CN113919148A - Rock nonlinear creep model building method - Google Patents

Rock nonlinear creep model building method Download PDF

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CN113919148A
CN113919148A CN202111150288.7A CN202111150288A CN113919148A CN 113919148 A CN113919148 A CN 113919148A CN 202111150288 A CN202111150288 A CN 202111150288A CN 113919148 A CN113919148 A CN 113919148A
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creep
stress
rock
model
nonlinear
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CN113919148B (en
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刘智振
曹平
刘京铄
孟刚
樊至
黄超
周超
雍伟勋
邓慧娟
赵庆雄
肖峰
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Central South University
Sinohydro Bureau 8 Co Ltd
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Sinohydro Bureau 8 Co Ltd
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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

Rock nonlinear creep model building method
Technical Field
The invention belongs to the field of rock rheological modeling, and particularly relates to a rock nonlinear creep model building method.
Background
The biggest difference between the underwater tunnel and the conventional underground tunnel is that the surrounding rock of the underwater tunnel is in a high-water environment, the self weight of water acts on the surrounding rock of the tunnel as additional stress, and meanwhile, the mechanical property of the rock can be obviously degraded by the water. The service life of the tunnel is generally decades, and as the service time is prolonged, the tunnel surrounding rock can deform or even damage in relation to time under the action of a certain load. Therefore, it is particularly important to construct a proper mechanical model to predict the relationship between the tunnel surrounding rock and the service time under the action of the stable load, namely rock rheology. Rock rheology refers to the property of rock deformation to increase over time under constant load. The rheological analysis is carried out on the rock, the rheological constitutive property of the rock can be comprehensively reflected, the dependency relationship between the stress and the strain of the rock and the time under the action of constant load can be obtained, theoretical support is provided for predicting the long-term stability of rock engineering, the rheological mechanical property of the rock in different stress states can be revealed, the scientific time-varying relationship between the stress and the strain and the time history is further established, and a theoretical basis is provided for scientifically and reasonably evaluating the stability of the rock engineering.
The most basic rheological constitutive model commonly used at present is formed by combining basic rheological element elements in a series connection mode, a parallel connection mode and a series-parallel connection mode. The three basic rheological elements comprise an elastic element (H), a plastic element (Y) and a viscous element (N), and the basic rheological model formed by the three basic elements comprises a Saint-Venum body (H-Y), a Maxwell body (H-N), a Kelvin body (H | N), a generalized Kelvin body, a Boetn-Thomson body, an ideal viscoplastic body (N | Y), a Burgers body, a Western body, a Bingham body and the like. At present, the main method for establishing a rock rheological constitutive model comprises the following steps: (1) directly fitting a rock rheological test curve by an empirical equation method through a rheological test of the rock or the rock mass; (2) according to the rheological test result, establishing a rock rheological constitutive model by adopting series-parallel combination of model elements, and then determining undetermined rheological element model parameters by methods such as identification and parameter inversion of the element model; (3) a rock rheological constitutive model is established by adopting a nonlinear rheological element theory, an internal time theory, fracture mechanics and damage mechanics theory. However, the method cannot consider the deformation characteristics of the rock under different stress levels, and the modeling mode is not accurate.
Disclosure of Invention
The invention aims to provide a rock nonlinear creep model building method which can accurately build a rheological constitutive model.
The invention provides a rock nonlinear creep model establishing method, which comprises the following steps:
s1, carrying out a rock uniaxial compression test to obtain the average compression strength of the rock;
s2, performing a rock creep test in a graded loading mode according to the average compression strength of the rock;
s3, drawing a rock full strain-time curve obtained by a rock creep test and a graded strain-time curve of the rock under different stress levels;
s4, classifying graded strain-time curves of the rock under different stress levels;
s5, identifying the type of the rheological element of the creep model according to the graded strain-time curves of the rock under different stress levels, and constructing an initial creep model;
s6, fitting a nonlinear relation between the creep rate of the rock in the accelerated creep stage and the corresponding creep time history;
and S7, obtaining a constitutive equation and a creep equation of the rock nonlinear creep model by adopting the identified creep model and a nonlinear relation between the fitted creep rate of the rock accelerated creep stage and the corresponding creep time history.
And step S1, repeating the indoor rock uniaxial compression test for a plurality of times, and calculating the average uniaxial compression strength of the rock.
In step S2, the step loading manner includes adding a preset stress increment to each step.
In step S3, the rock full strain-time curve obtained by the rock creep test includes: the creep curve in the low stress state finally tends to a horizontal straight line with the slope of 0; the creep curve in the medium stress state finally tends to a straight line with a fixed slope; the curves of instantaneous creep, deceleration creep, stable creep and acceleration creep in a high stress state, wherein the high stress state is a nonlinear curve;
the step S4 includes that the method specifically includes the following steps of dividing the curves into the forms of instantaneous creep and deceleration creep in a low stress state according to the graded strain-time curves of the rock under different stress levels; curves of instantaneous creep, retarded creep and steady creep for medium stress conditions; transient creep, deceleration creep, steady creep and accelerated creep for high stress conditions.
The step S5 includes the following steps:
A1. dividing the creep model into a plurality of elements, and identifying the element types of the creep model;
A2. establishing a constitutive equation or a creep equation of the element according to the graded strain-time curves under different stress levels, comprising: the Hooke body is a spring element with instantaneous strain characteristics; the Newton body is an adhesive element with elastic after-effect properties; a switching element and a plastic element having a stress threshold; a non-linear adhesive element having a non-linear characteristic.
