CN110274835B - Method for improving Burgers rock shear creep model - Google Patents
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Abstract
The invention discloses a method for improving a Burgers rock shear creep model, which comprises the following steps: s1, aiming at the time difference of rock shear strength in a creep state, constructing a nonlinear element which is formed by connecting a plastic element and a viscous element in parallel and describes the mechanical property of the rock in an accelerated creep stage; s2, describing an aging damage function D (t) of the rock in an accelerated creep stage by adopting Kachanov law widely applied to the field of rheology; s3, determining the shear strength tau based on the age-related damage function D (t)dSpecific expression ofd(t); s4, measuring the residual intensity taurIntroducing shear strength function taud(t) constructing a modified shear strength function τ taking into account residual strengthd(t); s5, correcting the shear strength function taud(t) substituting into the nonlinear element of step S1, determining an element constitutive equation γ (t); s6, introducing the element constitutive equation gamma (t) into the classical Burgers model constitutive equation to obtain an improved Burgers model constitutive equation gamma accurately reflecting the mechanical behavior of the full creep processB(t)。
Description
Technical Field
The invention belongs to the technical field of engineering, and particularly relates to a method for improving a Burgers rock shear creep model.
Background
The creep is an important mechanical property of rock, influences the long-term stability of rock engineering, obtains the stress and deformation characteristics of the rock from the viewpoint of rock rheology and a method, and is well matched with the reality. Therefore, the research on the creep characteristics of the rock is of great significance, and many scholars establish a creep constitutive model through empirical formulas and element combination models and find that the rock creep has remarkable nonlinear characteristics, wherein the creep acceleration stage is most obvious. Traditional constitutive models such as Nishihara models and Burgers models cannot reflect the nonlinearity of rock creep because the parameters of combined elements of the traditional constitutive models are constant.
In order to accurately reflect the rheological mechanical properties of the rock mass, a related scholars perform a series of nonlinear improvements on the traditional combination model. A four-element creep model capable of simulating three creep stages is established, for example, in the documents "Tang H, et al.A new rock cross model based on variable-order derivatives and continuous dam mechanisms [ J ]. Bulletin of Engineering genetics and the Environment,2017,77(1):375-383 ]. As another example, a nonlinear damage creep model of a high-stress soft rock mass is established based on a damage mechanics theory in a document' Cao P, et al. In the document "Wang JB, et al. Creep properties and damage model for salt rock under low-frequency cyclic loading [ J ]. Geomemechanics and Engineering,2014,7(5): 569-. A Kelvin Model-based nonlinear Damage Creep Model of Coal petrography is established on the basis of the assumption that Damage is a function of stress level and time in the document Yang X B, et al, nonlinear Damage Creep Model of code or Rock containment Gas J Applied Mechanics and Materials 2012, 204-. A creep model based on a time fractional order derivative is proposed in the document Zhou H W, et al. A cruise coherent model for a salt based on fractional derivatives [ J ]. International Journal of Rock Mechanics and Mining Sciences,2011,48(1): 116-.
These models describe the non-linearity of the rock mass creep well, but it is generally accepted that the rock shear strength does not change with time, and in fact during creep, the rock mass shear strength decays with time due to the time-dependent accumulation of micro-damage and decays to a minimum at the end of failure. Moreover, the shear strength is an important mechanical property index of the rock mass, and the change of the shear strength is a macroscopic reflection of the adjustment and recombination of the microstructure of the rock mass, so that the timeliness of the shear strength in the creep process needs to be considered.
Disclosure of Invention
In order to overcome the limitation of insufficient description of the shear strength attenuation of the traditional creep model, the invention provides a method for improving a nonlinear Burgers rock shear creep model based on time-varying shear strength.
