CN107505204B - A method of damage constructive model of rock mass is established based on least energy consumption principle - Google Patents
A method of damage constructive model of rock mass is established based on least energy consumption principle Download PDFInfo
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Abstract
The present invention discloses a kind of method for establishing damage constructive model of rock mass based on least energy consumption principle, comprising: derives damage evolution equation based on least energy consumption principle；Damage evolution equation is combined to construct rock constitutive model under continuous damage theory frame；Derive the theory relation of rock triaxial compression test deformation parameter and model parameter, conventional triaxial compression test under different confining pressures is carried out to rock, obtains stress-axial direction of sample under corresponding confining pressure, the mechanical strength parameter of radial strain relation curve and rock sample and strain parameter；Damage threshold is determined by test result and recognizes model parameter.The dilatation starting characteristic of models coupling rock in the present invention determines the damage threshold in damage of rock Evolution, the model of proposition can preferably reflect nonlinear mechanics character of the rock material under complex stress condition, especially consider that the constitutive model after damage threshold influences is higher to the fitting precision for surrendering section after rock material, there is very big reference significance and applying value to the rock engineering safety analysis under complex stress condition.
Description
Technical field
The present invention relates to a kind of methods for establishing damage constructive model of rock mass based on least energy consumption principle, belong to geotechnical engineering
Technical field.
Background technique
The three-dimensional stress environment of very long geological changes process and complexity makes rock interior produce a large amount of discontinuous and shapes
The microdefects such as the irregular crack gap of state, micro-crack, joint, mechanical response of the microdefect under different stress conditions determine it
With significant macro non-linear mechanical characteristic.A large amount of high rock slopes and large underground hole excavation project practice have shown that, rock
The Research on Mechanical Properties of stone is particularly important to the safe design of geotechnical structure and stability analysis.Therefore, it establishes and is able to reflect rock
The constitutive model of nonlinear mechanics characteristic of the stone under complex stress condition is always one of the research hotspot of ground circle.
Based on effective stress concept and J.Lemaitre equivalent strain hypothesis, passes through continuous damage theory and introduce statistics rule
Rule, establishes a kind of important method that Statistical Damage Constitutive Model For Rock has developed into study of rocks constitutive relation.But rock becomes
Shape damage is not only influenced by the microdefect of material internal random distribution, also closely related with stress state suffered by rock micro-unit,
Thus there is certain limitation.
The essence of rock deformation and failure is that its internal energy dissipates and the overall process of release, energy dissipation be damage of rock by
The internally-powered of development is walked, therefore, when studying the nonlinear constitutive relation of rock under complex stress condition, scholars are can not backheating
Under mechanical frame, damage of rock EVOLUTION EQUATION is derived based on energy dissipation basic principle and establishes the rock of consideration energy dissipation
This structure of elastic damage, the weakening strength process of rock material can be reflected by defining damage variable more from energy dissipation measuring angle, still
Rarely have scholar that least energy consumption principle is applied to the foundation of damage of rock EVOLUTION EQUATION, and the damage sheet established based on energy principle
The rarer influence for considering damage threshold in structure model.
Summary of the invention
Goal of the invention: the present invention is accurate description Rock Nonlinear constitutive relation and solves the deficiency of above-mentioned existing theory,
Propose a kind of method that damage constructive model of rock mass is established based on least energy consumption principle, this method from energy principle, according to
According to damage of rock develop in energy dissipation process meet the objective law of least energy consumption principle, introduce rock and unify energy surrender
Criterion establishes the new lesions constitutive model based on least energy consumption principle as energy consumption constraint condition, and model includes that parameter is few
And determine that parameter makes model parameter have physical significance according to indoor experimental data, consider damage threshold to damage evolution law
Influence after, ensure that model to after rock surrender section fitting precision.
Technical solution: a method of damage constructive model of rock mass is established based on least energy consumption principle, comprising the following steps:
Step 1: derive damage evolution equation based on least energy consumption principle: the damage development of rock interior is to meet minimum
The energy dissipation process for the principle that consumes energy, it is assumed that by unique consumption of the irreversible strain as deformation and failure caused by damage
Energy mechanism, derives damage of rock EVOLUTION EQUATION according to least energy consumption principle；
Step 2: building damage constructive model of rock mass: according to isotropism basic assumption, under continuous damage theory frame
Construct damage constructive model of rock mass in conjunction with damage evolution equation, and derive rock conventional triaxial compression test deformation parameter with
The theory relation expression formula of model parameter；
Step 3: indoor ordinary triaxial test is carried out to rock: stress-axis of rock to be measured is obtained by laboratory test
To, radial strain relation curve, processing obtains bulk strain-axial strain relation curve, and determines rock sample according to test data
Mechanical strength parameter and strain parameter；
Step 4: parameter identification and damage threshold determine: recognizing model parameter according to test result, consider the dilatation of rock
Starting characteristic determines damage threshold by bulk strain-axial strain relation curve stationary point, establishes the rock for considering that damage threshold influences
Stone Damage Constitutive Model.
