CN113919148A - A method for building nonlinear creep model of rock - Google Patents

Abstract

The invention discloses a rock nonlinear creep model building method, which comprises the steps of carrying out indoor rock uniaxial compression test to obtain the average compression strength of rock; carrying out an indoor rock creep test in a graded loading mode; drawing a rock full strain-time curve obtained by an indoor rock creep test and classification of the graded strain-time curves of the rock under different stress levels; identifying the element type of the creep model, and constructing an initial creep model; fitting a nonlinear relation between the creep rate of the rock accelerated creep stage and the corresponding creep time history; and finally obtaining a constitutive equation and a creep equation of the rock nonlinear creep model. The method considers the anisotropy, inhomogeneity and nonlinear characteristics of the rock, can well describe the characteristics of instantaneous creep, deceleration creep, stable creep or accelerated creep of the rock in different stress states, can accurately describe the nonlinear characteristics of the rock at each creep stage, and has wider applicability.

Description

A method for building nonlinear creep model of rock

technical field

The invention belongs to the field of rock rheological modeling, in particular to a method for establishing a nonlinear creep model of rock.

Background technique

The biggest difference between an underwater tunnel and a conventional underground tunnel is not only that the surrounding rock of the underwater tunnel is in a high water environment, but also that the self-weight of water acts on the surrounding rock of the tunnel as an additional stress, and at the same time, water can significantly degrade the mechanical properties of the rock. The service life of a tunnel is generally several decades. With the extension of the service time, the surrounding rock of the tunnel will undergo time-related deformation or even damage under a certain load. Therefore, it is particularly important to construct an appropriate mechanical model to predict the relationship between the tunnel surrounding rock under stable load and the service time, that is, rock rheology. Rock rheology refers to the property of increasing rock deformation over time under constant load. The rheological analysis of the rock can comprehensively reflect the rheological constitutive properties of the rock, and can obtain the dependence relationship between the stress and strain of the rock and time under the action of constant load, which provides a basis for predicting the long-term stability of rock mass engineering. Theoretical support can reveal the rheological properties of rocks under different stress states, further establish a scientific time-varying relationship between stress and strain and time history, and provide a theoretical basis for scientifically and rationally evaluating the stability of rock mass engineering.

The most basic rheological constitutive model commonly used at present is composed of basic rheological elements in series, parallel and mixed connection. The three basic rheological elements include elastic element (H), plastic element (Y) and viscous element (N). body (H-N), Kelvin body (H|N), generalized Kelvin body (generalized Kelvin body), Boyding-Thomson body, ideal viscoplastic body (N|Y), Burgers body, Nishiplasma and Bingham body Mu body etc. At present, the main methods of establishing rock rheological constitutive models include: (1) directly fitting the rock rheological test curve with the empirical equation method through the rheological test of the rock or rock mass; (2) according to the rheological test results, The rock rheological constitutive model is established by using the series-parallel combination of model elements, and then the undetermined rheological element model parameters are determined by means of element model identification and parameter inversion; (3) nonlinear rheological Element theory, internal time theory, fracture mechanics and damage mechanics theory are used to establish rock rheological constitutive model. However, the above methods cannot take into account the deformation characteristics of rocks under different stress levels, and the modeling method is inaccurate.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for establishing a nonlinear creep model of rock, which can accurately establish a rheological constitutive model.

The method for establishing the rock nonlinear creep model provided by the present invention includes the following steps:

S1. Carry out a rock uniaxial compression test to obtain the average compressive strength of the rock;

S2. According to the average compressive strength of the rock, the rock creep test is carried out by using a graded loading method;

S3. Draw the total strain-time curve of the rock obtained by the rock creep test and the graded strain-time curve of the rock under different stress levels;

S4. Classify the graded strain-time curves of rocks under different stress levels;

S5. Identify the types of rheological elements of the creep model according to the graded strain-time curves of the rock under different stress levels, and construct an initial creep model;

S6. Fit the nonlinear relationship between the creep rate and the corresponding creep time history in the accelerated creep stage of the rock;

S7. Using the identified creep model and the fitted nonlinear relationship between the creep rate in the accelerated creep stage of the rock and the corresponding creep time history, the constitutive equation and the creep equation of the rock nonlinear creep model are obtained.

The step S1 includes repeating several indoor rock uniaxial compression tests to calculate the average uniaxial compressive strength of the rock.

In the step S2, the step-by-step loading method includes adding a preset stress increment for each step.

In the step S3, the full strain-time curve of the rock obtained by the rock creep test includes: the curve in the form of instantaneous creep and deceleration creep in the low stress state, and the creep curve in the low stress state finally tends to a level with a slope of 0. Straight line; the curve of transient creep, deceleration creep and stable creep in medium stress state, the creep curve in medium stress state eventually tends to a straight line with a fixed slope; instantaneous creep, deceleration creep and stable creep in high stress state The curve of creep and accelerated creep, the high stress state is a nonlinear curve;

The step S4 includes: according to the graded strain-time curves of the rock under different stress levels, it is specifically divided into curves in the form of instantaneous creep and deceleration creep in a low stress state; instantaneous creep and deceleration creep in a medium stress state. and stable creep curves; transient creep, decelerated creep, stable creep and accelerated creep curves for high stress states.

The described step S5 includes the following steps:

A1. Divide the creep model into several components, and identify the component types of the creep model;

A2. Establish the constitutive equation or creep equation of the element according to the graded strain-time curves under different stress levels, including: Hooke body is a spring element with instantaneous strain characteristics; Newton body is a viscous element with elastic after-effect properties ; switching elements and plastic elements with stress thresholds; nonlinear viscous elements with nonlinear properties.