In the step a2, the rheological element includes a basic rheological element, and the basic rheological element includes:
B1. transient deformation characteristics of creep deformation are described by using a Hooke body, and the constitutive equation of the Hooke body is as follows:
σ'＝E'ε'
where 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 characteristic of creep deformation is described by a Newton body, and the creep equation of the Newton body is as follows:
Figure BDA0003286993130000031
where σ "represents the stress of the medium stress state model; η "represents the viscosity coefficient of the medium stress state model; ε "represents the strain rate corresponding to the stress applied to the intermediate stress state model as σ";
B3. setting a stress threshold value sigma of a switching elementKWhen the stress σ to which the switching element is subjected is smaller than the stress threshold σ of the switching elementKWhen the switch element is closed, all the elements connected in parallel with the switch element do not play a role; when the stress sigma of the switch element is larger than the threshold value sigma of the switch stressKWhen the switch element is turned on, a plurality of elements connected in parallel with the switch element play a role;
B4. the strain of the plastic element is represented by: when the plastic element is subjected to a stress less than the yield limit σ of the plastic elementsWhen, the strain is 0; when the plastic element is subjected to a stress greater than the yield limit sigma of the plastic elementsWhen it is used, the strain is not 0.
And step S7, fitting the non-linear relation between the creep rate of the rock accelerated creep stage and the corresponding creep time history according to the initial creep model established in step S5 and step S6, and establishing a constitutive model and a creep model of the rock non-linear creep model in a low stress state, a medium stress state and a high stress state respectively by combining the rule that when the creep elements are connected in series, the stress of all the elements is equal to the applied stress, and the strain is the sum of all the series elements.
The step S7 includes the following steps:
C1. when stress sigma < sigma is appliedK＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; calculating a creep model constitutive equation;
when the generalized Kelvin body, the switching element and the plastic element are connected in series in sequence; the step C1 includes when the stress σ < σ is appliedK＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; the obtained creep model constitutive equation is as follows:
Figure BDA0003286993130000041
wherein epsilon01＝ε0+ε1η1，ε0For instantaneous creep,. epsilon1For retarding creep in the creep stage, η1Viscosity coefficient of Newton's body in generalized Kelvin body; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA0003286993130000047
represents the first derivative of stress σ with respect to time;
C2. when pressure σ is appliedK＜σ＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; calculating a constitutive equation of the creep model;
said step C2 includes applying a pressure σK＜σ＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; the obtained creep model constitutive equation is as follows:
Figure BDA0003286993130000042
wherein epsilon012＝ε0+ε1+ε2，
Figure BDA0003286993130000043
Represents epsilon012A first derivative with respect to time;
Figure BDA0003286993130000044
represents epsilon012A second derivative with respect to time; epsilon0For instantaneous creep,. epsilon1For retarding creep in the creep phase, e2Creep in the stable creep phase; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA0003286993130000045
represents the first derivative of stress σ with respect to time;
Figure BDA0003286993130000046
represents the second derivative of the stress σ with respect to time;
C3. when stress σ > σ is appliedsBy the structure of the Burger modelCalculating an constitutive equation of the rock nonlinear creep model by using the constitutive equation of the nonlinear viscoplastomer and the equation of the nonlinear viscoplastomer;
step C3, the constitutive equation of the nonlinear creep model of the rock is:
Figure BDA0003286993130000051
where σ represents the applied stress; sigmaKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; epsilon01＝ε0+ε1η1，ε0For instantaneous creep,. epsilon1For retarding creep in the creep stage, η1Viscosity coefficient of Newton's body in generalized Kelvin body; epsilon012＝ε0+ε1+ε2，ε2Creep in the stable creep phase;
Figure BDA0003286993130000052
represents epsilon012A first derivative with respect to time;
Figure BDA0003286993130000053
represents epsilon012A second derivative with respect to time;
Figure BDA0003286993130000054
represents the first derivative of epsilon with respect to time;
Figure BDA0003286993130000055
represents the second derivative of epsilon with respect to time; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA0003286993130000056
represents the first derivative of stress σ with respect to time;
Figure BDA0003286993130000057
represents the second derivative of the stress σ with respect to time;
C4. and solving a creep equation of the rock nonlinear creep model.
Step C4 includes setting the stress applied at the initial moment to be sigma0；σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; when sigma is0＜σK＜σsThe creep deformation is the sum of the deformation of the Hookean body and the deformation of the Kelvin body; when sigma isK＜σ0＜σsWhen the creep deformation is the creep deformation of the Burger model; when sigma is0≥σsThe creep deformation is the sum of the creep deformation of the burgers model and the creep deformation of the ideal viscoplastic body.
In step C4, the creep equation of the rock nonlinear creep model includes:
Figure BDA0003286993130000061
where ε represents the total strain produced by the model; t represents the time elapsed during the accelerated creep phase; sigma0Is the stress applied at the initial moment; sigmaKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1And the elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown.
The rock nonlinear creep model building method provided by the invention considers the anisotropy, inhomogeneity and remarkable nonlinear characteristics of the rock. The transient creep and deceleration creep characteristics of the rock in a low stress state, the transient creep, deceleration creep and stable creep characteristics of a medium stress state, the transient creep, deceleration creep, stable creep and acceleration creep characteristics of a high stress state can be well described, the nonlinear characteristics of each creep stage of the rock can be accurately described, and the rock nonlinear creep model provided by the invention has wider applicability.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention.
FIG. 2 is a graphical representation of a creep test global strain-time curve according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of a creep test superimposed strain-time curve according to an embodiment of the present invention.
FIG. 4 is a schematic view of a non-linear creep model according to an embodiment of the present invention.