Further, in said step 1, the damage development of rock interior is the energy consumption for meeting least energy consumption principle
The process of dissipating, can determine as follows rock material damage evolution equation:
(1) the energy absorbing device expression formula as caused by damage of rock is provided according to the law of thermodynamics；
(2) the constraint condition F (σ of damage of rock energy consumption process is determined based on rock stress-strain stress relation1,σ3), based on each
The specific function representation that damage variable is determined with least energy consumption principle is assumed to same sex damage；Consider the dilatation starting of rock material
Characteristic is introduced into damage threshold concept into damage evolution equation formula, and the damage development of rock energy consumption damage process has so been determined
Equation；
Irreversible strain rate caused by damagingAs unique energy consumption mechanism during the rock failure mechanism of rock, according to strain
The principle of equal effects, it is assumed that rock is isotropic elastoplastic damage and load is undertaken by non-damaged portion rock material, fixed in conjunction with broad sense Hooke
Rule, determines any time rock failure mechanism of rock strain rate as caused by damaging parameter D (t)It is expressed as
In formula: σi, σj, σkFor the stress of 3 principal direction of stress；υ is material Poisson ratio；E0It is first before damage of rock
Beginning elasticity modulus, power consumption rate caused by defining damage of rock according to the law of thermodynamics are
In formula: σiFor act on rock unit 3 principal direction of stress nominal principal stress,It can not caused by damage
Inverse strain rate；
Unloading test (σ is added for rock normal triaxial1>σ2=σ3), power consumption rate expression formula is reduced to
υ is material Poisson ratio, is based on rock stress-strain stress relation, introduces rock and unifies energy yield criterion as rock
Constraint condition F (the σ of sample damage energy consumption process1,σ3), it is represented by corresponding to the constraint condition under normal triaxial stress path
In formula: α and β is rock material parameter, and shear strain can be closed with the numerical value of volumetric energy when characterizing initial yield
System；For internal friction angle；G and K is modulus of shearing and bulk modulus；According to least energy consumption principle: material is in energy consumption damage process
Any time t, power consumption rate Ψ should be in the corresponding constraint condition F (σ that consumes energy1,σ3) under take stay value, introduce Lagrange multiplier undetermined
λ*After be represented byAdded in rock ordinary triaxial test with constant displacement rate control
When load, rock sample axial strain is directly proportional to the time, can set t=K1ε1, wherein K1To load parameter, enableConsider damage
Hurting threshold value influences and arranges to derive that damage variable is
In formula: ε0For damage threshold strain； It is the relevant parameter for characterizing material property with c, determines the above ginseng in combination with laboratory test results
Number.
Further, in the step 2: according to strain equivalence principle, considering that rock is isotropic elastoplastic damage and outer lotus
Load is undertaken by non-damaged portion rock material, and the effective stress σ ' that non-damaged portion material is borniStill meet broad sense elasticity
Hooke's law, then under continuous damage theory frame, the Damage Constitutive of rock material is expressed as
σi=E0εi(1-D)+v(σ1+σ2+σ3-σi) (i=1,2,3)
In formula: D is damage variable；σiFor nominal principal stress；υ is material Poisson ratio, and the damage brought into step 1 is drilled
Change equation, derives that damage of rock this structure based on least energy consumption principle is expressed as
In formula: ε0For damage threshold strain, model parameterIt need to derive and determine in conjunction with results of triaxial compressive test with c；σ1t
Axial deviatoric stress is surveyed for test, is expressed as σ1t=σ1-σ3, i.e., practical axial apparent stress σ1With confining pressure σ3Difference.