The method for improving the Burgers rock shear creep model comprises the following steps:
s1, aiming at the time difference of rock shear strength in a creep state, constructing a nonlinear element gamma which is formed by connecting a plastic element and a viscous element in parallel and describes the mechanical property of the rock in an accelerated creep stage; wherein the plastic element parameter τdThe actual shear strength of the rock is represented, the value of the actual shear strength changes along with time, the viscous element represents the shear strain rate of the rock, and the parameter eta is linearly unchanged;
s2, describing an aging damage function D (t) of the rock in an accelerated creep stage by adopting Kachanov law widely applied to the field of rheology;
s3, determining the shear strength tau based on the age damage function D (t) in the step S2dSpecific expression ofd(t)；
S4, measuring the residual intensity taurIntroducing the shear strength function tau in the step S3d(t) constructing a modified shear strength function τ taking into account residual strengthd(t)；
S5, correcting the shear strength function tau in the step S4d(t) substituting into the nonlinear element of step S1, determining an element constitutive equation γ (t);
s6, introducing the element constitutive equation gamma (t) in the step S5 into the classical Burgers model constitutive equation to obtain accurate reflection of full creepImproved Burgers model constitutive equation gamma of engineering mechanical behaviorB(t)。
In the step S1, the expression of the nonlinear element is:
wherein τ is the applied shear stress, τdThe actual shear strength of the rock is represented, and eta represents the shear strain rate of the rock.
In the step S2, the method for obtaining the age damage function d (t) of the rock at the accelerated creep stage specifically includes the following steps:
s2.1, describing the creep damage D of the rock by adopting Kachanov law:
in the formula, A and delta are material constants determined by a creep test, and rho is stress borne by the rock;
s2.2, integrating the formula in S2.1 to obtain the complete damage moment tRFunction expression
tR＝[A(δ+1)ρδ]-1
In the formula, tRThe moment when the rock is completely damaged;
s2.3, based on the formulas of S2.1 and S2.2, with initial conditions to accelerate the beginning of the creep phase when D is 0; d is 1 when the damage is completely damaged, and the rock damage evolution equation in the accelerated creep stage is deduced:
in the formula tsThe moment when the rock enters an accelerated creep stage; t is tRThe moment when the rock is completely damaged; when t is equal to tsWhen D is 0; t is tRWhen D is 1.
Determining the rock shear strength expression tau in the step S3dThe method (t) specifically comprises the following steps:
s3.1, according to the injuryTheory of mechanics, shear strength τdThe expression is determined as:
τd＝τ(1-D)
wherein tau is a loading shear stress;
s3.2, substituting the expression of D (t) into the formula of S3.1 to obtain the shear strength time function tau based on the Kachanov lawd(t), the expression is:
in the formula:
the nonlinear element of the formula is provided for the mechanical characteristics of the accelerated creep stage of the rock, such as the accelerated creep stage (t is less than t)s) The shear strength tau will not decay during accelerated creep, taud(t) No attenuation Damage D is 0, so t is<ts, φ (t) is 1.
The step S4 obtains a modified shear strength function τ considering the residual strengthdThe method (t) specifically comprises the following steps:
s4.1 residual Strength τ consisting of Friction force according to Mohr-Coulomb criterionrThe expression of (a) is:
τr＝σtanα
in the formula, sigma is normal stress, and alpha is a rock internal friction angle;
s4.2, according to the residual strength of the rock after the shear failure, the rock shear strength tau in the step S3 is subjected tod(t) carrying out correction to obtain a corrected shear strength time function taud(t) is:
improved shear strength function when t is t ═ tsTime, τd＝τ，t＝tRTime, τd＝τrAnd the actual shearing characteristics of the rock are met.