FIG. 5 is a graph of accelerated creep rate-duration experimental data fit for the accelerated creep phase according to an embodiment of the present invention.
FIG. 6 is a schematic diagram comparing creep test results under different stresses with fitting results of a rock nonlinear creep model according to an embodiment of the present invention.
Detailed Description
FIG. 1 is a schematic flow chart of the method of the present invention: the invention provides a rock nonlinear creep model establishing method, which comprises the following steps:
s1, performing an indoor rock uniaxial compression test to obtain the average compression strength of the rock;
s2, performing an indoor rock creep test in a graded loading mode according to the average compression strength of the rock;
s3, drawing a rock full strain-time curve obtained by an indoor rock creep test and a graded strain-time curve of the rock under different stress levels;
s4, classifying graded strain-time curves of the rock under different stress levels;
s5, identifying the type of the rheological element of the creep model according to the graded strain-time curves of the rock under different stress levels, and constructing an initial creep model;
s6, fitting a nonlinear relation between the creep rate of the rock in the accelerated creep stage and the corresponding creep time history;
and S7, obtaining a constitutive equation and a creep equation of the rock nonlinear creep model by adopting the identified creep model and a nonlinear relation between the fitted creep rate of the rock accelerated creep stage and the corresponding creep time history.
The method further comprises the steps of fitting the graded strain-time curves of the rock under different stress levels by adopting a creep equation of the rock nonlinear creep model, inverting relevant parameters of the creep equation of the rock nonlinear creep model, comparing test results of the rock nonlinear creep model, and judging whether the obtained creep equation of the rock nonlinear creep model is accurate or not.
Step S1 includes repeating the indoor rock uniaxial compression test 3 times, and calculating the average uniaxial compression strength of the rock in this embodiment to be 20 MPa.
In this example, the rock samples used in the uniaxial compression test and creep test of rock in the room at steps S1 and S2 were in accordance with the standard of rock mechanics testing specified by the International Society for Rock Mechanics (ISRM) code for rock mechanics in the room, and the rock samples had the size of
Figure BDA0003286993130000071
In the step S2, the step loading manner includes adding a preset stress increment to each step; in this embodiment the predetermined stress increment comprises
Figure BDA0003286993130000072
Setting 8-level creep load including 6MPa, 8MPa, 10MPa, 12MPa, 14MPa, 16MPa, 18MPa and 20 MPa.
In step S3, the rock full strain-time curve obtained by the rock creep test includes: the instantaneous creep and deceleration creep form curves of the low stress state, wherein the low stress state is a horizontal straight line; the instantaneous creep, the deceleration creep and the stable creep of the medium stress state, wherein the medium stress state is a straight line with a slope; the model of the high stress state can be accurately established by the method disclosed by the invention.
The step S4 includes classifying the curves into the forms of instantaneous creep and deceleration creep according to the graded strain-time curves of the rock under different stress levels; curves of instantaneous creep, retarded creep and steady creep for medium stress conditions; transient creep, deceleration creep, steady creep and accelerated creep for high stress conditions.
The step S5 includes the following steps:
A1. identifying the type of a rheological element of a creep model according to a strain-time creep curve obtained by a rock creep test;
A2. establishing a model according to the graded strain-time curves under different stress levels, wherein the model comprises the following rheological elements: the Hooke body is a spring element with instantaneous strain characteristics; the Newton body is an adhesive element with elastic after-effect properties; the switching element and the plastic element are creep model elements having a stress threshold; a non-linear adhesive element having a non-linear characteristic.
Step a2, the rheological element comprises a basic rheological element, and the basic rheological element for describing the creep deformation characteristics of the rock comprises:
B1. the transient deformation characteristic of creep deformation can be described by a Hooke body, the constitutive equation of which is as follows:
σ'＝E'ε'
where σ' represents the stress of the low stress state model; e' represents the elastic modulus of the low stress state model; ε 'represents the strain corresponding to the stress applied to the low stress state model at σ'.
B2. The elastic aftereffect characteristic of creep deformation can be described by a Newton body, the creep equation of which is:
Figure BDA0003286993130000081
where σ "represents the stress of the medium stress state model; η "represents the viscosity coefficient of the medium stress state model; ε "represents the strain rate corresponding to the stress σ" applied to the medium stress state model.
B3. If the switching element (with switch adhesive), the plastic element (non-linear adhesive plastic) and the general model (generalized Kelvin body) are connected in series; setting a stress threshold value sigma of a switching elementKThe switching element has a stress threshold effect, which is: when the stress sigma to which the switching element is subjected is smaller than the stress threshold sigma of the switching elementKWhen the switch element is closed, all the elements connected in parallel with the switch element do not work; when the stress sigma of the switch element is larger than the threshold value sigma of the switch stressKWhen the switching element is turned on, all elements connected in parallel with the switching element may function; the switching element is only used for control, only has stress threshold effect, and does not distribute stress.
B4. The strain of the plastic element is represented by: when the plastic element is subjected to a stress less than the yield limit σ of the plastic elementsWhen, the strain is 0; when the plastic element is subjected to a stress greater than the yield limit sigma of the plastic elementsWhen it is used, the strain is not 0.
In step S6, the nonlinear relationship between the creep rate of the accelerated creep stage of the rock and the corresponding creep time history includes:
conventional creep elements are all linear and it is not reasonable to describe the non-linear character of the rock with conventional creep elements. In order to take into account the non-linear character of rock creep, improvements to conventional linear creep elements are required. The generalized Kelvin model and the Burgers model are considered to be capable of well describing the transient creep, the deceleration creep and the stable creep stage characteristics of the rock. To further characterize the non-linearity of the accelerated creep phase of the rock, the creep rate of the accelerated creep phase of the creep test is fitted to the accelerated creep phase duration, i.e., the accelerated creep phase creep rate versus duration is determined.