In the step A2, the rheological element includes a basic rheological element, and the basic rheological element includes:

B1. The instantaneous deformation characteristics of creep deformation are described by the Hooke body. The constitutive equation of the Hooke body is:

σ'=E'ε'

Among them, σ' represents the stress of the low-stress state model; E' represents the elastic modulus of the low-stress state model; ε' represents the corresponding strain when the stress applied to the low-stress state model is σ';

B2. The elastic after-effect characteristics of creep deformation are described by the Newton body. The creep equation of the Newton body is:

Among them, σ” represents the stress of the medium-stress state model; η” represents the viscosity coefficient of the medium-stress state model; ε” represents the corresponding strain rate when the stress applied to the medium-stress state model is σ”;

B3. Set the stress threshold σ _K of the switching element, when the stress σ received by the switching element is less than the stress threshold σ _K of the switching element, the switching element is turned off, and all elements connected in parallel with the switching element do not function; when the switching element is subjected to When the stress σ is greater than the switching stress threshold σ _K , the switching element is turned on, and several elements connected in parallel with the switching element play a role;

B4. The strain of the plastic element is expressed as: when the stress on the plastic element is less than the yield limit σ _s of the plastic element, the strain is 0; when the stress on the plastic element is greater than the yield limit σ _s of the plastic element, the strain is not 0.

In the step S7, according to the initial creep model constructed in step S5 and the nonlinear relationship between the creep rate in the accelerated creep stage of the rock determined by fitting in step S6 and the corresponding creep time history, combined with the series connection of the creep elements. , the stress of all elements is equal to the applied stress, the strain is the rule of the sum of all series elements, and the constitutive model and creep model of the rock nonlinear creep model under low stress state, medium stress state and high stress state are established respectively.

The step S7 includes the following steps:

C1. When the applied stress σ < σ _K < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; calculate the constitutive equation of the creep model;

When the generalized Kelvin body, the switching element and the plastic element are connected in series in sequence; the step C1 includes when the applied stress σ<σ _K <σ _s , σ _K is the stress threshold value of the switching element; σ _s is the plastic element The yield limit of ; the obtained constitutive equation of the creep model is:

表示应力σ对时间的一阶导数；Among them, ε ₀₁ =ε ₀ +ε ₁ η ₁ , ε ₀ is the instantaneous creep, ε ₁ is the creep in the deceleration creep stage, η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; E ₀ is the generalized Kelvin body The elastic coefficient of the series Hooke body in the body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

C2. When the applied pressure σ _K <σ < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; calculate the constitutive equation of the creep model;

The step C2 includes when the applied pressure σ _K <σ < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; the obtained constitutive equation of the creep model is:

表示ε₀₁₂对时间的一阶导数；

表示ε₀₁₂对时间的二阶导数；ε₀为瞬时蠕变，ε₁为减速蠕变阶段的蠕变，ε₂为稳定蠕变阶段的蠕变；η₁为广义Kelvin体中Newton体的黏滞系数；η₂表示带开关黏性体中Newton体的黏滞系数；E₀表示广义Kelvin体中串联Hooke体的弹性系数；E₁表示广义Kelvin体中并联Hooke体的弹性系数；

表示应力σ对时间的一阶导数；

表示应力σ对时间的二阶导数；where ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ ,

represents the first derivative of ε ₀₁₂ with respect to time;

represents the second derivative of ε ₀₁₂ with respect to time; ε ₀ is the instantaneous creep, ε ₁ is the creep in the deceleration creep stage, ε ₂ is the creep in the stable creep stage; η ₁ is the viscosity of the Newton body in the generalized Kelvin body hysteresis coefficient; η ₂ represents the viscous coefficient of the Newton body in the viscous body with switch; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time;

C3. When the applied stress σ>σ _s , the constitutive equation of the rock nonlinear creep model is calculated by the constitutive equation of the Burgers model and the constitutive equation of the nonlinear viscoplastic body;

Described step C3, including the constitutive equation of rock nonlinear creep model is:

表示ε₀₁₂对时间的一阶导数；

表示ε₀₁₂对时间的二阶导数；

表示ε对时间的一阶导数；

表示ε对时间的二阶导数；η₂表示带开关黏性体中Newton体的黏滞系数；η₃(t)表示非线性黏塑性体中非线性黏性体的黏滞系数；E₀表示广义Kelvin体中串联Hooke体的弹性系数；E₁表示广义Kelvin体中并联Hooke体的弹性系数；

表示应力σ对时间的一阶导数；

表示应力σ对时间的二阶导数；Among them, σ represents the applied stress; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; ε ₀₁ =ε ₀ +ε ₁ η ₁ , ε ₀ is the instantaneous creep, and ε ₁ is the deceleration creep creep in the variable stage, η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ , ε ₂ is the creep in the stable creep stage;

represents the first derivative of ε ₀₁₂ with respect to time;

represents the second derivative of ε ₀₁₂ with respect to time;

represents the first derivative of ε with respect to time;

represents the second derivative of ε with respect to time; η ₂ represents the viscosity coefficient of the Newton body in the viscous body with switch; η ₃ (t) represents the viscosity coefficient of the nonlinear viscous body in the nonlinear viscoplastic body; E ₀ represents The elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time;

C4. Solve the creep equation of the rock nonlinear creep model.

The step C4 includes setting the stress applied at the initial moment as σ ₀ ; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; when σ ₀ <σ _K <σ _s , the creep The deformation is the sum of the deformation of the Hookean body and the deformation of the Kelvin body; when σ _K <σ ₀ <σ _s , the creep deformation is the Burgers model creep deformation; when σ ₀ ≥σ _s , the creep deformation is The sum of the creep deformation of the Burgers model and that of an ideal viscoplastic body.

In the step C4, the creep equation of the rock nonlinear creep model includes:

Among them, ε is the total strain generated by the model; t is the creep time in the accelerated creep stage; σ ₀ is the stress applied at the initial moment; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element ; η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; η ₂ is the viscosity coefficient of the Newton body in the viscous body with switch; η ₃ (t) is the viscosity of the nonlinear viscous body in the nonlinear viscoplastic body Hysteresis coefficient; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body.

The method for establishing the rock nonlinear creep model provided by the present invention takes into account the anisotropy, heterogeneity and significant nonlinear characteristics of the rock. It can well describe the characteristics of transient creep and deceleration creep of rock in low stress state, transient creep, deceleration creep and stable creep characteristics of medium stress state, transient creep, deceleration creep and stability of high stress state. The creep and accelerated creep characteristics can more accurately describe the nonlinear characteristics of each creep stage of the rock, and the rock nonlinear creep model provided by the present invention has wider applicability.

Description of drawings

FIG. 1 is a schematic flow chart of the method of the present invention.