Further, in the step 3, the cutting of sillar undisturbed is polished into upper and lower end face level, smooth-sided compression candles
Diameter is 50mm, is highly 100mm standard cylinder sample, applies confining pressure to predetermined value to rock sample by hydrostatic conditions and keeps steady
It is fixed, load is controlled using axial displacement, axial deviatoric stress to rock sample is applied to rock sample with 0.02mm/min rate and is destroyed, it is entire to add
During load, servo test macro automatically records the axial deviatoric stress value σ of application1t, axial strain ε1With radial strain ε3, finally
Calculate bulk strain εv.Show that stress-axial direction, radial strain relation curve and the axial strain-volume of rock sample are answered after processing
Become relation curve, and calculates the mechanical strength parameter E of rock sample0, internal friction angleWith Poisson ratio υ.
Further, in the step 4, the load-deformation curve of rock sample is analyzed, based on rock sample under low confining pressure
Strain softening characteristic, determine model parameter using the extremum characteristic of its load-deformation curveAnd c, i.e.,Wherein σs、ε1s、ε3sRock corresponds to load-deformation curve under respectively specific confining pressure
Deviatoric stress, axial strain and radial strain at peak point.Derive that model parameter is expressed as
In conjunction with the dilatation starting characteristic of rock material, the mechanical property that damage threshold is determined as corresponding rock material is started
Initial yield stress when reduction, i.e. volume dilatation starting point, according to the resulting bulk strain-axial direction of laboratory test in step 3
Strain curve determines that the axial strain at stationary point is damage threshold strain stress0。
The present invention compares the prior art, has the following beneficial effects:
(1) this method is nonlinear mechanics character of the accurate description rock material under complex stress condition, from energy original
Reason is set out, and damage of rock EVOLUTION EQUATION is derived with the extremum characteristic of energy absorbing device, to establish rock elasticity Damage Constitutive mould
Type opens a new route；
(2) mechanical property that damage threshold is defined as corresponding rock material is started to initial yield stress when reduction, energy
The weakening strength feature of deformation and failure is enough fully demonstrated, and the model for considering damage threshold influence is bent to after rock
The nonlinear constitutive relation fitting precision for taking section is higher, has very to the rock engineering Safety Evaluation Analysis under complex stress condition
Big reference significance and applying value.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is three axis servo test macro schematic diagram of rock needed for carrying out laboratory test in the present invention；
Fig. 3 is the breccia lava sample for laboratory test, wherein (a) 6MPa, (b) 8MPa, (c) 10MPa；
Fig. 4 is deviatoric stress-axial direction of the breccia lava under triaxial stress path, radial strain curve, wherein (a) σ3=
6MPa, (b) σ3=8MPa, (c) σ3=10MPa；
Fig. 5 is breccia lava bulk strain-axial strain trial curve；
Fig. 6 is the Damage Constitutive Model established using least energy consumption principle to the fitting result of indoor experimental data, wherein
(a)σ3=6MPa, (b) σ3=8MPa, (c) σ3=10MPa.
Specific embodiment
Combined with specific embodiments below, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention
Rather than limit the scope of the invention, after the present invention has been read, those skilled in the art are to various equivalences of the invention
The modification of form falls within the application range as defined in the appended claims.
As shown in Figure 1, a kind of method that damage constructive model of rock mass is established based on least energy consumption principle, including following step
It is rapid:
Step 1: derive damage evolution equation based on least energy consumption principle: the damage development of rock interior is to meet minimum
The energy dissipation process for the principle that consumes energy, it is assumed that by unique consumption of the irreversible strain as deformation and failure caused by damage
Energy mechanism, derives damage of rock EVOLUTION EQUATION according to least energy consumption principle；
Step 2: building damage constructive model of rock mass: according to isotropism basic assumption, under continuous damage theory frame
Construct damage constructive model of rock mass in conjunction with damage evolution equation, and derive rock conventional triaxial compression test deformation parameter with
The theory relation expression formula of model parameter；
Step 3: indoor ordinary triaxial test is carried out to rock: stress-axis of rock to be measured is obtained by laboratory test
To, radial strain relation curve, processing obtains bulk strain-axial strain relation curve, and determines rock sample according to test data
Mechanical strength parameter and strain parameter；
Step 4: parameter identification and damage threshold determine: recognizing model parameter according to test result, consider the dilatation of rock
Starting characteristic determines damage threshold by bulk strain-axial strain relation curve stationary point, establishes the rock for considering that damage threshold influences
Stone Damage Constitutive Model.