The method for determining the nonlinear element constitutive equation γ (t) in step S5 includes:
s5.1, and combining the formulas in formulas S1-S4, the nonlinear element constitutive equation γ (t) can be written as:
s5.2. binding initial condition t ═ tsAnd γ is 0, the resulting component shear strain equation is:
through the above 5 steps, a concrete expression formula of d (t) and γ (t) can be obtained, in the formula, there is a material constant δ determined by creep test, the value of which changes with the difference of material properties, and rock mechanical properties represented by the δ value, here, we can calculate the values of d (t) and γ (t) under different model parameters δ by using or adopting a controlled variable method, and obtain the reflection condition of the δ value on the rock macro-micro mechanical properties, which specifically includes the following steps: firstly, a control variable method is adopted, parameters except delta in an element constitutive equation gamma (t) are set as constants, and values of D (t) and gamma (t) under different deltas are respectively calculated; secondly, drawing corresponding D-t, gamma-t curves, and obtaining the reflection condition of the delta value to the macro-micro mechanical property of the rock. The method can obtain the material property reflected by the delta value through calculation and analysis, so that the mechanical property of the material can be obtained from the inverted delta value after the model is fitted to the test data.
Obtaining an improved Burgers model constitutive equation gamma in the step S6BThe method (t) specifically comprises the following steps:
the Burgers model is a creep model widely applied to soft rock, can better describe the mechanical properties of a rock at an attenuation creep stage and a stable creep stage, but lacks the description of the mechanical properties at an acceleration creep stage; therefore, the nonlinear viscoplasticity element is introduced on the basis of the original Burgers model, and an improved Burgers model capable of reflecting the mechanical behavior at the accelerated creep stage is established;
s6.1, the constitutive equation of the classical Burgers model is as follows:
wherein τ is the applied shear stress, γ is the shear strain, GMMaxwell bulk modulus of elasticity; etaMIs the Maxwell bulk viscosity coefficient; gKKelvin bulk modulus of elasticity; etaKIs the Kelvin bulk viscosity coefficient;
the shear strain equation is as follows,
s6.2, introducing the constitutive equation gamma (t) of the nonlinear element in the step S5 into a classical Burgers model to obtain an improved Burgers model constitutive equation gammaB(t)：
In the formula, τSThe long-term shear strength of the rock.
The invention has the beneficial effects that: 1. the time difference of the rock shear strength in a creep state is described by adopting a Kachanov creep damage law, a nonlinear viscoplasticity element capable of reflecting the mechanical property in an accelerated creep stage is established on the basis, the model parameters are simple, and the physical mechanical significance is clear. 2. The parameter delta in the nonlinear viscoplasticity element can reflect macro-micro mechanical characteristics in the accelerated creep process of the rock, and the shear strain and the strain rate are inversely proportional to delta as delta is smaller and the shear strain and the strain rate are higher. When delta is less than 0, the rock damage evolution rate is attenuated along with time, and the smaller delta is, the more serious the attenuation is; when delta is greater than 0, the rock damage evolution rate increases with time, and the larger delta, the more obvious the increase. In addition, delta can reflect the evolution of internal cracks of the rock in the creep process. 3. The nonlinear viscoplasticity element provided by the invention is introduced into a classical Burgers model, the new model can accurately reflect the macro-micro mechanical properties of the rock full creep process, and the rationality of the Burgers shear creep model is improved and verified by comparing a model calculated value with a test value and a classical Burgers model calculated value.
Drawings
FIG. 1 is a schematic diagram of the change of rock mass shear strength with time during creep.
FIG. 2 is a schematic representation of a non-linear viscoplastic component based on aged shear strength.
FIG. 3 is a graph of shear strain η versus time for various δ conditions.
FIG. 4 is a D-time plot of the injury factor under different delta conditions.
FIG. 5 is a schematic diagram of a classical Burgers model.
Fig. 6 is a schematic diagram of a nonlinear Burgers model based on time-varying shear strength.
FIG. 7 is a schematic view of a sample loading and apparatus; (a) sample loading model, (b) test equipment.
FIG. 8 is a comparison of experimental values with calculated values from the modified Burgers model.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
Example 1
S1, constructing a nonlinear element (shown in figure 2) which is formed by connecting a plastic element and a viscous element in parallel and describes the mechanical property of the rock in the accelerated creep stage aiming at the time difference of the rock shear strength in the creep state, wherein the parameter tau of the plastic element isdCharacterizing the actual shear strength of the rock, the value of which varies with time, viscous elementsAnd (3) representing the shear strain rate of the rock, wherein the parameter eta is linearly unchanged.