FIG. 2 is a schematic diagram of the whole strain-time curve of the creep test according to the embodiment of the present invention.

FIG. 3 is a schematic diagram of a superimposed strain-time curve of a creep test according to an embodiment of the present invention.

FIG. 4 is a schematic diagram of a nonlinear creep model according to an embodiment of the present invention.

FIG. 5 is a schematic diagram of fitting of accelerated creep rate-duration test data in an accelerated creep stage according to an embodiment of the present invention.

FIG. 6 is a schematic diagram showing the comparison between the creep test results under different stresses and the fitting results of the rock nonlinear creep model according to an embodiment of the present invention.

Detailed ways

Figure 1 is a schematic flow chart of the method of the present invention: the method for establishing a nonlinear creep model of this rock provided by the present invention comprises the following steps:

S1. Perform an indoor rock uniaxial compression test to obtain the average compressive strength of the rock;

S2. According to the average compressive strength of the rock, the indoor rock creep test is carried out by using a graded loading method;

S3. Draw the total strain-time curve of the rock obtained from the indoor rock creep test and the graded strain-time curve of the rock under different stress levels;

S4. Classify the graded strain-time curves of rocks under different stress levels;

S5. Identify the types of rheological elements of the creep model according to the graded strain-time curves of the rock under different stress levels, and construct an initial creep model;

S6. Fit the nonlinear relationship between the creep rate and the corresponding creep time history in the accelerated creep stage of the rock;

S7. Using the identified creep model and the fitted nonlinear relationship between the creep rate in the accelerated creep stage of the rock and the corresponding creep time history, the constitutive equation and the creep equation of the rock nonlinear creep model are obtained.

The method further includes: using the creep equation of the rock nonlinear creep model to fit the graded strain-time curves of the rock under different stress levels, inverting the relevant parameters of the creep equation of the rock nonlinear creep model, and comparing The test results of the rock nonlinear creep model are used to judge whether the obtained creep equation of the rock nonlinear creep model is accurate.

The step S1 includes repeating the indoor rock uniaxial compression test three times, and the average uniaxial compression strength of the rock in this embodiment is calculated to be 20MPa.

In this embodiment, the rock samples used in the indoor rock uniaxial compression test and the indoor rock creep test in steps S1 and S2 are the indoor rock mechanics test regulations specified by the International Society of Rock Mechanics (ISRM) for indoor rock mechanics test regulations. sample standard, the rock sample size is

设置8级蠕变荷载，包括6MPa、8MPa、10MPa、12MPa、14MPa、16MPa、18MPa和20MPa。In the step S2, the step-by-step loading method includes adding a preset stress increment to each stage; in this embodiment, the preset stress increment includes:

Set 8 creep loads, including 6MPa, 8MPa, 10MPa, 12MPa, 14MPa, 16MPa, 18MPa and 20MPa.

In the step S3, the total rock strain-time curve obtained by the rock creep test includes: the curve in the form of instantaneous creep and deceleration creep in the low stress state, the low stress state is a horizontal straight line; the instantaneous creep in the medium stress state is a horizontal line; The curves of creep, deceleration creep and stable creep, the medium stress state is a straight line with a slope; the curves of instantaneous creep, deceleration creep, stable creep and accelerated creep in the high stress state, the high stress state is a curve Non-linear curve, the present invention can accurately establish the model of high stress state.

The step S4 includes, according to the graded strain-time curves of the rock under different stress levels, specifically divided into curves in the form of instantaneous creep and deceleration creep in a low stress state; instantaneous creep and deceleration creep in a medium stress state. and stable creep curves; transient creep, decelerated creep, stable creep and accelerated creep curves for high stress states.

The described step S5 includes the following steps:

A1. According to the strain-time creep curve obtained by the rock creep test, identify the rheological element type of the creep model;

A2. Build a model according to the graded strain-time curves under different stress levels. The model should include the following rheological elements: Hooke body is a spring element with instantaneous strain characteristics; Newton body is a viscous element with elastic after-effect properties; The switching element and the plastic element are creep model elements with a stress threshold; nonlinear viscous elements with nonlinear characteristics.

In the step A2, the rheological elements include basic rheological elements, and the basic rheological elements used to describe the characteristics of rock creep deformation include:

B1. The transient deformation characteristics of creep deformation can be described by Hooke body. The constitutive equation of Hooke body is:

σ'=E'ε'

Among them, σ' represents the stress of the low-stress state model; E' represents the elastic modulus of the low-stress state model; ε' represents the corresponding strain when the stress applied to the low-stress state model is σ'.

B2. The elastic after-effect characteristics of creep deformation can be described by Newton body. The creep equation of Newton body is:

Among them, σ” represents the stress of the medium-stress state model; η” represents the viscosity coefficient of the medium-stress state model; ε” represents the corresponding strain rate when the stress applied to the medium-stress state model is σ”.

B3. If the switching element (with switching viscous body), the plastic element (non-linear viscoplastic body) and the general model (generalized Kelvin body) are connected in series; the stress threshold value σ _K of the switching element is set, and the switching element has the stress threshold effect, The stress threshold effect is: when the stress σ of the switching element is less than the stress threshold σ _K of the switching element, the switching element is turned off, and all the elements connected in parallel with the switching element do not work; when the stress σ of the switching element is greater than the switching stress threshold value When σ _K , the switching element is turned on, and all the elements connected in parallel with the switching element may play a role; the switching element is only used for control, only has the stress threshold effect, and does not share the stress.

B4. The strain of the plastic element is expressed as: when the stress on the plastic element is less than the yield limit σ _s of the plastic element, the strain is 0; when the stress on the plastic element is greater than the yield limit σ _s of the plastic element, the strain is not 0.

In the step S6, the nonlinear relationship between the creep rate in the rock accelerated creep stage and the corresponding creep time history includes:

The traditional creep elements are all linear, and it is unreasonable to use the traditional creep elements to describe the nonlinear characteristics of rocks. In order to consider the nonlinear characteristics of rock creep, the traditional linear creep element needs to be improved. Considering that the generalized Kelvin model and Burgers model can describe the characteristics of the transient creep, deceleration creep and stable creep stages of rock well. In order to further describe the nonlinear characteristics of the accelerated creep stage of rock, the relationship between the creep rate and the duration of the accelerated creep stage can be determined by fitting the creep rate of the accelerated creep stage and the duration of the accelerated creep stage of the creep test. .

