coefficient of the plastic element.

[0118] So far, the rock creep stress prediction model has been completely determined (the schematic diagram of the model is as shown in Figure 6 ), the physical and mechanical meanings of the model parameters are clear, and it is applicable to describe the mechanical behavior of the whole creep process. Its feasibility can be verified through experimental examples.

[0119] Example 1

[0120] In order to verify the improved Burgers model proposed by the present invention, substitute the indoor test data into the constitutive equation of the Burgers model

[0121] ε(t) to verify the effectiveness and rationality of the model through experiments.

[0122] In this example, mudstone specimens are selected for indoor uniaxial creep tests. The specimens are standard cylinders with a diameter of 50 mm and a height of 100 mm. The specific mechanical parameters are shown in Table 1.

[0123] Table 1 Mudstone material parameters

[0124] Material E (GPa) μ c (MPa) Ψ (°) <![CDATA[σ s (MPa)]]> Shale 11.2 0.24 3.2 24 6.33

[0125] The test instrument uses a YSR-05 rock rheometer ( Figure 7) This instrument is computer-controlled, with electrical, pneumatic, and hydraulic inter-regulation, and can complete uniaxial and triaxial creep tests. The axial load control rate is 400 N / s, and the measurement accuracy is 0.001 mm. The test loading process is shown in Figure 8 , and the axial load is kept constant during the loading process, and the stable time for each load level is 48 h.

[0126] Immediately stop the test after time failure, and process the test data in the acceleration stage, such as Figure 9 . Use the classical Burgers model and the improved Burgers model to fit the test results, and the curve is as shown in Figure 9 . And according to the test data, the creep parameters of the improved Burgers model are obtained by the Levenberg-Marquardt algorithm, as shown in Table 2.

[0127] Table 2 Creep parameters of the improved Burgers model for mudstone

[0128]

[0129] In Table 2, E M is the elastic modulus of the Maxwell body, η M is the viscous coefficient of the Maxwell body, E K is the elastic modulus of the Kelvin body, η K is the viscoelastic coefficient of the Kelvin body, η P is the plastic coefficient of the plastic element, k is the strength coefficient, n is the strain hardening index, k and n are related to material hardening, α is the material proportionality constant, and ξ is the material shape constant.

[0130] Thanks to the improved Burgers model settings disclosed in the present invention, these parameters can explain the rheological properties of rock creep deformation. The elastic modulus corresponds to elastic deformation, the viscoelastic modulus and viscoelastic coefficient correspond to viscoelastic deformation, the viscous modulus corresponds to viscous deformation, and the plastic modulus corresponds to plastic deformation. It can be seen that the improved Burgers creep model proposed by the present invention can explain the whole process of creep, especially has a good description effect on the non-linear deformation in the acceleration stage of mudstone, and has a higher fitting degree with the test data, verifying the rationality and superiority of the model.

[0131] Example 2

[0132] In order to verify the improved Burgers model proposed by the present invention, the detection data under actual working conditions are substituted into the constitutive equation ε(t) of the Burgers model, and the applicability of the model in explaining the deformation of specific projects is verified through actual projects.

[0133] In this embodiment, the working conditions of Dengjiashan Tunnel located in Nanchong, China are selected. The total length of Dengjiashan Tunnel is 620 m, the maximum buried depth is 250 m, the in-situ stress is taken as 6.5 MPa, the plane alignment is a straight line, the surrounding rock of grade V is 480 m, and the surrounding rock of grade IV is 140 m. The geomorphology in the tunnel site area belongs to the deeply cut hilly and low mountain geomorphic unit, located in the eastern wing of Huaxi syncline. The rock strata occur in a monoclinic form, with a gentle dip angle of 6°. The dip direction of the rock strata is consistent with the route alignment. The rock strata are interbedded with sandstone and mudstone. The uniaxial compressive strength of the rock sample is 7.8 MPa, and the long-term strength is 5.4 MPa.

[0134] Figure 10 It is a schematic diagram of the monitoring points of the tunnel section. Point A is the settlement measurement point of the tunnel crown, and BC and DE are the convergence measurement points of the tunnel perimeter. By monitoring and measuring the surrounding rock of the tunnel, the deformation value of the surrounding rock after tunnel excavation and before the secondary lining can be obtained.