Method And Principle:
The damage and failure process of rock is a kind of process for consuming energy, regards the thermodynamics change procedure of system as one
Kind balance is broken, and the process of reconstruction, when generating damage in rock, current equilibrium state is broken, and energy dissipation tends to be steady
Periodically, system is in new equilibrium state again.Therefore, the damage development of rock is the energy dissipation mistake for meeting least energy consumption principle
Journey, using material in any time of energy consumption process, power consumption rate all takes this characteristic of instantaneous minimum value, so analyzes and derives
The concrete functional form of damage evolution equation of the rock under complex stress condition out.
Rock constitutive model accurate description material is damage threshold in the key of the nonlinear constitutive relation of rear surrender section
Accurate determination.The dilatation starting characteristic for analyzing rock, showing the damage development process of rock material, there are Thresholds, work as axis
Reach threshold epsilon to strain0After start to develop, strain in damage threshold ε0Preceding rock is in the linear elastic deformation stage, considers material
This dilatation characteristic is based on rock indoor triaxial compression test data, determines in conjunction with bulk strain-axial strain curve rule bent
Corresponding axial strain is damage threshold at line stationary point.
In said step 1, the damage development of rock interior is the energy dissipation process for meeting least energy consumption principle, can
Rock material damage evolution equation is determined as follows:
(1) the energy absorbing device expression formula as caused by damage of rock is provided according to the law of thermodynamics；
(2) the constraint condition F (σ of damage of rock energy consumption process is determined based on rock stress-strain stress relation1,σ3), based on each
The specific function representation that damage variable is determined with least energy consumption principle is assumed to same sex damage；Consider the dilatation starting of rock material
Characteristic is introduced into damage threshold concept into damage evolution equation formula, and the damage development of rock energy consumption damage process has so been determined
Equation；
Irreversible strain caused by damagingAs unique energy consumption mechanism during the rock failure mechanism of rock, according to strain equivalence
Principle, it is assumed that rock is isotropic elastoplastic damage and load is undertaken by non-damaged portion rock material, in conjunction with generalized Hooke law, really
Make any time rock failure mechanism of rock strain rate as caused by damaging parameter D (t)It is expressed as
In formula: σi, σj, σkFor the stress of 3 principal direction of stress；υ is material Poisson ratio；E0It is first before damage of rock
Beginning elasticity modulus, power consumption rate caused by defining damage of rock according to the law of thermodynamics are
In formula: σiFor act on rock unit 3 principal direction of stress nominal principal stress,It can not caused by damage
Inverse strain rate；
Unloading test (σ is added for rock normal triaxial1>σ2=σ3), power consumption rate expression formula is reduced to
υ is material Poisson ratio, is based on rock stress-strain stress relation, introduces rock and unifies energy yield criterion as rock
Constraint condition F (the σ of sample damage energy consumption process1,σ3), it is represented by corresponding to the constraint condition under normal triaxial stress path
In formula: α and β is rock material parameter, and shear strain can be closed with the numerical value of volumetric energy when characterizing initial yield
System；For internal friction angle；G and K is modulus of shearing and bulk modulus；According to least energy consumption principle: material is in energy consumption damage process
Any time t, power consumption rate Ψ should be in the corresponding constraint condition F (σ that consumes energy1,σ3) under take stay value, introduce Lagrange multiplier undetermined
λ*After be represented byAdded in rock ordinary triaxial test with constant displacement rate control
When load, rock sample axial strain is directly proportional to the time, can set t=K1ε1, wherein K1To load parameter, enableConsider damage
Hurting threshold value influences and arranges to derive that damage variable is
In formula: ε0For damage threshold strain； It is the relevant parameter for characterizing material property with c, determines the above ginseng in combination with laboratory test results
Number.
In the step 2: according to strain equivalence principle, considering rock for isotropic elastoplastic damage and external load is not by damaging
Traumatic part divides rock material to undertake, and the effective stress σ ' that non-damaged portion material is borniStill meet broad sense elasticity Hooke's law,
Then under continuous damage theory frame, the Damage Constitutive of rock material is expressed as
σi=Eoεi(1-D)+v(σ1+σ2+σ3-σi) (i=1,2,3)
In formula: D is damage variable；σiFor nominal principal stress；υ is material Poisson ratio, and the damage brought into step 1 is drilled
Change equation, derives that damage of rock this structure based on least energy consumption principle is expressed as
In formula: ε0For damage threshold strain, model parameterIt need to derive and determine in conjunction with results of triaxial compressive test with c；σ1t
Axial deviatoric stress is surveyed for test, is expressed as σ1t=σ1-σ3, i.e., practical axial apparent stress σ1With confining pressure σ3Difference.