Referring to fig. 1, the creep process may be divided into three stages: i-decay creep phase, II-stabilization creep phase, III-acceleration creep phase. When the external load exceeds the rock yield strength, internal microcracks begin to develop, causing damage and degradation of continuity over time, resulting in shear strength τdThe attenuation is continuous. When the external stress tau exceeds the long-term strength tau of the rocksWhile the rock shear strength tau in the decaying creep phase and in the steady creep phasedAnd deteriorates over time. After the damage is accumulated to a certain degree, the creep curve reaches the boundary point of stable creep and accelerated creep, and the rock shear strength tau at the momentdThe acceleration a is equal to the loading stress tau and is 0; after entering the accelerated creep stage, the damage of the rock is rapidly intensified, and the degraded shear strength taudIs not enough to resist the loading stress, instability begins to occur, and the strain acceleration a is increased from 0; shear strength tau after complete destruction of rockdDecay to residual intensity taur。
The constitutive equation of the nonlinear element can be obtained according to the following formula:
wherein τ is the applied shear stress, τdThe actual shear strength of the rock is represented, and eta represents the shear strain rate of the rock.
S2, describing an aging damage function D (t) of the rock in an accelerated creep stage by adopting Kachanov law widely applied to the field of rheology;
for a creep state, Kachanov provides Kachanov's law based on a Norton power law formula, rock damage in the creep state can be well described, and the expression is as follows:
in the formula, A and delta are material constants determined by a creep test, and rho is stress borne by the rock;
the time to complete damage of creep can be integrated by equation (2):
tR＝[A(δ+1)ρδ]-1 (3)
in the formula, tRThe moment when the rock is completely damaged.
Based on formula (2) and formula (3), D ═ 0 at the beginning of the accelerated creep phase in combination with the initial conditions; when D is 1, the damage evolution equation of the rock in the accelerated creep stage can be obtained:
in the formula tsThe moment when the rock enters an accelerated creep stage; when t is equal to tsWhen D is 0; t is tRWhen D is 1.
S3, determining the shear strength tau based on the age-related damage function D (t)dSpecific expression ofd(t)；
According to the theory of damage mechanics and the shear strength tau at the beginning of the accelerated creep phase mentioned in step S1dEqual to the loaded shear stress tau, the time function tau of the shear strength of the accelerated creep phase characterised by the plastic elementd(t) can be written as:
τd(t)＝τ(1-D) (5)
substituting formula (4) into formula (5) to obtain the shear strength time function tau based on Kachanov's lawd(t), the expression is:
in the formula:
the nonlinear element of the formula is provided for the mechanical characteristics of the accelerated creep stage of the rock, such as the non-accelerated creep stage (tda)Less than ts) The shear strength tau will not decay during accelerated creep, taud(t) No attenuation Damage D is 0, so t is<ts, φ (t) is 1.
S4, measuring the residual intensity taurIntroducing shear strength function taud(t) constructing a modified shear strength function τ taking into account residual strengthd(t)。
In practice, the rock still has a certain residual strength tau after shearing failurerIn view of this, equation (6) is corrected so that t becomes tRTime, τd＝τrThe improved shear strength time function is:
under natural conditions, the shear strength of the rock is composed of cohesive force and friction force, after shear failure, the cohesive force is almost completely lost, and the friction force becomes the shear strength tau of the rockdThe major source of (c);
residual Strength τ provided by Friction according to Mohr-Coulomb criterionrCan be expressed as:
τr＝σtanα (9)
in the formula, sigma is normal stress, and alpha is a rock internal friction angle;
accordingly, substituting formula (9) for formula (8) yields a shear strength time function based on the Mohr-Coulomb criterion:
improved shear strength function when t is t ═ tsTime, τd＝τ，t＝tRTime, τd＝τrAnd the actual shearing characteristics of the rock are met.