Figure BDA0003286993130000091
R2＝0.9943
Wherein,
Figure BDA0003286993130000092
represents the creep rate in the accelerated creep phase; A. b and m represent fitting coefficients; t represents the time elapsed during the accelerated creep phase; r represents the fitting coefficient, and the closer to 1, the closer the fitting result is to the test result.
The step S7 includes fitting the initial creep model constructed in step S5 and the step S6 to determine a nonlinear relationship between the creep rate at the accelerated creep stage of the rock and the corresponding creep time history, and deriving a constitutive model and a creep model of the nonlinear creep model of the rock in a low stress state, a medium stress state and a high stress state respectively by combining a rule that when creep elements are connected in series, the stress of all elements is equal to the applied stress, and the strain is the sum of all series elements, specifically:
C1. when stress sigma < sigma is appliedK＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; the obtained creep model constitutive equation is as follows:
Figure BDA0003286993130000093
wherein epsilon01＝ε0+ε1η1，ε0For instantaneous creep,. epsilon1For retarding creep in the creep stage, η1Viscosity coefficient of Newton's body in generalized Kelvin body; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA0003286993130000101
representing the first derivative of the stress sigma with respect to time.
C2. When pressure σ is appliedK＜σ＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; the obtained creep model constitutive equation is as follows:
Figure BDA0003286993130000102
wherein epsilon012＝ε0+ε1+ε2，
Figure BDA0003286993130000103
Represents epsilon012A first derivative with respect to time;
Figure BDA0003286993130000104
represents epsilon012A second derivative with respect to time; epsilon0For instantaneous creep,. epsilon1For retarding creep in the creep phase, e2Creep in the stable creep phase; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA0003286993130000109
represents the first derivative of stress σ with respect to time;
Figure BDA00032869931300001010
represents the second derivative of the stress σ with respect to time;
C3. when stress σ > σ is appliedsThe creep model provided by the invention is a series connection of a Burger model and an ideal viscoplastomer, and the constitutive equation of the rock nonlinear creep model can be obtained by deducing the constitutive equation of the Burger model and the constitutive equation of the nonlinear viscoplastomer:
since the burgers model is in series with an ideal viscoplastomer:
Figure BDA0003286993130000105
where σ represents the applied stress; sigmaBStress representing a bergs model；σNRepresenting the stress of an ideal viscoplastomer; ε represents the total strain produced by the model; epsilon012＝ε0+ε1+ε2，ε1For retarding creep in the creep phase, e2To stabilize creep in the creep phase,. epsilon3To accelerate creep in the creep phase;
Figure BDA0003286993130000106
represents the first derivative of epsilon with respect to time;
Figure BDA0003286993130000107
represents epsilon012A first derivative with respect to time;
Figure BDA0003286993130000108
represents epsilon3First derivative with respect to time.
And combining the steps C1-C2 to obtain a constitutive equation:
Figure BDA0003286993130000111
where σ represents the applied stress;
Figure BDA0003286993130000112
represents the first derivative of stress σ with respect to time;
Figure BDA0003286993130000113
represents the second derivative of the stress σ with respect to time; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers;
Figure BDA0003286993130000114
represents the first derivative of epsilon with respect to time;
Figure BDA0003286993130000115
representing the second derivative of epsilon with respect to time.
Finally, the following steps are obtained:
Figure BDA0003286993130000116
where σ represents the applied stress; sigmaKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; epsilon01＝ε0+ε1η1，ε0For instantaneous creep,. epsilon1For retarding creep in the creep stage, η1Viscosity coefficient of Newton's body in generalized Kelvin body; epsilon012＝ε0+ε1+ε2，ε2Creep in the stable creep phase;
Figure BDA0003286993130000117
represents epsilon012A first derivative with respect to time;
Figure BDA0003286993130000118
represents epsilon012A second derivative with respect to time;
Figure BDA0003286993130000119
represents the first derivative of epsilon with respect to time;
Figure BDA00032869931300001110
represents the second derivative of epsilon with respect to time; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA00032869931300001111
represents the first derivative of stress σ with respect to time;
Figure BDA00032869931300001112
representing the second derivative of the stress sigma with respect to time.
C4. Solving a creep equation of the rock nonlinear creep model:
the stress applied at the initial time, i.e. at time t-0, is σ0(ii) a When sigma is0＜σK＜σsThe creep deformation is the sum of the deformation of the Hookean body and the deformation of the Kelvin body; when sigma isK＜σ0＜σsWhen the creep deformation is the creep deformation of the Burger model; when sigma is0≥σsWhen the creep deformation is the sum of the creep deformation of the Burger model and the creep deformation of an ideal viscoplastomer; the creep equation for an ideal viscoplastomer is:
Figure BDA0003286993130000121
where ε represents the total strain produced by the model; t represents the time elapsed during the accelerated creep phase; sigma0Is the stress applied at the initial moment; sigmasIs the yield limit of the plastic element; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers;
combining the creep equation of the ideal viscoplastomer with the nonlinear relation between the creep rate of the rock accelerated creep stage and the corresponding creep time history provided in the step S6 to obtain:
Figure BDA0003286993130000122
wherein A, B and m represent fitting coefficients; t represents the time elapsed during the accelerated creep phase; sigma0Is the stress applied at the initial moment; sigmasIs the yield limit of the plastic element; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers;
finally obtaining a creep equation of the rock nonlinear creep model:
Figure BDA0003286993130000123
where ε represents the total strain produced by the model; t represents the time elapsed during the accelerated creep phase; sigma0Is the stress applied at the initial moment; sigmaKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1And the elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown.