In the step 3, for carrying out three axis servo test macro such as Fig. 2 institute of rock of laboratory test in the present invention
Show.Three axis servo test macro of rock includes axial bias servo loading system, confining pressure servo loading system, high-performance rubber
Set, axial displacement measuring appliance (LVDT), hoop strain meter and data sensor-based system.Axial bias servo loading system is used for foundation
Different loading methods, which is stablized, applies axial deviatoric stress；Confining pressure servo loading system is used to apply hydrostatic to the indoor rock sample of pressure
Pressure, and confining pressure is kept constant by sensor and SERVO CONTROL microcomputer；High-performance rubber case is for completely cutting off rock sample and test
Hydraulic oil in cabin prevents from being seeped into rock sample internal influence test accuracy in hydraulic oil, and does not constrain rock sample deformation；2 axial directions
Deviation meter (LVDT) is mounted in pressure chamber base for acquiring the axial displacement data of rock sample；Hoop strain meter is fixed on
In the middle part of rock sample, it is radially expanded and deforms with rock sample, for acquiring the deformation data of sample radially；The connection of data sensor system passes
Servo-controlled machines is arrived in sensor and SERVO CONTROL microcomputer, acquisition in real time and record data and feedback.
In the step 3, conventional triaxial compression test is carried out to breccia lava rock sample, by breccia lava original state
Sillar cutting is polished into that upper and lower end face is horizontal and height and diameter are than the standard cylinder sample for 2:1, it is of the invention in rock sample side light
Sliding, diameter 50mm is highly 100mm, as shown in Figure 3.Rock sample is installed in test apparatus pressure chamber, is pressed using servo-system
Hydrostatic conditions apply confining pressure to rock sample and to predetermined value and keep stable, are controlled and are loaded using axial displacement, with 0.02mm/
Min rate applies axial deviatoric stress to rock sample to rock sample and destroys, and automatically records institute by data sensor system in entire loading procedure
The axial deviatoric stress value σ of application1t, axial strain ε1Value and radial strain ε3Value arranges and calculates bulk strain εv=ε1+2ε3。
Deviatoric stress-axial strain of the breccia lava under different confining pressures, deviatoric stress-radial strain are drawn based on test data
Relation curve and axial strain-bulk strain relation curve distinguish as shown in Figure 4 and Figure 5,4 curve straightway of analysis chart, arrange
The mechanical strength parameter E of rock sample is calculated0, internal friction angleWith Poisson ratio υ, determine to correspond to the peak under different confining pressures
Intensity σ at values, axial strain ε1sWith radial strain ε3s；Bulk strain-axial strain relationship determines curve according to figure 5
Corresponding damage threshold strain stress at stationary point0。
In the step 4, based on the strain softening feature that rock sample in Fig. 4 shows under low confining pressure, the present invention is based on angles
Deviatoric stress-strain curve extremum characteristic of gravel lava recognizes model parameterAnd c, it should meet at peak of curve
Bring the peak strength σ that laboratory test obtains intos, peak value axial direction strain stress1sWith peak value radial strain ε3s, arrange and derive
Show that model parameter is
Model parameter is recognized by indoor threeaxis test results and brings damage constructive model of rock mass obtained in step 2 into,
The breccia lava Damage Constitutive Model parameter obtained is as shown in table 1；Based on above-mentioned Damage Constitutive Model to rock sample nonlinear mechanics
Behavior carries out model, obtains the theory relation curve of breccia lava Damage Constitutive Model as shown in fig. 6, by theoretical curve and examination
Curve comparison is tested, the theoretical constitutive relation under three groups of confining pressures and laboratory test curve coincide substantially, show former based on minimum energy dissipation
The damage constructive model of rock mass that reason is established preferably can load answering for each stage by simulation rock before the peak under complex stress condition
Power-strain stress relation especially reflects the nonlinear mechanics characteristic that section is surrendered after rock preferable.