S5, converting the shear strength function taud(t) substituting into the nonlinear element of step S1, determining an element constitutive equation γ (t);
combining equations (1) - (10), the nonlinear element constitutive equation γ (t) can be written as:
binding initial condition t ═ tsAnd γ is 0, the resulting component shear strain equation is:
and S6, calculating D (t) and gamma (t) values under different model parameters delta by adopting a control variable method, and obtaining the reflection condition of the delta value on the macro-micro mechanical properties of the rock.
And (3) respectively calculating the values of D (t) and gamma (t) under different deltas by adopting a control variable method and setting parameters except delta in an element constitutive equation gamma (t) as constants. And drawing corresponding D-t, gamma-t curves to obtain the reflection condition of the delta value on the macro-micro mechanical properties of the rock.
Under the assumption of>τs(rock long term shear strength) in the case of the reference Zhou H W, Wang C P, Han B B, et al. A crop constitutive model for salt rock based on reactive derivatives [ J]The controlled-variable method of parameter sensitivity analysis in International Journal of Rock Mechanics and Mining Sciences,2011,48(1):116- "121"; the parameters in formula (12) are defined as η ═ 1.2GPa · h,. tau. ═ 3.33MPa,. sigma. 1MPa,. alpha. 60 °, ts＝0.26h，tRThe shear strain-time curves (fig. 3) and damage factor D-time curves (fig. 4) for different δ cases were calculated as 0.73 h.
As can be seen from fig. 3 and 4, the shear strain and the strain rate increase as δ decreases, and the shear strain and the strain rate are inversely proportional to δ. Analyzing the change rule of the damage factor D under different delta conditions, when delta is<At 0, the curve shows a convex type, and the rock damage evolution rate
(first derivative of the impairment factor with respect to time) decays over time, and the smaller the δ, the more severe the decay trend; when δ is 0, the slope of the curve is constant, so to speakOpen rock damage evolution rate
The damage is linearly increased after being fixed and unchanged; delta>At 0, the curve shows a concave pattern, and the rock damage evolution rate
The growth is increased with time, and the larger the δ, the more pronounced the growth trend. In addition, the rock damage evolution rate is closely related to the propagation degree of the internal cracks, and the more intensely the internal cracks propagate, the higher the corresponding damage evolution rate. In the process of loading the rock, due to the difficult observation and the transient expansion characteristic of the internal cracks, the observation of the evolution situation of the internal cracks is difficult to a certain extent, but in the nonlinear viscoplastic element provided by the invention, the evolution situation of the internal cracks of the rock can be reflected by the size of the parameter delta, so that a new reference method can be provided for observing the evolution situation of the internal cracks of the rock.
S7, introducing the element constitutive equation gamma (t) into the classical Burgers model constitutive equation to obtain an improved Burgers model constitutive equation gamma accurately reflecting the mechanical behavior of the full creep processB(t)。
The Burgers model is a creep model widely applied to soft rock, can better describe the mechanical properties of a rock in a decay creep stage and a stable creep stage, and lacks description of the mechanical properties in an acceleration creep stage. The invention introduces the nonlinear viscoplasticity element on the basis of the original Burgers model and establishes an improved Burgers model capable of reflecting the mechanical behavior at the accelerated creep stage.
The classical Burgers model constitutive equation is:
wherein τ is the applied shear stress, γ is the shear strain, GMMaxwell bulk modulus of elasticity; etaMIs the Maxwell bulk viscosity coefficient; gKKelvin bulk modulus of elasticity; etaKThe Kelvin bulk viscosity coefficient.
The shear strain equation is:
the model schematic diagram is shown in FIG. 5;
introducing the nonlinear element constitutive equation gamma (t) in the step S5 into the classical Burgers model to obtain an improved Burgers model constitutive equation gammaB(t)：
In the formula, τSThe long-term shear strength of the rock.