R²＝0.9943

R ² =0.9943

表示加速蠕变阶段的蠕变速率；A、B和m表示拟合系数；t表示加速蠕变阶段蠕变经历的时间；R表示拟合系数，越接近1，表示拟合结果与试验结果越接近。in,

Represents the creep rate in the accelerated creep stage; A, B and m represent the fitting coefficient; t represents the creep time in the accelerated creep stage; R represents the fitting coefficient, and the closer it is to 1, the closer the fitting result is to the test result. near.

The step S7 includes the initial creep model constructed in step S5 and the nonlinear relationship between the creep rate in the accelerated creep stage of the rock determined by fitting in step S6 and the corresponding creep time history, combined with the series connection of creep elements. When the stress of all elements is equal to the applied stress, the strain is the rule of the sum of all series elements, and the constitutive model and creep model of the rock nonlinear creep model under low stress state, medium stress state and high stress state are deduced respectively. ,Specifically:

C1. When the applied stress σ < σ _K < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; the obtained constitutive equation of the creep model is:

表示应力σ对时间的一阶导数。Among them, ε ₀₁ =ε ₀ +ε ₁ η ₁ , ε ₀ is the instantaneous creep, ε ₁ is the creep in the deceleration creep stage, η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; E ₀ is the generalized Kelvin body The elastic coefficient of the series Hooke body in the body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time.

C2. When the applied pressure σ _K <σ < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; the obtained constitutive equation of the creep model is:

表示ε₀₁₂对时间的一阶导数；

表示ε₀₁₂对时间的二阶导数；ε₀为瞬时蠕变，ε₁为减速蠕变阶段的蠕变，ε₂为稳定蠕变阶段的蠕变；η₁为广义Kelvin体中Newton体的黏滞系数；η₂表示带开关黏性体中Newton体的黏滞系数；E₀表示广义Kelvin体中串联Hooke体的弹性系数；E₁表示广义Kelvin体中并联Hooke体的弹性系数；

表示应力σ对时间的一阶导数；

表示应力σ对时间的二阶导数；where ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ ,

represents the first derivative of ε ₀₁₂ with respect to time;

represents the second derivative of ε ₀₁₂ with respect to time; ε ₀ is the instantaneous creep, ε ₁ is the creep in the deceleration creep stage, ε ₂ is the creep in the stable creep stage; η ₁ is the viscosity of the Newton body in the generalized Kelvin body hysteresis coefficient; η ₂ represents the viscous coefficient of the Newton body in the viscous body with switch; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time;

C3. When the applied stress σ>σ _s , the creep model provided by the present invention is the series connection of the Burgers model and the ideal viscoplastic body, and the constitutive equation of the rock nonlinear creep model can be obtained through the present Burgers model. The constitutive equation and the constitutive equation of the nonlinear viscoplastic body are derived:

Since the Burgers model is in series with an ideal viscoplastic body:

表示ε对时间的一阶导数；

表示ε₀₁₂对时间的一阶导数；

表示ε₃对时间的一阶导数。Among them, σ represents the applied stress; σ _B represents the stress of the Burgers model; σ _N represents the stress of the ideal viscoplastic body; ε represents the total strain generated by the model; ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ ,ε ₁ is the creep in the deceleration creep stage, ε ₂ is the creep in the stable creep stage, and ε ₃ is the creep in the accelerated creep stage;

represents the first derivative of ε with respect to time;

represents the first derivative of ε ₀₁₂ with respect to time;

represents the first derivative _of ε3 with respect to time.

Combining steps C1-C2, the constitutive equation is obtained:

表示应力σ对时间的一阶导数；

表示应力σ对时间的二阶导数；E₀表示广义Kelvin体中串联Hooke体的弹性系数；E₁表示广义Kelvin体中并联Hooke体的弹性系数；η₁为广义Kelvin体中Newton体的黏滞系数；η₂表示带开关黏性体中Newton体的黏滞系数；η₃(t)表示非线性黏塑性体中非线性黏性体的黏滞系数；

表示ε对时间的一阶导数；

表示ε对时间的二阶导数。where σ represents the applied stress;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body; η ₁ is the viscosity of the Newton body in the generalized Kelvin body coefficient; η ₂ represents the viscosity coefficient of the Newton body in the viscous body with switch; η ₃ (t) represents the viscosity coefficient of the nonlinear viscous body in the nonlinear viscoplastic body;

represents the first derivative of ε with respect to time;

represents the second derivative of ε with respect to time.

Finally got:

表示ε₀₁₂对时间的一阶导数；

表示ε₀₁₂对时间的二阶导数；

表示ε对时间的一阶导数；

表示ε对时间的二阶导数；η₂表示带开关黏性体中Newton体的黏滞系数；η₃(t)表示非线性黏塑性体中非线性黏性体的黏滞系数；E₀表示广义Kelvin体中串联Hooke体的弹性系数；E₁表示广义Kelvin体中并联Hooke体的弹性系数；

表示应力σ对时间的一阶导数；

表示应力σ对时间的二阶导数。Among them, σ represents the applied stress; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; ε ₀₁ =ε ₀ +ε ₁ η ₁ , ε ₀ is the instantaneous creep, and ε ₁ is the deceleration creep creep in the variable stage, η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ , ε ₂ is the creep in the stable creep stage;

represents the first derivative of ε ₀₁₂ with respect to time;

represents the second derivative of ε ₀₁₂ with respect to time;

represents the first derivative of ε with respect to time;

represents the second derivative of ε with respect to time; η ₂ represents the viscosity coefficient of the Newton body in the viscous body with switch; η ₃ (t) represents the viscosity coefficient of the nonlinear viscous body in the nonlinear viscoplastic body; E ₀ represents The elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time.