The method comprises the following steps in the specific implementation process:
firstly, developing an indoor rock uniaxial compression test;
the method is characterized in that a tunnel engineering penetrating a river is taken as a background, and surrounding rocks penetrating the river are stroke argillaceous sandstone. Rock samples for conducting uniaxial compression and creep tests were obtained from the field. For 3 sizes of
Figure BDA0003286993130000133
The cylindrical rock sample is subjected to 3 uniaxial compression tests, and the 3 uniaxial compression test results show that the average uniaxial compression strength value of the stroke argillaceous sandstone is about 20 MPa.
Step two, developing an indoor rock grading loading creep test;
the step loading mode is adopted, and the size of sampling the same project is
Figure BDA0003286993130000131
The cylindrical rock sample is subjected to a graded loading creep test. Setting the stress level of a creep test to be 8-grade loading level, setting the initial loading stress level to be 6MPa and setting the stress increment of each grade of loading according to the average uniaxial compressive strength of the medium-stroke argillaceous sandstone obtained in the step one
Figure BDA0003286993130000132
Is 2 MPa.
Step three, creep test result processing:
first, a full-range strain-time curve of the stroke-affected argillaceous sandstone is directly drawn for the uniaxial compressive creep test result, and fig. 2 is a schematic diagram of the full-range strain-time curve of the creep test according to the embodiment of the present invention. The full-process strain-time curve of the stroke argillaceous sandstone obtained by the graded loading creep test is processed by adopting a superposition method to obtain a graded strain-time curve, and fig. 3 is a schematic diagram of the creep test superposition strain-time curve of the embodiment of the invention.
Step four, classifying the rock creep curves;
as shown in fig. 3, the rock sample undergoes transient deformation at the instant when axial stress is applied, after which the strain-time curve begins to deflect towards the time axis. When the axial stress levels are 6MPa, 8MPa, 10MPa and 12MPa, the creep-time curve forms are highly consistent, and all the creep-time curves comprise instantaneous creep and deceleration creep stages, and the creep rate finally tends to 0 along with the extension of the stress action time, so that the creep rate is classified as a low-stress level creep curve; when the axial stress levels are 14MPa and 16MPa, the creep-time curves are similar in form, and all contain instantaneous creep, deceleration creep and stable creep stages, the stable creep stages are added compared with the low-stress-level creep curve, and the creep rate finally tends to a certain constant along with the extension of the stress action time, so that the creep rate is classified as a medium-stress-level creep curve; when the axial stress level is continuously increased to 18MPa and 20MPa, the creep-time curve forms are very similar, a stable creep stage and an accelerated creep stage are added compared with a low-stress-level creep curve, an accelerated creep stage is added compared with a medium-stress-level creep curve, the creep rate finally tends to infinity along with the extension of the stress action time, and the creep failure of the sample finally occurs, so that the sample is classified as a high-stress-level creep curve.
Identifying a creep model, and constructing an initial creep model;
establishing a model according to graded strain-time curves at different stress levels, comprising: the Hooke body is a spring element with instantaneous strain characteristics; the Newton body is an adhesive element with elastic after-effect properties; a switching element and a plastic element having a stress threshold; a non-linear adhesive element having a non-linear characteristic. Referring to fig. 3, a rock non-linear creep model according to an embodiment of the present invention is provided, in which an adhesive is serially connected to a switch and then serially connected to a non-linear viscoplastic through a generalized Kelvin model. FIG. 4 is a schematic diagram of a non-linear creep model according to an embodiment of the present invention:
1) the transient deformation characteristic of creep deformation can be described by a Hooke body, the constitutive equation of which is as follows:
σ'＝E'ε'
where σ' represents the stress of the low stress state model; e' represents the elastic modulus of the low stress state model; ε 'represents the strain corresponding to the stress applied to the low stress state model at σ'.
2) The elastic aftereffect characteristic of creep deformation can be described by a Newton body, the creep equation of which is:
Figure BDA0003286993130000141
where σ "represents the stress of the medium stress state model; η "represents the viscosity coefficient of the medium stress state model; ε "represents the strain rate corresponding to the stress σ" applied to the medium stress state model.
3) Stress threshold value of switch element is sigmaK，σKHaving a stress threshold effect, i.e. when the switching element is subjected to a stress sigma less than the stress threshold sigma of the switching elementKWhen the switch element is closed, all the elements connected in parallel with the switch element do not work; when the stress sigma applied to the switching element is greater than the stress threshold sigma of the switching elementKWhen the switching element is open, all elements in parallel with the switching element may function. The switch element only plays a control role, only has a stress threshold effect, and does not distribute stress.
4) The strain of the plastic element is represented by: when the plastic element is subjected to stressLess than the yield limit σ of the plastic elementsWhen, the strain is 0; when the plastic element is subjected to a stress greater than the yield limit sigma of the plastic elementsWhen it is used, the strain is not 0.