[0135] Under the action of in-situ stress and without the support of lining, the surrounding rock of the tunnel will continuously produce creep deformation. Therefore, it is particularly important to predict the deformation of the surrounding rock of the tunnel through a creep model.

[0136] Figure 11 It shows a comparative analysis chart of the monitoring and measurement values of the settlement measurement point A of the tunnel crown, and the convergence measurement points BC and DE of the tunnel perimeter in Dengjiashan Tunnel and the calculated values of the improved Burgers model of the present invention. It can be seen that the improved Burgers creep model proposed by the present invention can explain the creep deformation of the surrounding rock of the tunnel after excavation, can predict the deformation of the surrounding rock, and verifies the accuracy and feasibility of the model in actual working conditions.

[0137] The present invention has the following beneficial effects: Based on the Ramberg-Osgood plastic equation, the present invention constructs a plastic strain expression of the plastic element related to the time variable, with simple parameters and clear physical and mechanical meanings. At the same time, based on the probability density function of rock damage, the present invention establishes a time-dependent damage function of the rock during the creep process, and then obtains the constitutive equation of the element stress of the plastic deformation. By introducing it into the Burgers creep model, a rock creep stress prediction model reflecting the mechanical properties changing with time t during the whole creep process is constructed. This rock creep stress prediction model can explain the whole process of rock creep, can judge the creep failure state through the long-term strength of the rock, and can further provide prediction and analysis for rock deformation. Its accuracy and feasibility have been verified by the comparative analysis of the monitored deformation values in actual working conditions and the calculated values of the model.

[0138] The rock creep stress prediction model proposed by the present invention contains elastic modulus, viscoelastic modulus, viscoelastic coefficient, viscous coefficient and plastic coefficient, can explain the elastic, viscoelastic, viscous and plastic deformations during creep, and can predict the whole process of rock deformation more comprehensively.

[0139] It will be understood that the present invention is described by way of some embodiments, and those skilled in the art will appreciate that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the present invention. Under the teaching of the present invention, these features and embodiments can be modified to suit the specific circumstances and materials without departing from the spirit and scope of the present invention. The embodiments described herein are only a part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and illustrated herein in the drawings can be arranged and designed in a variety of different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

Claims

1. A rock deformation prediction method based on full-process elastoplastic creep analysis, characterized in that, It includes the following steps: S1. For the plastic deformation behavior of rock that exceeds the long-term strength during creep, the plastic strain expression ε of the plastic element related to the time variable is constructed. P ; S2. Based on the probability density function of rock damage, establish the aging damage function D(t) of the rock during the creep process; S3. Substitute the time-dependent damage function D(t) into the plastic strain expression ε of the plastic element. P In the equation ε, the viscosity coefficient of the damaged plastic element is considered, and the element stress constitutive equation ε about plastic deformation is obtained. PD (t); S4. Substitute the constitutive equation of element stress ε PD (t) into the Burgers creep model to construct a rock creep stress prediction model ε(t) that reflects the variation of mechanical properties with time t during the entire creep process; the expression of the rock creep stress prediction model ε(t) of the mechanical properties during the entire process in step S4 is: In the system of equations, σ is the applied stress, σ s is the long-term strength of the rock, E M is the elastic modulus of the Maxwell body, η M is the viscosity coefficient of the Maxwell body, E K is the elastic modulus of the Kelvin body, η K is the viscoelastic coefficient of the Kelvin body, k is the strength coefficient, n is the strain hardening index, k and n are related to material hardening, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, t is the time interval, η P is the plastic coefficient of the plastic element; S5. Use the rock creep stress prediction model ε(t) to calculate the strain of the rock undergoing creep deformation at the specified prediction time, and conduct deformation prediction on the rock.

2. The rock deformation prediction method based on full-process elastic-plastic creep analysis according to claim 1 is characterized in that: In the step S1, the plastic element ε related to the time variable P has the following plastic strain expression: where ε P is the plastic strain of the plastic element, σ is the applied stress, and σ s is the long-term strength of the rock, η P represents the plastic coefficient of the plastic element, k is the strength coefficient, n is the strain hardening index, k and n are related to material hardening, and τ is the time variable.