C4. Solve the creep equation of the rock nonlinear creep model:

Suppose the stress applied at the initial moment, namely t=0, is σ ₀ ; when σ ₀ <σ _K <σ _s , the creep deformation is the sum of the deformation of the Hookean body and the deformation of the Kelvin body; when σ _K <σ ₀ When <σ _s , the creep deformation is the creep deformation of the Burgers model; when σ ₀ ≥σ _s , the creep deformation is the sum of the creep deformation of the Burgers model and the ideal viscoplastic body; The creep equation for an ideal viscoplastic body is:

Among them, ε is the total strain generated by the model; t is the creep time in the accelerated creep stage; σ ₀ is the stress applied at the initial moment; σ _s is the yield limit of the plastic element; η ₃ (t) is the nonlinear viscosity The viscosity coefficient of the nonlinear viscous body in the plastic body;

Combining the creep equation of the ideal viscoplastic body with the nonlinear relationship between the creep rate and the corresponding creep time history in the accelerated creep stage of the rock proposed in step S6, we can obtain:

Among them, A, B, and m represent the fitting coefficients; t represents the creep time in the accelerated creep stage; σ ₀ is the stress applied at the initial moment; σ _s is the yield limit of the plastic element; η ₃ (t) represents the non- Viscosity coefficient of nonlinear viscous bodies in linear viscoplastic bodies;

Finally, the creep equation of the rock nonlinear creep model is obtained:

Among them, ε is the total strain generated by the model; t is the creep time in the accelerated creep stage; σ ₀ is the stress applied at the initial moment; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element ; η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; η ₂ is the viscosity coefficient of the Newton body in the viscous body with switch; η ₃ (t) is the viscosity of the nonlinear viscous body in the nonlinear viscoplastic body Hysteresis coefficient; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body.

In the specific implementation process of this method, the following steps are included:

Step 1. Carry out indoor rock uniaxial compression test;

的圆柱体岩样进行3次单轴压缩试验，3次单轴压缩试验结果表明中风化泥质砂岩的平均单轴压缩强度值为20MPa左右。Taking a river crossing tunnel project as the background, the surrounding rock of the river crossing tunnel is moderately weathered argillaceous sandstone. Obtain rock samples from the field for uniaxial compression and creep testing. for 3 sizes

The cylindrical rock samples were subjected to three uniaxial compression tests, and the results of the three uniaxial compression tests showed that the average uniaxial compressive strength of the moderately weathered argillaceous sandstone was about 20MPa.

Step 2. Carry out the indoor rock graded loading creep test;

的圆柱体岩样开展分级加载蠕变试验。根据步骤一中得到的中风化泥质砂岩的平均单轴压缩强度，将蠕变试验应力水平设置为8级加载水平，初始加载应力水平设为6MPa，每级加载的应力增量

为2MPa。Using the hierarchical loading method, the sample size of the same project is

The cylindrical rock samples were subjected to graded loading creep tests. According to the average uniaxial compressive strength of the moderately weathered argillaceous sandstone obtained in step 1, the creep test stress level is set to 8 loading levels, the initial loading stress level is set to 6 MPa, and the stress increment of each loading stage is set

is 2MPa.

Step 3. Creep test result processing:

First, the whole-course strain-time curve of the weathered argillaceous sandstone is drawn directly from the results of the uniaxial compression creep test, as shown in FIG. The overall strain-time curve of the moderately weathered argillaceous sandstone obtained by the graded loading creep test is processed by the superposition method, and the obtained graded strain-time curve, as shown in FIG. 3, is the superimposed strain-time curve of the creep test according to the embodiment of the present invention. Schematic.

Step 4. Classify the rock creep curve;

As shown in Fig. 3, when the axial stress is applied, the rock sample is deformed instantaneously, and then the strain-time curve begins to deflect toward the time axis. When the axial stress levels are 6MPa, 8MPa, 10MPa, and 12MPa, the creep-time curves are highly consistent, including instantaneous creep and deceleration creep stages. With the extension of the stress action time, the creep rate eventually tends to 0, which is classified as a low stress level creep curve; when the axial stress level is 14MPa and 16MPa, the creep-time curves are similar in shape, including transient creep, deceleration creep and stable creep stages. Compared with the low stress level creep curve, there are more stable creep stages. With the extension of the stress action time, the creep rate finally tends to a certain constant, which is classified as the medium stress level creep curve; when the axial stress level continues The creep-time curves when increased to 18MPa and 20MPa are very similar, there are more stable creep stages and accelerated creep stages than the low stress level creep curve, and more accelerated creep stages than the medium stress level creep curve, With the prolongation of the stress action time, the creep rate eventually tends to infinity, and the specimen finally creeps to failure, which is classified as a high stress level creep curve.

Step 5: Identify the creep model, and construct the initial creep model;

The model is established according to the graded strain-time curves under different stress levels, including: Hooke body is a spring element with instantaneous strain characteristics; Newton body is a viscous element with elastic aftereffect properties; Switch elements and plastic elements with stress thresholds ; a nonlinear viscous element with nonlinear properties. FIG. 3 is a rock nonlinear creep model according to an embodiment of the present invention. The rock nonlinear creep model provided in this embodiment is a generalized Kelvin model connected in series to switch viscous bodies and then connect nonlinear viscoplastic bodies in series. Figure 4 is a schematic diagram of the nonlinear creep model of the embodiment of the present invention:

1) The instantaneous deformation characteristics of creep deformation can be described by the Hooke body. The constitutive equation of the Hooke body is:

σ'=E'ε'

Among them, σ' represents the stress of the low-stress state model; E' represents the elastic modulus of the low-stress state model; ε' represents the corresponding strain when the stress applied to the low-stress state model is σ'.

2) The elastic after-effect characteristics of creep deformation can be described by Newton body. The creep equation of Newton body is:

Among them, σ” represents the stress of the medium-stress state model; η” represents the viscosity coefficient of the medium-stress state model; ε” represents the corresponding strain rate when the stress applied to the medium-stress state model is σ”.

3) The stress threshold value of the switching element is σ _K , and σ _K has the stress threshold effect, that is, when the stress σ of the switching element is less than the stress threshold σ _K of the switching element, the switching element is turned off, and all the elements connected in parallel with the switching element are not connected. When the stress σ of the switching element is greater than the stress threshold σ _K of the switching element, the switching element is turned on, and all the elements connected in parallel with the switching element may function. The switching element only plays a control role, only has the stress threshold effect, and does not share the stress.