Damage constructive model of rock mass parameter value of the table 1 based on least energy consumption principle
Present invention firstly provides the methods for establishing damage constructive model of rock mass based on least energy consumption principle, according to minimum energy dissipation
Principle derives damage of rock EVOLUTION EQUATION with the extremum characteristic of energy absorbing device, to establish rock in three-dimensional stress item
Damage Constitutive Model under part using laboratory triaxial compression test identification model parameter and determines that damage threshold strains；Compared to
Common damage constructive model of rock mass, the model in the present invention defines damage variable from energy dissipation measuring angle can be preferably anti-
Reflect the weakening strength process of rock material；Model in the present invention is few comprising parameter and determines that parameter makes according to indoor experimental data
Obtaining model parameter has physical significance；The dilatation starting characteristic of models coupling rock in the present invention determines that damage of rock develops and advises
Damage threshold in rule can preferably reflect influence of the damage threshold to damage evolution law, especially consideration damage threshold shadow
Constitutive model after sound is higher to the fitting precision for surrendering section after rock material, to the rock engineering safety under complex stress condition
Analysis has certain reference significance.
Claims (2)
1. a kind of method for establishing damage constructive model of rock mass based on least energy consumption principle, which comprises the following steps:
Step 1: derive damage evolution equation based on least energy consumption principle: the damage development of rock interior is to meet minimum energy dissipation
The energy dissipation process of principle, it is assumed that by unique energy consumption machine of the irreversible strain as deformation and failure caused by damage
System, derives damage of rock EVOLUTION EQUATION according to least energy consumption principle；
Step 2: it building damage constructive model of rock mass: according to isotropism basic assumption, is combined under continuous damage theory frame
Damage evolution equation constructs damage constructive model of rock mass, and derives rock conventional triaxial compression test deformation parameter and model
The theory relation expression formula of parameter；
Step 3: indoor ordinary triaxial test is carried out to rock: stress-axial direction, the diameter of rock to be measured are obtained by laboratory test
To strain curve, processing obtains bulk strain-axial strain relation curve, and the mechanics of rock sample is determined according to test data
Intensive parameter and strain parameter；
Step 4: parameter identification and damage threshold determine: recognizing model parameter according to test result, consider the dilatation starting of rock
Characteristic determines damage threshold by bulk strain-axial strain relation curve stationary point, establishes the rock damage for considering that damage threshold influences
Hurt constitutive model；
In said step 1, the damage development of rock interior is the energy dissipation process for meeting least energy consumption principle, by as follows
Step determines rock material damage evolution equation:
(1) the energy absorbing device expression formula as caused by damage of rock is provided according to the law of thermodynamics；
(2) the constraint condition F (σ of damage of rock energy consumption process is determined based on rock stress-strain stress relation1, σ3), based on each to same
Property damage assume and least energy consumption principle determines the specific function representation of damage variable；It is special to consider that the dilatation of rock material originates
Property, damage threshold concept is introduced into damage evolution equation formula, and the damage development side of rock energy consumption damage process has so been determined
Journey；
Irreversible strain rate caused by damagingAs unique energy consumption mechanism during the rock failure mechanism of rock, according to strain equivalence original
Reason, it is assumed that rock is isotropic elastoplastic damage and load is undertaken by non-damaged portion rock material, in conjunction with generalized Hooke law, is determined
Any time rock failure mechanism of rock strain rate as caused by damaging parameter D (t) outIt is expressed as
In formula: σi, σj, σkFor the stress of 3 principal direction of stress；υ is material Poisson ratio；E0For the initial bullet before damage of rock
Property modulus, power consumption rate caused by defining damage of rock according to the law of thermodynamics are
In formula: σiFor act on rock unit 3 principal direction of stress nominal principal stress,It is irreversible caused by damage to answer
Variability；
Unloading test (σ is added for three axis of rock1> σ2=σ3), power consumption rate expression formula is reduced to
Based on rock stress-strain stress relation, introduces rock and unify constraint of the energy yield criterion as rock sample damage energy consumption process
Condition F (σ1, σ3), it is expressed as corresponding to the constraint condition under normal triaxial stress path