Step six, fitting a nonlinear relation between the creep rate of the rock accelerated creep stage and the corresponding creep time history;
conventional creep elements are all linear and it is not reasonable to describe the non-linear character of the rock with conventional creep elements. In order to take into account the non-linear character of rock creep, improvements to conventional linear creep elements are required. The generalized Kelvin model and the Burgers model are considered to be capable of well describing the transient creep, the deceleration creep and the stable creep stage characteristics of the rock. To further describe the non-linear characteristic of the accelerated creep stage of the rock, fitting the creep rate of the accelerated creep stage and the duration of the accelerated creep stage of the creep test in the second step, i.e. determining the relationship between the creep rate and the duration of the accelerated creep stage, as shown in fig. 5, which is a fitting diagram of the accelerated creep rate-duration test data of the accelerated creep stage according to the embodiment of the present invention, the fitting relationship is:
Figure BDA0003286993130000151
R2＝0.9943
wherein,
Figure BDA0003286993130000152
represents the creep rate in the accelerated creep phase; A. b and m represent fitting coefficients; t represents the time elapsed during the accelerated creep phase; r represents the fitting coefficient, and the closer to 1, the closer the fitting result is to the test result.
Seventhly, deducing a constitutive equation and a creep equation of the rock nonlinear creep model;
fitting and determining a nonlinear relation between the creep rate of the rock accelerated creep stage and the corresponding creep time history according to the initial creep model constructed in the fifth step and the sixth step, and respectively deducing a constitutive model and a creep model of the rock nonlinear creep model in a low stress state, a medium stress state and a high stress state by combining a rule that when creep elements are connected in series, the stress of all the elements is equal to the applied stress, and the strain is the sum of all the series elements.
(1) When stress sigma < sigma is appliedK＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; the obtained creep model constitutive equation is as follows:
Figure BDA0003286993130000153
wherein epsilon01＝ε0+ε1η1，ε0For instantaneous creep,. epsilon1For retarding creep in the creep stage, η1Viscosity coefficient of Newton's body in generalized Kelvin body; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA0003286993130000155
representing the first derivative of the stress sigma with respect to time.
(2) When a pressure σ is appliedK＜σ＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; the obtained creep model constitutive equation is as follows:
Figure BDA0003286993130000154
wherein epsilon012＝ε0+ε1+ε2，
Figure BDA0003286993130000161
Represents epsilon012A first derivative with respect to time;
Figure BDA0003286993130000162
represents epsilon012A second derivative with respect to time; epsilon0For instantaneous creep，ε1For retarding creep in the creep phase, e2Creep in the stable creep phase; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA0003286993130000163
represents the first derivative of stress σ with respect to time;
Figure BDA0003286993130000164
representing the second derivative of the stress sigma with respect to time.
(3) When the stress σ > σ is appliedsThe creep model provided by the invention is a series connection of a Burger model and an ideal viscoplastomer, and the constitutive equation of the rock nonlinear creep model can be obtained by deducing the constitutive equation of the Burger model and the constitutive equation of the nonlinear viscoplastomer:
since the burgers model is in series with an ideal viscoplastomer:
Figure BDA0003286993130000165
where σ represents the applied stress; sigmaBRepresenting the stress of the bergs model; sigmaNRepresenting the stress of an ideal viscoplastomer; ε represents the total strain produced by the model; epsilon012＝ε0+ε1+ε2，ε1For retarding creep in the creep phase, e2To stabilize creep in the creep phase,. epsilon3To accelerate creep in the creep phase;
Figure BDA0003286993130000166
represents the first derivative of epsilon with respect to time;
Figure BDA0003286993130000167
represents epsilon012A first derivative with respect to time;
Figure BDA0003286993130000168
represents epsilon3First derivative with respect to time.
And (3) combining the steps (1) to (2) to obtain a constitutive equation:
Figure BDA0003286993130000169
where σ represents the applied stress;
Figure BDA00032869931300001610
represents the first derivative of stress σ with respect to time;
Figure BDA00032869931300001611
represents the second derivative of the stress σ with respect to time; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers;
Figure BDA00032869931300001612
represents the first derivative of epsilon with respect to time;
Figure BDA00032869931300001613
representing the second derivative of epsilon with respect to time.
Finally, the following steps are obtained:
Figure BDA0003286993130000171
where σ represents the applied stress; sigmaKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; epsilon01＝ε0+ε1η1，ε0For instantaneous creep，ε1For retarding creep in the creep stage, η1Viscosity coefficient of Newton's body in generalized Kelvin body; epsilon012＝ε0+ε1+ε2，ε2Creep in the stable creep phase;
Figure BDA0003286993130000172
represents epsilon012A first derivative with respect to time;
Figure BDA0003286993130000173
represents epsilon012A second derivative with respect to time;
Figure BDA0003286993130000174
represents the first derivative of epsilon with respect to time;
Figure BDA0003286993130000175
represents the second derivative of epsilon with respect to time; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure BDA0003286993130000176
represents the first derivative of stress σ with respect to time;
Figure BDA0003286993130000177
representing the second derivative of the stress sigma with respect to time.
(4) Solving a creep equation of the rock nonlinear creep model:
the stress applied at the initial time, i.e. at time t-0, is σ0(ii) a When sigma is0＜σK＜σsThe creep deformation is the sum of the deformation of the Hookean body and the deformation of the Kelvin body; when sigma isK＜σ0＜σsWhen the creep deformation is the creep deformation of the Burger model; when sigma is0≥σsIn which creep deformation is of the Burger modelThe sum of the creep deformation and the creep deformation of an ideal viscoplastic body; the creep equation for an ideal viscoplastomer is:
Figure BDA0003286993130000178
wherein ε represents the strain induced; t represents the time elapsed during the accelerated creep phase; sigma0Is the stress applied at the initial moment; sigmasIs the yield limit of the plastic element; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers;
combining the creep equation of the ideal viscoplastomer with the nonlinear relation between the creep rate of the rock accelerated creep stage and the corresponding creep time history provided in the step six to obtain:
Figure BDA0003286993130000181
wherein A, B and m represent fitting coefficients; t represents the time elapsed during the accelerated creep phase; sigma0Is the stress applied at the initial moment; sigmasIs the yield limit of the plastic element; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers;
obtaining a creep equation of a final rock nonlinear creep model:
Figure BDA0003286993130000182
wherein ε represents the strain induced; t represents the time elapsed during the accelerated creep phase; sigma0Is the stress applied at the initial moment; sigmaKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1And the elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown.