4) The strain of the plastic element is expressed as: when the stress on the plastic element is less than the yield limit σ _s of the plastic element, the strain is 0; when the stress on the plastic element is greater than the yield limit σ _s of the plastic element, the strain is not 0.

Step 6: Fitting the nonlinear relationship between the creep rate and the corresponding creep time history in the accelerated creep stage of the rock;

The traditional creep elements are all linear, and it is unreasonable to use the traditional creep elements to describe the nonlinear characteristics of rocks. In order to consider the nonlinear characteristics of rock creep, the traditional linear creep element needs to be improved. Considering that the generalized Kelvin model and Burgers model can describe the characteristics of the transient creep, deceleration creep and stable creep stages of rock well. In order to further describe the nonlinear characteristics of the accelerated creep stage of the rock, the creep rate of the accelerated creep stage of the creep test in step 2 and the duration of the accelerated creep stage are fitted to determine the creep rate of the accelerated creep stage and the duration of the accelerated creep stage. The relationship over time, as shown in FIG. 5, is a schematic diagram of the accelerated creep rate-duration test data fitting in the accelerated creep stage according to the embodiment of the present invention, and the fitting relationship is as follows:

R²＝0.9943

R ² =0.9943

表示加速蠕变阶段的蠕变速率；A、B和m表示拟合系数；t表示加速蠕变阶段蠕变经历的时间；R表示拟合系数，越接近1，表示拟合结果与试验结果越接近。in,

Represents the creep rate in the accelerated creep stage; A, B and m represent the fitting coefficient; t represents the creep time in the accelerated creep stage; R represents the fitting coefficient, and the closer it is to 1, the closer the fitting result is to the test result. near.

Step 7. Derive the constitutive equation and creep equation of the rock nonlinear creep model;

According to the initial creep model constructed in step 5 and the nonlinear relationship between the creep rate and the corresponding creep time history in the accelerated creep stage of the rock determined by fitting in step 6, when the creep elements are connected in series, the The stress is equal to the applied stress, and the strain is the rule of the sum of all series elements, and the constitutive model and creep model of the nonlinear creep model of rock under low stress state, medium stress state and high stress state are deduced respectively.

(1) When the applied stress σ < σ _K < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; the obtained constitutive equation of the creep model is:

表示应力σ对时间的一阶导数。Among them, ε ₀₁ =ε ₀ +ε ₁ η ₁ , ε ₀ is the instantaneous creep, ε ₁ is the creep in the deceleration creep stage, η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; E ₀ is the generalized Kelvin body The elastic coefficient of the series Hooke body in the body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time.

(2) When the applied pressure σ _K <σ < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; the obtained constitutive equation of the creep model is:

表示ε₀₁₂对时间的一阶导数；

表示ε₀₁₂对时间的二阶导数；ε₀为瞬时蠕变，ε₁为减速蠕变阶段的蠕变，ε₂为稳定蠕变阶段的蠕变；η₁为广义Kelvin体中Newton体的黏滞系数；η₂表示带开关黏性体中Newton体的黏滞系数；E₀表示广义Kelvin体中串联Hooke体的弹性系数；E₁表示广义Kelvin体中并联Hooke体的弹性系数；

表示应力σ对时间的一阶导数；

表示应力σ对时间的二阶导数。where ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ ,

represents the first derivative of ε ₀₁₂ with respect to time;

represents the second derivative of ε ₀₁₂ with respect to time; ε ₀ is the instantaneous creep, ε ₁ is the creep in the deceleration creep stage, ε ₂ is the creep in the stable creep stage; η ₁ is the viscosity of the Newton body in the generalized Kelvin body hysteresis coefficient; η ₂ represents the viscous coefficient of the Newton body in the viscous body with switch; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time.

(3) When the applied stress σ>σ _s , the creep model provided by the present invention is the series connection of the Burgers model and the ideal viscoplastic body, and the constitutive equation of the rock nonlinear creep model can be obtained by the Burgers model The constitutive equation of and the constitutive equation of nonlinear viscoplastic body are derived:

Since the Burgers model is in series with an ideal viscoplastic body:

表示ε对时间的一阶导数；

表示ε₀₁₂对时间的一阶导数；

表示ε₃对时间的一阶导数。Among them, σ represents the applied stress; σ _B represents the stress of the Burgers model; σ _N represents the stress of the ideal viscoplastic body; ε represents the total strain generated by the model; ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ ,ε ₁ is the creep in the deceleration creep stage, ε ₂ is the creep in the stable creep stage, and ε ₃ is the creep in the accelerated creep stage;

represents the first derivative of ε with respect to time;

represents the first derivative of ε ₀₁₂ with respect to time;

represents the first derivative _of ε3 with respect to time.

Combining steps (1)-(2), the constitutive equation is obtained:

表示应力σ对时间的一阶导数；

表示应力σ对时间的二阶导数；E₀表示广义Kelvin体中串联Hooke体的弹性系数；E₁表示广义Kelvin体中并联Hooke体的弹性系数；η₁为广义Kelvin体中Newton体的黏滞系数；η₂表示带开关黏性体中Newton体的黏滞系数；η₃(t)表示非线性黏塑性体中非线性黏性体的黏滞系数；

表示ε对时间的一阶导数；

表示ε对时间的二阶导数。where σ represents the applied stress;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body; η ₁ is the viscosity of the Newton body in the generalized Kelvin body coefficient; η ₂ represents the viscosity coefficient of the Newton body in the viscous body with switch; η ₃ (t) represents the viscosity coefficient of the nonlinear viscous body in the nonlinear viscoplastic body;

represents the first derivative of ε with respect to time;

represents the second derivative of ε with respect to time.

Finally got:

表示ε₀₁₂对时间的一阶导数；

表示ε₀₁₂对时间的二阶导数；

表示ε对时间的一阶导数；

表示ε对时间的二阶导数；η₂表示带开关黏性体中Newton体的黏滞系数；η₃(t)表示非线性黏塑性体中非线性黏性体的黏滞系数；E₀表示广义Kelvin体中串联Hooke体的弹性系数；E₁表示广义Kelvin体中并联Hooke体的弹性系数；

表示应力σ对时间的一阶导数；

表示应力σ对时间的二阶导数。Among them, σ represents the applied stress; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; ε ₀₁ =ε ₀ +ε ₁ η ₁ , ε ₀ is the instantaneous creep, and ε ₁ is the deceleration creep creep in the variable stage, η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ , ε ₂ is the creep in the stable creep stage;

represents the first derivative of ε ₀₁₂ with respect to time;

represents the second derivative of ε ₀₁₂ with respect to time;

represents the first derivative of ε with respect to time;

represents the second derivative of ε with respect to time; η ₂ represents the viscosity coefficient of the Newton body in the viscous body with switching; η ₃ (t) represents the viscosity coefficient of the nonlinear viscous body in the nonlinear viscoplastic body; E ₀ represents The elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time.