In formula: α and β is rock material parameter, and shear strain can be with the numerical relation of volumetric energy when characterizing initial yield；
For internal friction angle；G and K is modulus of shearing and bulk modulus；According to least energy consumption principle: material is any energy consumption damage process
Moment t, power consumption rate Ψ should be in the corresponding constraint condition F (σ that consumes energy1, σ3) under take stay value, introduce Lagrange multiplier λ undetermined*Table afterwards
It is shown asWhen in rock ordinary triaxial test with the load of constant displacement rate control, rock
Sample axial strain is directly proportional to the time, if t=K1ε1, wherein K1To load parameter, enableConsider that damage threshold influences
And it arranges and derives that damage variable is
In formula: ε0For damage threshold strain； It is the relevant parameter for characterizing material property with c, determines the above ginseng in conjunction with laboratory test results
Number；
In the step 2: according to strain equivalence principle, considering rock for isotropic elastoplastic damage and external load is by non-pars affecta
Rock material is divided to undertake, and the effective stress σ ' that non-damaged portion material is borniStill meet broad sense elasticity Hooke's law, then exists
Under continuous damage theory frame, the Damage Constitutive of rock material is expressed as
σi=E0εi(1-D)+υ(σ1+σ2+σ3-σi) (i=1,2,3)
In formula: D is damage variable；σiFor nominal principal stress；υ is material Poisson ratio, brings the damage development side in step 1 into
Journey derives that damage of rock this structure based on least energy consumption principle is expressed as
In formula: ε0For damage threshold strain, model parameterIt need to derive and determine in conjunction with results of triaxial compressive test with c；σ1tFor examination
The axial deviatoric stress of actual measurement is tested, σ is expressed as1t=σ1-σ3, i.e., practical axial apparent stress σ1With confining pressure σ3Difference；
In the step 4, the load-deformation curve of rock sample is analyzed, the strain softening characteristic based on rock sample under low confining pressure,
Model parameter is determined using the extremum characteristic of its load-deformation curveAnd c, i.e.,Its
Middle σs、ε1s、ε3sUnder respectively specific confining pressure rock correspond to load-deformation curve peak point at deviatoric stress, axial strain and
Radial strain derives that model parameter is expressed as
In conjunction with the dilatation starting characteristic of rock material, the mechanical property that damage threshold is determined as corresponding rock material is started to weaken
When initial yield stress, i.e. volume dilatation starting point, according to the resulting bulk strain-axial strain of laboratory test in step 3
Curve determines that the axial strain at stationary point is damage threshold strain stress0。
2. the method for establishing damage constructive model of rock mass based on least energy consumption principle as described in claim 1, which is characterized in that
In the step 3, the cutting of sillar undisturbed is polished into upper and lower end face level, the diameter of smooth-sided compression candles is 50mm, is highly
100mm standard cylinder sample applies confining pressure to rock sample by hydrostatic conditions and to predetermined value and keeps stable, using axial displacement control
System load applies axial deviatoric stress to rock sample to rock sample with 0.02mm/min rate and destroys, in entire loading procedure, servo test
System automatically records the axial deviatoric stress value σ of application1t, axial strain ε1With radial strain ε3, finally calculate bulk strain εv,
Stress-axial direction, radial strain relation curve and axial strain-bulk strain relation curve of rock sample are obtained after processing, and are calculated
The mechanical strength parameter E of rock sample out0, internal friction angleWith Poisson ratio υ.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104361211A (en) * | 2014-10-24 | 2015-02-18 | 中冶长天国际工程有限责任公司 | Construction and application method of statistical damage constitutive model of rock |
| CN104949868A (en) * | 2015-05-21 | 2015-09-30 | 中国矿业大学 | Blasting damaged rock sample preparation and micro-macro combined damage degree determination method |
| CN105181435A (en) * | 2015-10-15 | 2015-12-23 | 中国石油大学(华东) | Method of establishing elastic-plastic mechanical constitutive model made of rock material |
-
2017
- 2017-07-12 CN CN201710566746.2A patent/CN107505204B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104361211A (en) * | 2014-10-24 | 2015-02-18 | 中冶长天国际工程有限责任公司 | Construction and application method of statistical damage constitutive model of rock |
| CN104949868A (en) * | 2015-05-21 | 2015-09-30 | 中国矿业大学 | Blasting damaged rock sample preparation and micro-macro combined damage degree determination method |
| CN105181435A (en) * | 2015-10-15 | 2015-12-23 | 中国石油大学(华东) | Method of establishing elastic-plastic mechanical constitutive model made of rock material |
Non-Patent Citations (3)
| Title |
|---|
| HOW TO USE DAMAGE MECHANICS;Jean LEMAITRE;《Nuclear Engineering and Design》;19841230(第80期);233-245 * |
| 基于岩石统一能量屈服准则的硬岩损伤模型;周辉等;《岩土力学》;20160330;第37卷(第3期);609-614 * |
| 基于能量原理盐岩的损伤本构模型;郭建强;《中南大学学报(自然科学版)》;20131230;第44卷(第12期);5046-5050 * |
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