Step eight, parameter inversion and model verification;
the creep equation of the final rock nonlinear creep model provided by the invention is calculated by using numerical calculation analysis software with a custom function fitting function,
Figure BDA0003286993130000191
compiling the data into a software self-defined function module, fitting the creep test data obtained in the step two, and inverting the parameters, E, in the rock nonlinear creep model provided by the invention0、E1、η1、η2A, B and m, and obtaining the creep parameters of the rock nonlinear creep model provided by the invention under different stress levels through inversion calculation, which is shown in table 1.
TABLE 1 rock nonlinear creep model parameters
Figure BDA0003286993130000192
As shown in Table 1, the weathering argillaceous sandstone creep test data in the fitting of the rock nonlinear creep model provided by the invention have fitting confidence coefficient of more than 0.95 under 8 stress levels, good fitting effect, and particularly have fitting confidence coefficient of more than 0.99 for the rock creep test result under a high stress state, which shows that the rock nonlinear creep model provided by the invention can well describe rock creep characteristics of different stress levels. And finally, comparing the creep test result of the weathered argillaceous sandstone in the second step with the fitting result of the rock nonlinear creep model provided by the invention, and as shown in fig. 6, comparing the creep test result under different stresses with the fitting result of the rock nonlinear creep model in the embodiment of the invention. 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, and the stress in FIG. 6h is 20 MPa. Fig. 5 shows that the fitting result can better predict the test result trend under different stress levels.

Claims (10)

1. A rock nonlinear creep model building method is characterized by comprising the following steps:
s1, carrying out a rock uniaxial compression test to obtain the average compression strength of the rock;
s2, performing a rock creep test in a graded loading mode according to the average compression strength of the rock;
s3, drawing a rock full strain-time curve obtained by a rock creep test and a graded strain-time curve of the rock under different stress levels;
s4, classifying graded strain-time curves of the rock under different stress levels;
s5, identifying the type of the rheological element of the creep model according to the graded strain-time curves of the rock under different stress levels, and constructing an initial creep model;
s6, fitting a nonlinear relation between the creep rate of the rock in the accelerated creep stage and the corresponding creep time history;
and S7, obtaining a constitutive equation and a creep equation of the rock nonlinear creep model by adopting the identified creep model and a nonlinear relation between the fitted creep rate of the rock accelerated creep stage and the corresponding creep time history.
2. The method of claim 1, wherein the step S1 comprises repeating the indoor uniaxial compression test of the rock several times to calculate the average uniaxial compression strength of the rock.
3. The method of claim 1, wherein the step S2 of applying step-wise loading comprises adding a predetermined stress increment to each step.
4. The method of claim 3, wherein the rock creep test is performed to obtain a full strain-time curve of the rock according to step S3, which comprises: the creep curve in the low stress state finally tends to a horizontal straight line with the slope of 0; the creep curve in the medium stress state finally tends to a straight line with a fixed slope; the curves of instantaneous creep, deceleration creep, stable creep and acceleration creep in a high stress state, wherein the high stress state is a nonlinear curve;
the step S4 includes that the method specifically includes the following steps of dividing the curves into the forms of instantaneous creep and deceleration creep in a low stress state according to the graded strain-time curves of the rock under different stress levels; curves of instantaneous creep, retarded creep and steady creep for medium stress conditions; transient creep, deceleration creep, steady creep and accelerated creep for high stress conditions.
5. The method for establishing a nonlinear creep model in rock according to any of claims 1 to 4, wherein said step S5 comprises the steps of:
A1. dividing the creep model into a plurality of elements, and identifying the element types of the creep model;
A2. establishing a constitutive equation or a creep equation of the element according to the graded strain-time curves under different stress levels, comprising: the Hooke body is a spring element with instantaneous strain characteristics; the Newton body is an adhesive element with elastic after-effect properties; a switching element and a plastic element having a stress threshold; a non-linear adhesive element having a non-linear characteristic.
6. The method of claim 5, wherein in step A2, the rheological element comprises a basic rheological element, and the basic rheological element comprises:
B1. transient deformation characteristics of creep deformation are described by using a Hooke body, and the constitutive equation of the Hooke body is as follows:
σ'＝E'ε'
where 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 characteristic of creep deformation is described by a Newton body, and the creep equation of the Newton body is as follows:
Figure FDA0003286993120000021
where σ "represents the stress of the medium stress state model; η "represents the viscosity coefficient of the medium stress state model; ε "represents the strain rate corresponding to the stress applied to the intermediate stress state model as σ";
B3. setting a stress threshold value sigma of a switching elementKWhen the stress σ to which the switching element is subjected is smaller than the stress threshold σ of the switching elementKWhen the switch element is closed, all the elements connected in parallel with the switch element do not play a role; when the stress sigma of the switch element is larger than the threshold value sigma of the switch stressKWhen the switch element is turned on, a plurality of elements connected in parallel with the switch element play a role;
B4. the strain of the plastic element is represented by: when the plastic element is subjected to a stress less than the yield limit σ of the plastic elementsWhen, the strain is 0; when the plastic element is subjected to a stress greater than the yield limit sigma of the plastic elementsWhen it is used, the strain is not 0.