(4) Solve the creep equation of the rock nonlinear creep model:

Suppose the stress applied at the initial moment, namely t=0, is σ ₀ ; when σ ₀ <σ _K <σ _s , the creep deformation is the sum of the deformation of the Hookean body and the deformation of the Kelvin body; when σ _K <σ ₀ When <σ _s , the creep deformation is the creep deformation of the Burgers model; when σ ₀ ≥σ _s , the creep deformation is the sum of the creep deformation of the Burgers model and the ideal viscoplastic body; The creep equation for an ideal viscoplastic body is:

Among them, ε is the generated strain; t is the creep time in the accelerated creep stage; σ ₀ is the stress applied at the initial moment; σ _s is the yield limit of the plastic element; η ₃ (t) is the nonlinear viscoplastic body The viscosity coefficient of the medium nonlinear viscous body;

Combining the creep equation of the ideal viscoplastic body with the nonlinear relationship between the creep rate and the corresponding creep time history in the accelerated creep stage of the rock proposed in step 6, we can obtain:

Among them, A, B, and m represent the fitting coefficients; t represents the creep time in the accelerated creep stage; σ ₀ is the stress applied at the initial moment; σ _s is the yield limit of the plastic element; η ₃ (t) represents the non- Viscosity coefficient of nonlinear viscous bodies in linear viscoplastic bodies;

Obtain the creep equation for the final rock nonlinear creep model:

Among them, ε represents the generated strain; t represents the creep time in the accelerated creep stage; σ ₀ is the stress applied at the initial moment; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; η ₂ is the viscosity coefficient of the Newton body in the viscous body with switch; η ₃ (t) is the viscosity coefficient of the nonlinear viscous body in the nonlinear viscoplastic body ; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body.

Step 8, parameter inversion and model verification;

Using numerical calculation and analysis software with a custom function fitting function, the creep equation of the final rock nonlinear creep model provided by the present invention,

Compile into the software self-defined function module, fit the creep test data obtained in step 2, and invert the parameters in the rock nonlinear creep model provided by the present invention, E ₀ , E ₁ , η ₁ , η ₂ , A, B and m, the creep parameters of the rock nonlinear creep model provided by the present invention under different stress levels obtained through inversion calculation are shown in Table 1.

Table 1 Parameters of rock nonlinear creep model

As shown in Table 1, using the rock nonlinear creep model provided by the present invention to fit the weathered argillaceous sandstone creep test data, the fitting confidence levels under 8 stress levels are all above 0.95, and the fitting effect is very good , especially for the rock creep test results under high stress state, the fitting confidence is above 0.99, indicating that the rock nonlinear creep model provided by the present invention can well describe the rock creep characteristics of different stress levels at the same time. Finally, compare the creep test results of the moderately weathered argillaceous sandstone in step 2 with the fitting results of the rock nonlinear creep model provided by the present invention, as shown in FIG. Schematic diagram of the comparison of fitting results of rock nonlinear creep model. The stress in Fig. 6a is 6MPa, the stress in Fig. 6b is 8MPa, the stress in Fig. 6c is 10MPa, the stress in Fig. 6d is 12MPa, the stress in Fig. 6e is 14MPa, the stress in Fig. 6f is 16MPa, the stress in Fig. 6g is 18MPa, the stress in Fig. The stress of 6h is 20MPa. Figure 5 shows that the fitting results can better predict the trend of test results under different stress levels.

Claims (10)

1. a rock nonlinear creep model establishment method is characterized in that comprising the steps: S1. Carry out a rock uniaxial compression test to obtain the average compressive strength of the rock; S2. According to the average compressive strength of the rock, the rock creep test is carried out by using a graded loading method; S3. Draw the total strain-time curve of the rock obtained by the rock creep test and the graded strain-time curve of the rock under different stress levels; S4. Classify the graded strain-time curves of rocks under different stress levels; S5. Identify the types of rheological elements of the creep model according to the graded strain-time curves of the rock under different stress levels, and construct an initial creep model; S6. Fit the nonlinear relationship between the creep rate and the corresponding creep time history in the accelerated creep stage of the rock; S7. Using the identified creep model and the fitted nonlinear relationship between the creep rate in the accelerated creep stage of the rock and the corresponding creep time history, the constitutive equation and the creep equation of the rock nonlinear creep model are obtained. 2 . The method for establishing a nonlinear creep model of rock according to claim 1 , wherein the step S1 includes repeating several indoor rock uniaxial compression tests to calculate the average uniaxial compressive strength of the rock. 3 . 3 . The method for establishing a rock nonlinear creep model according to claim 1 , wherein in the step S2 , the step-by-step loading method includes adding a preset stress increment for each stage. 4 . 4. The method for establishing a nonlinear creep model of rock according to claim 3, wherein in the step S3, the full strain-time curve of the rock obtained by the rock creep test comprises: instantaneous creep and deceleration in a low stress state The creep form curve, the low stress state creep curve eventually tends to a horizontal straight line with a slope of 0; the curve of the instantaneous creep, deceleration creep and stable creep in the medium stress state, the medium stress state creep curve eventually tends to A straight line with a fixed slope; curves of instantaneous creep, deceleration creep, steady creep and accelerated creep for high stress states, and a nonlinear curve for high stress states; The step S4 includes: according to the graded strain-time curves of the rock under different stress levels, it is specifically divided into curves in the form of instantaneous creep and deceleration creep in a low stress state; instantaneous creep and deceleration creep in a medium stress state. and stable creep curves; transient creep, decelerated creep, stable creep and accelerated creep curves for high stress states. 5. The method for establishing a rock nonlinear creep model according to one of claims 1-4, wherein the step S5 comprises the following steps: A1. Divide the creep model into several components, and identify the component types of the creep model; A2. Establish the constitutive equation or creep equation of the element according to the graded strain-time curves under different stress levels, including: Hooke body is a spring element with instantaneous strain characteristics; Newton body is a viscous element with elastic after-effect properties ; switching elements and plastic elements with stress thresholds; nonlinear viscous elements with nonlinear properties. 6. The method for establishing a nonlinear creep model of rock according to claim 5, wherein in the step A2, the rheological element comprises a basic rheological element, and the basic rheological element comprises: B1. The instantaneous deformation characteristics of creep deformation are described by the Hooke body. The constitutive equation of the Hooke body is: σ'=E'ε' Among them, σ' represents the stress of the low-stress state model; E' represents the elastic modulus of the low-stress state model; ε' represents the corresponding strain when the stress applied to the low-stress state model is σ'; B2. The elastic after-effect characteristics of creep deformation are described by the Newton body. The creep equation of the Newton body is:

Among them, σ” represents the stress of the medium-stress state model; η” represents the viscosity coefficient of the medium-stress state model; ε” represents the corresponding strain rate when the stress applied to the medium-stress state model is σ”; B3. Set the stress threshold σ _K of the switching element. When the stress σ of the switching element is less than the stress threshold σ _K of the switching element, the switching element is turned off, and all elements connected in parallel with the switching element do not function; when the switching element is subjected to When the stress σ is greater than the switching stress threshold σ _K , the switching element is turned on, and several elements connected in parallel with the switching element play a role; B4. The strain of the plastic element is expressed as: when the stress on the plastic element is less than the yield limit σ _s of the plastic element, the strain is 0; when the stress on the plastic element is greater than the yield limit σ _s of the plastic element, the strain is not 0. 7. The method for establishing a nonlinear creep model of rock according to claim 5, characterized in that in step S7, the initial creep model constructed in step S5 and the rock accelerated creep stage creep determined by fitting in step S6 The nonlinear relationship between the rate and the corresponding creep time history, combined with the creep elements in series, the stress of all elements is equal to the applied stress, the strain is the rule of the sum of all series elements, and the low stress state and medium stress state are established respectively. Constitutive and Creep Models for Nonlinear Creep Models of Rocks in State and High Stress State. 8. The method for establishing a rock nonlinear creep model according to claim 7, wherein the step S7 comprises the following steps: C1. When the applied stress σ < σ _K < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; calculate the constitutive equation of the creep model; C2. When the applied pressure σ _K <σ < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; calculate the constitutive equation of the creep model; C3. When the applied stress σ>σ _s , the constitutive equation of the rock nonlinear creep model is calculated by the constitutive equation of the Burgers model and the constitutive equation of the nonlinear viscoplastic body; C4. Solve the creep equation of the rock nonlinear creep model. 9. The method for establishing a rock nonlinear creep model according to claim 8, wherein the step C4 comprises: setting the stress applied at the initial moment as σ ₀ ; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; when σ ₀ <σ _K <σ _s , the creep deformation is the sum of the deformation of the Hookean body and the deformation of the Kelvin body; when σ _K <σ ₀ <σ _s , the creep deformation is Creep deformation of the Burgers model; when σ ₀ ≥ σ _s , the creep deformation is the sum of the creep deformation of the Burgers model and that of an ideal viscoplastic body. 10. The method for establishing a nonlinear creep model of rock according to claim 9, characterized in that when the generalized Kelvin body, the switching element and the plastic element are connected in series in sequence; the step C1 includes when the applied stress σ<σ When _K < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; the obtained constitutive equation of the creep model is:

Among them, ε ₀₁ =ε ₀ +ε ₁ η ₁ , ε ₀ is the instantaneous creep, ε ₁ is the creep in the deceleration creep stage, η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; E ₀ is the generalized Kelvin body The elastic coefficient of the series Hooke body in the body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time; The step C2 includes that when the applied pressure σ _K <σ < σ _s , σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; the obtained constitutive equation of the creep model is:

where ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ ,

represents the first derivative of ε ₀₁₂ with respect to time;

represents the second derivative of ε ₀₁₂ with respect to time; ε ₀ is the instantaneous creep, ε ₁ is the creep in the deceleration creep stage, ε ₂ is the creep in the stable creep stage; η ₁ is the viscosity of the Newton body in the generalized Kelvin body hysteresis coefficient; η ₂ represents the viscous coefficient of the Newton body in the viscous body with switch; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time; Described step C3, including the constitutive equation of rock nonlinear creep model is:

Among them, σ represents the applied stress; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element; ε ₀₁ =ε ₀ +ε ₁ η ₁ , ε ₀ is the instantaneous creep, and ε ₁ is the deceleration creep creep in the variable stage, η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; ε ₀₁₂ =ε ₀ +ε ₁ +ε ₂ , ε ₂ is the creep in the stable creep stage;

represents the first derivative of ε ₀₁₂ with respect to time;

represents the second derivative of ε ₀₁₂ with respect to time;

represents the first derivative of ε with respect to time;

represents the second derivative of ε with respect to time; η ₂ represents the viscosity coefficient of the Newton body in the viscous body with switching; η ₃ (t) represents the viscosity coefficient of the nonlinear viscous body in the nonlinear viscoplastic body; E ₀ represents The elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body;

represents the first derivative of stress σ with respect to time;

represents the second derivative of stress σ with respect to time; In the step C4, the creep equation of the rock nonlinear creep model includes:

Among them, ε is the total strain generated by the model; t is the creep time in the accelerated creep stage; σ ₀ is the stress applied at the initial moment; σ _K is the stress threshold value of the switching element; σ _s is the yield limit of the plastic element ; η ₁ is the viscosity coefficient of the Newton body in the generalized Kelvin body; η ₂ is the viscosity coefficient of the Newton body in the viscous body with switch; η ₃ (t) is the viscosity of the nonlinear viscous body in the nonlinear viscoplastic body Hysteresis coefficient; E ₀ represents the elastic coefficient of the series Hooke body in the generalized Kelvin body; E ₁ represents the elastic coefficient of the parallel Hooke body in the generalized Kelvin body.

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