So far, the improved Burgers model constitutive equation is completely determined (a model schematic diagram is shown in FIG. 6), and the model parameter physical and mechanical significance is clear, so that the model is suitable for describing the mechanical behavior of the creep in three stages, however, the feasibility of the model is verified by a test example.
Example 2 test example validation
Substituting indoor test data into constitutive equation gamma of improved Burgers modelB(t) and determining the long-term intensity τ thereofsAnd verifying the effectiveness and the rationality of the model through a test, and obtaining the rock micro-damage characteristic through an inverted parameter delta.
In order to verify the rationality of the improved Burgers model provided by the invention, sandstone samples are selected to carry out an indoor creep shear test, the size of the samples is 10cm multiplied by 10cm, and the specific mechanical parameters are shown in Table 1. From other tests on sandstone, it is found that the long-term shear strength under the normal stress condition of 1.56MPa is 2.8 to 3MPa, and the loading shear stress is set to be 3.36MPa higher than the long-term shear strength in order to obtain a test curve including an accelerated creep stage.
TABLE 1 sandstone Material parameters
The test instrument adopts an RYL-600 microcomputer controlled rock shearing rheometer (figure 7), consists of a host, a measurement and control system and a computer system, can simultaneously measure the biaxial bilateral deformation value of a test sample, has the measurement precision of 0.001mm, performs loading control through force or deformation, and performs a shearing creep test on the rock test sample under the conditions of constant temperature and constant humidity. The load loading rate of each stage was set to 300N/s and the sample loading model was as shown in FIG. 7. During the test, the normal stress is applied to 1.56MPa, the shear stress is applied to 3.36MPa after the normal deformation is stable, and the normal stress and the shear stress are kept constant in the loading process.
Immediately after the test piece was destroyed, the test was stopped, and a shear creep curve at the accelerated creep stage was plotted, as shown in fig. 8. The test curves were fitted using the modified Burgers shear creep model and compared to the results of the classical Burgers model fitting, as shown in fig. 8. Therefore, the improved Burgers shear creep model provided by the invention has better fitting effect with test data, and the superiority of the model is verified. And by testing curve fitting, relevant calculation parameters in the improved Burgers shear creep model can be obtained, as shown in Table 2. As can be seen from Table 2, the parameter δ is-0.58. According to the rock damage characteristic reflected by the delta in the sensitivity analysis of the step S6, it can be known that in the accelerated creep stage, the damage evolution rate of the sandstone attenuates along with time, and the maximum damage rate occurs in the initial stage of the accelerated creep, which indicates that the crack propagation in the sandstone is most severe at the beginning of the accelerated creep, and then the severe degree of the expansion slows down along with time until the sandstone is finally completely destroyed.
TABLE 2 results of parametric inversion of modified Burgers models
While the embodiments of the invention have been described in detail in connection with the accompanying drawings, it is not intended to limit the scope of the invention. Various modifications and changes may be made by those skilled in the art without inventive step within the scope of the appended claims.
Claims (7)
1. A method of improving a Burgers rock shear creep model, comprising the steps of:
s1, aiming at the time difference of rock shear strength in a creep state, constructing a nonlinear element gamma which is formed by connecting a plastic element and a viscous element in parallel and describes the mechanical property of the rock in an accelerated creep stage; wherein the plastic element parameter τdThe actual shear strength of the rock is represented, the value of the actual shear strength changes along with time, the viscous element represents the shear strain rate of the rock, and the parameter eta is linearly unchanged;
s2, describing an aging damage function D (t) of the rock in an accelerated creep stage by adopting Kachanov law widely applied to the field of rheology;
s3, determining the shear strength tau based on the age damage function D (t) in the step S2dSpecific expression ofd(t)；
S4, measuring the residual intensity taurIntroducing the shear strength function tau in the step S3d(t) constructing a modified shear strength function τ taking into account residual strengthd(t)；
S5, correcting the shear strength function tau in the step S4d(t) substituting into the nonlinear element of step S1, determining an element constitutive equation γ (t);
s6, introducing the element constitutive equation gamma (t) in the step S5 into the classical Burgers model constitutive equation to obtain an improved Burgers model constitutive equation gamma accurately reflecting the mechanical behavior of the full creep processB(t)；
In the step S1, the constitutive equation of the nonlinear element is:
wherein τ is the applied shear stress, τdThe actual shear strength of the rock is represented, and eta represents the shear strain rate of the rock.