7. A method of establishing a nonlinear creep model in rock according to claim 5, characterized in that step S7 is performed by fitting the determined nonlinear relationship between creep rate at accelerated creep stage of rock and corresponding creep time history according to the initial creep model established in step S5 and step S6, and in combination with the rule that when creep elements are connected in series, the stress of all elements is equal to the applied stress, and the strain is the sum of all elements connected in series, a constitutive model and a creep model of the nonlinear creep model in rock in low stress state, medium stress state and high stress state are respectively established.
8. The method of claim 7, wherein said step S7 includes the steps of:
C1. when stress sigma < sigma is appliedK＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; calculating a creep model constitutive equation;
C2. when pressure σ is appliedK＜σ＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; calculating a constitutive equation of the creep model;
C3. when stress σ > σ is appliedsCalculating the constitutive equation of the rock nonlinear creep model through the constitutive equation of the Burger model and the constitutive equation of the nonlinear viscoplastomer;
C4. and solving a creep equation of the rock nonlinear creep model.
9. Method of establishing a non-linear creep model in rock according to claim 8, characterized in that step C4 includes setting the stress applied at the initial moment to be σ0；σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; when sigma is0＜σK＜σsThe creep deformation is the sum of the deformation of the Hookean body and the deformation of the Kelvin body; when sigma isK＜σ0＜σsWhen the creep deformation is the creep deformation of the Burger model; when sigma is0≥σsThe creep deformation is the sum of the creep deformation of the burgers model and the creep deformation of the ideal viscoplastic body.
10. The method of establishing a nonlinear creep model in rock according to claim 9, characterized in that when the generalized Kelvin body, the switching elements and the plastic elements are connected in series in sequence; the step C1 includes when the stress σ < σ is appliedK＜σsWhen, σKIs the stress threshold of the switching element;σsis the yield limit of the plastic element; the obtained creep model constitutive equation is as follows:
Figure FDA0003286993120000031
wherein epsilon01＝ε0+ε1η1，ε0For instantaneous creep,. epsilon1For retarding creep in the creep stage, η1Viscosity coefficient of Newton's body in generalized Kelvin body; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure FDA0003286993120000032
represents the first derivative of stress σ with respect to time;
said step C2 includes applying a pressure σK＜σ＜σsWhen, σKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; the obtained creep model constitutive equation is as follows:
Figure FDA0003286993120000041
wherein epsilon012＝ε0+ε1+ε2，
Figure FDA0003286993120000042
Represents epsilon012A first derivative with respect to time;
Figure FDA0003286993120000043
represents epsilon012A second derivative with respect to time; epsilon0For instantaneous creep,. epsilon1For retarding creep in the creep phase, e2Creep in the stable creep phase; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Indicating the viscosity of a tape switchViscosity coefficient of Newton's body in vivo; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure FDA0003286993120000044
represents the first derivative of stress σ with respect to time;
Figure FDA0003286993120000045
represents the second derivative of the stress σ with respect to time;
step C3, the constitutive equation of the nonlinear creep model of the rock is:
Figure FDA0003286993120000046
where σ represents the applied stress; sigmaKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; epsilon01＝ε0+ε1η1，ε0For instantaneous creep,. epsilon1For retarding creep in the creep stage, η1Viscosity coefficient of Newton's body in generalized Kelvin body; epsilon012＝ε0+ε1+ε2，ε2Creep in the stable creep phase;
Figure FDA0003286993120000047
represents epsilon012A first derivative with respect to time;
Figure FDA0003286993120000048
represents epsilon012A second derivative with respect to time;
Figure FDA0003286993120000049
represents the first derivative of epsilon with respect to time;
Figure FDA00032869931200000410
represents the second derivative of epsilon with respect to time; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1The elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown;
Figure FDA00032869931200000411
represents the first derivative of stress σ with respect to time;
Figure FDA00032869931200000412
represents the second derivative of the stress σ with respect to time;
in step C4, the creep equation of the rock nonlinear creep model includes:
Figure FDA0003286993120000051
where ε represents the total strain produced by the model; t represents the time elapsed during the accelerated creep phase; sigma0Is the stress applied at the initial moment; sigmaKIs the stress threshold of the switching element; sigmasIs the yield limit of the plastic element; eta1Viscosity coefficient of Newton's body in generalized Kelvin body; eta2Represents the viscosity coefficient of Newton body in the viscous body with the switch; eta3(t) represents a viscosity coefficient of a nonlinear plastomer among the nonlinear plastomers; e0The elastic coefficient of a series Hooke body in the generalized Kelvin body is shown; e1And the elastic coefficient of a parallel Hooke body in the generalized Kelvin body is shown.
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CN116011191A (en) * 2022-12-13 2023-04-25 广西大学 Model construction method for representing rock creep start and acceleration under true triaxial
CN116011191B (en) * 2022-12-13 2024-05-10 广西大学 Model construction method for representing rock creep start and acceleration under true triaxial
CN116611269B (en) * 2023-07-19 2023-10-13 中国矿业大学(北京) Elastic viscous element model construction method, solving method, equipment and storage medium
CN116611269A (en) * 2023-07-19 2023-08-18 中国矿业大学(北京) Elastic viscous element model construction method, solving method, equipment and storage medium
CN117252015A (en) * 2023-09-26 2023-12-19 重庆大学 Rock overall process creep simulation method
CN117252015B (en) * 2023-09-26 2024-05-10 重庆大学 Rock overall process creep simulation method
CN117909624A (en) * 2024-01-05 2024-04-19 西安建筑科技大学 Method for establishing rock damage creep model
CN117909624B (en) * 2024-01-05 2024-09-20 西安建筑科技大学 Method for establishing rock damage creep model

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