3. The rock deformation prediction method based on full-process elastic-plastic creep analysis according to claim 1 is characterized in that: In step S2, the expression of the aging damage function D(t) of the rock during the creep process is: D(t) = [1 - exp(-αt ξ )]; In the formula, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, τ is the time variable, and t is the time interval.

4. The rock deformation prediction method based on the whole-process elastoplastic creep analysis according to claim 1, characterized in that In step S3, the stress constitutive equation of the plastically deformed element ε PD The expression of (t) is: where k is the strength coefficient, n is the strain hardening index, k and n are related to material hardening, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, t is the time interval, σ is the applied stress, σ s is the long-term strength of the rock, and η P is the plasticity coefficient of the plastic element.

5. The rock deformation prediction method based on the whole-process elastoplastic creep analysis according to claim 3, characterized in that, In step S2, the method for obtaining the aging damage function D(t) of the rock during the creep process specifically includes the following steps: S2.

1. Obtain the total damage amount M of the rock within the time interval where the time variable τ is in [0, t] based on the probability density function of rock damage D It is as follows: Where, M D (τ) is the function of the total damage of the rock and the time variable τ, M V is the rock volume element, P(τ) is the probability density function with the time variable τ as the random variable followed by the damage of the rock volume element M V , τ is the time variable, τ ∈ [0, t]; The probability density function of the rock damage is: In the formula, α is the material proportionality constant, α > 0, ξ is the material shape constant, ξ > 0, and τ is the time variable; S2.

2. Define the time-dependent damage function D(t) of rock as the total amount of rock damage M D (τ) and rock volume unit M V The ratio of , we can get the expression: Where M D (τ) is the function of the total amount of rock damage and the time variable τ, M V is the rock volume unit, P(τ) is the rock volume unit M V The damage follows the probability density function with the time variable τ as the random variable, α is the material proportional constant, α>0, ξ is the material shape constant, ξ>0, τ is the time variable, τ∈[0,t].

6. The rock deformation prediction method based on the whole-process elastoplastic creep analysis according to claim 4, characterized in that, In step S3, the method for determining the element stress constitutive equation ε PD (τ) specifically includes the following steps: S3.

1. According to the damage mechanics theory, the plastic coefficient η of the plastic element considering the time-dependent damage of rock is PD Determined as: or PD =the P (1-D(t)); where η PD is the plastic coefficient of the plastic element considering the time-dependent damage of the rock, and η P is the plastic coefficient of the plastic element, and D(t) is the time-dependent damage function of the rock; S3.

2. Replace the plastic coefficient η of the damaged plastic element PD with the plastic coefficient η of the plastic element in step S1 P and substitute it into the plastic element expression in step S1. At the same time, substitute the expression of the rock aging damage function D(t) into the plastic element expression in step S1 to obtain the constitutive expression of the plastic element based on the statistical distribution of microcracks: where k is the strength coefficient, n is the strain hardening index, k and n are related to material hardening, α is the material proportionality constant with α > 0, ξ is the material shape constant with ξ > 0, t is the time interval, σ is the applied stress, and σ s is the long-term strength of the rock, and η P is the plasticity coefficient of the plastic element.

7. The rock deformation prediction method based on full-process elastic-plastic creep analysis according to claim 1 is characterized in that: In step S4, the method for improving the Burgers model specifically includes the following steps: S4.

1. The constitutive equation of the original Burgers model is: where ε B is the deformation of the material, σ is the applied stress, and E M is the elastic modulus of the Maxwell body, η M is the viscosity coefficient of the Maxwell body, E K is the elastic modulus of the Kelvin body, η K is the viscoelastic coefficient of the Kelvin body, and t is the time interval; S4.

2. Introduce the constitutive expression of the plastic element ε PD (t) obtained in step S3 into the original Burgers model constitutive equation in step S4.1 to obtain a group of rock creep stress prediction models ε(t) related to time.

8. The rock deformation prediction method based on the whole-process elastoplastic creep analysis according to claim 7, wherein The Maxwell mentioned refers to the Maxwell model, and the Maxwell model is a constitutive model obtained by connecting an elastic element and a viscoelastic element in series.

9. The rock deformation prediction method based on the whole-process elastoplastic creep analysis according to claim 7, characterized in that The Kelvin mentioned refers to the Kelvin model, and the Kelvin model is a constitutive model obtained by connecting an elastic element and a viscoelastic element in parallel.

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