2. The method for improving the Burgers rock shear creep model according to claim 1, wherein in the step S2, the method for obtaining the aging damage function D (t) of the accelerated creep stage of the rock specifically comprises the following steps:
s2.1, describing damage D of the rock in an accelerated creep stage by adopting Kachanov law:
wherein A, δ are material constants determined by a creep test; rho is the stress borne by the rock;
s2.2, integrating the formula in S2.1 to obtain the complete damage moment tRFunction expression
tR＝[A(δ+1)ρδ]-1
In the formula, tRThe moment when the rock is completely damaged;
s2.3, based on the formulas of S2.1 and S2.2, with initial conditions to accelerate the beginning of the creep phase when D is 0; d is 1 when the damage is completely damaged, and a creep state rock damage evolution equation is deduced
In the formula tsThe moment when the rock enters an accelerated creep stage; t is tRThe moment when the rock is completely damaged; when t is equal to tsWhen D is 0; t is tRWhen D is 1.
3. The method for improving Burgers rock shear creep model according to claim 1, wherein the step S3 is implemented by determining the rock shear strength expression τdThe method (t) specifically comprises the following steps:
s3.1, according to the theory of damage mechanics, the shear strength tau is measureddThe expression is determined as:
τd＝τ(1-D)
s3.2, substituting the expression of D (t) into the formula of S3.1 to obtain the shear strength time function tau based on the Kachanov lawd(t), the expression is:
in the formula:
4. the method for improving Burgers rock shear creep model according to claim 1, wherein the step S4 is implemented by obtaining a modified shear strength function τ considering residual strengthdThe method (t) specifically comprises the following steps:
s4.1 residual Strength τ consisting of Friction force according to Mohr-Coulomb criterionrThe expression of (a) is:
τr＝σtanα
wherein, σ is normal stress, and α is rock internal friction angle
S4.2, according to the residual strength of the rock after the shear failure, the rock shear strength tau in the step S3 is subjected tod(t) carrying out correction to obtain a corrected shear strength time function taud(t) is:
improved shear strength function when t is t ═ tsTime, τd＝τ，t＝tRTime, τd＝τrAnd the actual shearing characteristics of the rock are met.
5. The method for improving the Burgers rock shear creep model according to claim 1, wherein the method for determining the nonlinear element constitutive equation γ (t) in the step S5 is as follows:
s5.1, and combining the formulas in formulas S1-S4, the nonlinear element constitutive equation γ (t) can be written as:
s5.2. binding initial condition t ═ tsAnd γ is 0, the resulting component shear strain equation is:
6. the method for improving the Burgers rock shear creep model according to any one of claims 1-5, wherein according to the equations for obtaining D (t) and gamma (t), different model parameters delta are calculated by a controlled variable method, and the reflection condition of the delta value on the rock macro-micro mechanical property is obtained; the method specifically comprises the following steps: firstly, adopting a control variable method, setting parameters except delta in an element constitutive equation gamma (t) as constants, and respectively calculating D (t) and gamma (t) values under different deltas; secondly, drawing corresponding D-t, gamma-t curves, and obtaining the reflection condition of the delta value to the macro-micro mechanical property of the rock.
7. The method for improving the Burgers rock shear creep model according to claim 1, wherein the improved Burgers model constitutive equation γ is obtained in the step S6BThe method (t) specifically comprises the following steps:
s6.1, the constitutive equation of the classical Burgers model is as follows:
wherein τ is the applied shear stress, γ is the shear strain, GMMaxwell bulk modulus of elasticity; etaMIs the Maxwell bulk viscosity coefficient; gKKelvin bulk modulus of elasticity; etaKIs the Kelvin bulk viscosity coefficient;
the shear strain equation is as follows,
s6.2, introducing the constitutive equation gamma (t) of the nonlinear element in the step S5 into a classical Burgers model to obtain an improved Burgers model constitutive equation gammaB(t)：
In the formula, τSThe long-term shear strength of the rock.
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7499820B1 (en) * | 2005-06-30 | 2009-03-03 | Storage Technology Corporation | Method for generating a performance metric for a tensilized tape |
| CN105259035A (en) * | 2015-10-26 | 2016-01-20 | 中国石油大学(华东) | Method for establishing rock material ageing and elastic-plastic mechanics constitutive model |
| CN106198259A (en) * | 2016-07-05 | 2016-12-07 | 辽宁工程技术大学 | A kind of method determining rock monsteady state creep parameter |
| CN107748111A (en) * | 2017-10-13 | 2018-03-02 | 华北水利水电大学 | A kind of determination method of rock mass discontinuity Long-term Shear Strength |
| CN108843303A (en) * | 2018-07-19 | 2018-11-20 | 西南石油大学 | A kind of casing damage in oil-water well prediction technique based on mud stone creep model |
| CN109187199A (en) * | 2018-09-18 | 2019-01-11 | 中国石油大学(华东) | The viscoelasticity theory analysis method of anchored rock mass creep properties under uniaxial compression |
| CN109885980A (en) * | 2019-03-29 | 2019-06-14 | 中南大学 | Determine that Complete Damage Process constitutive model is sheared at the joint of yield point based on stress difference |
| CN109902444A (en) * | 2019-03-29 | 2019-06-18 | 中南大学 | A method of prediction wing crack propagation path |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP4750868B2 (en) * | 2009-03-19 | 2011-08-17 | 株式会社日立製作所 | Remaining life diagnosis method for bolts used at high temperatures |
-
2019
- 2019-07-12 CN CN201910628858.5A patent/CN110274835B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7499820B1 (en) * | 2005-06-30 | 2009-03-03 | Storage Technology Corporation | Method for generating a performance metric for a tensilized tape |
| CN105259035A (en) * | 2015-10-26 | 2016-01-20 | 中国石油大学(华东) | Method for establishing rock material ageing and elastic-plastic mechanics constitutive model |
| CN106198259A (en) * | 2016-07-05 | 2016-12-07 | 辽宁工程技术大学 | A kind of method determining rock monsteady state creep parameter |
| CN107748111A (en) * | 2017-10-13 | 2018-03-02 | 华北水利水电大学 | A kind of determination method of rock mass discontinuity Long-term Shear Strength |
| CN108843303A (en) * | 2018-07-19 | 2018-11-20 | 西南石油大学 | A kind of casing damage in oil-water well prediction technique based on mud stone creep model |
| CN109187199A (en) * | 2018-09-18 | 2019-01-11 | 中国石油大学(华东) | The viscoelasticity theory analysis method of anchored rock mass creep properties under uniaxial compression |
| CN109885980A (en) * | 2019-03-29 | 2019-06-14 | 中南大学 | Determine that Complete Damage Process constitutive model is sheared at the joint of yield point based on stress difference |
| CN109902444A (en) * | 2019-03-29 | 2019-06-18 | 中南大学 | A method of prediction wing crack propagation path |
Non-Patent Citations (2)
| Title |
|---|
| 不同加载路径下盐岩蠕变力学特性与盐岩储气库长期稳定性研究;王军保;《中国博士学位论文全文数据库，工程技术Ⅱ辑》;20130515(第5期);第67-71页 * |
| 岩石非线性黏弹塑性蠕变模型研究;佘学成;《岩石力学与工程学报》;20091031;第28卷(第10期);第2006-2011页 * |
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