CN105259035A - Method for establishing rock material ageing and elastic-plastic mechanics constitutive model - Google Patents

Abstract

The invention discloses a method for establishing a rock material ageing and elastic-plastic mechanics constitutive model. The method includes the steps that the triaxial short-long term test result of rock is used as the basis first, and the volumetric strains of a rock test piece under different test conditions are calculated; by drawing a stress-axial and lateral strain relation curve and a stress-volumetric strain relation curve, the yield criterion, the non-associated flow rule and the hardening criterion of the rock are determined, and an elastic-plastic mechanics model is established; then by combining material micro and fine damage attenuation ageing evolution dynamic equilibrium, the micro and fine ageing damage rule of the rock is determined, the model is popularized, a relation matrix of strain increment and stress increment at the ageing-elasticoplastic deformation stage is established, and accordingly the rock material ageing and elastic-plastic mechanics constitutive model is obtained. According to the model, the mechanics significance is definite, the expression is unique, the number of parameters is small and can be obtained based on the test results, hence, solving uniqueness and accuracy are guaranteed, and wide applicability and expansibility are achieved.

Description

A kind of construction method of rock material timeliness-plasto-elasticity constitutive model

Technical field

The present invention relates to the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model.

Background technology

Under load action, rock deformation has obvious time effect, also known as aging characteristic, closely related with engineering long-time stability.At present relevant with rock as petroleum engineering, mining engineering, hydraulic engineering and nuclear waste disposal engineering etc., the length of service all reaches tens to the centuries.Therefore, conduct a research for the evaluation of engineering long-time stability to rock timeliness-elastoplastic mechanical performance and safely there is important theory significance and construction value.

Constitutive model structure is the further investigation to rock mechanics, is also the key link connecting shop experiment, theoretical analysis and analogue simulation.This structure of mechanics not only can be described rock deformation mechanism accurately, also should reflect its internal injury failure mechanism.Therefore, the key content that timeliness-plasto-elasticity constitutive model is the short long-term mechanical characteristic of study of rocks is built.

Constantly perfect in recent years along with testing equipment and theory of mechanics, structure rock timeliness mechanic constitutive model obtains and develops rapidly, many scholars based on measured test data and binding isotherm mechanics principle, propose some timeliness mechanic constitutive model, but all have some limitations; Existing timeliness rheo-mechanics principle comprise empirical model, composition element model, interior time model and damage and fracture model.

Empirical model is based on Mineral rheology mechanical test, directly rheological curve empirical equation is given matching, thus sets up mathematic(al) experience formula model.Though this model simple, intuitive, there is significant limitation and error; Being mainly reflected in empirical model is only approach on mathematical formulae, and model parameter physical significance is also indefinite, cannot reflect the physical mechanics mechanism of the rock failure mechanism of rock, therefore be difficult to promote the use of, not possess applicability widely;

Component models rock is abstracted into a series of spring, damper and slider component to describe rheological test curve, think that said elements can be described rock elasticity, plasticity and stickiness, carry out the modes such as series, parallel to combine it, derive timeliness stream dependent element model.This model applicability, higher than empirical model, uses comparatively general at home, but also has some limitations and deficiency; Major embodiment component models only can reflect Mineral rheology phenomenon, can not describe sex change and destroy essence; And only can reflect rock viscoelasticity characteristic, accelerating rheology characteristic cannot be described; Therefore also do not possess applicability widely;

Endochronic theory model is based on irreversible thermodynamics law, by selecting endochronic time variable, utilize the theory of plasticity without yield surface, plastic yield levels of accumulation and material behavior endochronic time scale is introduced in rock deformation, and replaced the irreversible transformation history of Newtonian time and then tolerance rock, obtain rock evolution equation of internal variables thus, its constitutive relation of deriving.Document one " constitutive model of soft rock based on endochronic theory " (old Yuanjiang, Pan Changliang, Cao Ping, Wang Wenxing. China YouSe Acta Metallurgica Sinica, 2003,13 (3): 736-742) propose Mineral rheology constitutive model based on endochronic theory, but this model theory is comparatively complicated, and parameter is more, therefore to be more difficultly applied in the long-term mechanical characteristic analysis of actual rock engineering, to have some limitations;

Damage and fracture model destroys result based on grand mesoscale experiments and proposes, and mainly comprises rock microscopic damage model and macroscopic damage model.Micromechanical damage model is with based on rock interior micro-crack extension and then to construct that crack density and macroscopic damage variable close be core research contents; Macroscopic damage model selects macrovariable to describe damage variable, builds damage rheology model by equivalent stress principle.Document two " rock-soil material stream becomes and engineer applied " (Sun Jun. Beijing: China Construction Industry Press, 1999) think that Rheological Deformation damage causes, belong to the macroscopic view reflection of rock interior structure micro-variations, under higher stress, rock interior produces new damage and accumulates gradually, and then produce a large amount of micro-mechanical model and expand, present rheological characteristics.But this model is difficult to build three-dimensional constitutive relation, is not inconsistent under causing all being in three-dimensional stress effect with Practical Project rock; Therefore be applied to the long-term mechanical characteristic analysis of Practical Project and certainly will cause certain error.

In sum, still there is certain defect in the method for existing structure rock material timeliness-plasto-elasticity constitutive model.Rock material elasto-plastic Constitutive Model is expand according to the classical elastic plastic theory of metal material to obtain the earliest, comprises elasticity and the theory of plasticity; Theory of elasticity is mainly based on Hooke's law (Hooke'slaw) and then describe linear strain-stress relation; The theory of plasticity adopts incremental theory of plasticity usually, namely with the relation between incremental form reflection stress increment and strain increment.Rock secular distortion comprises significant elastic-plastic deformation, its essence can think the irreversible thermodynamics process that an energy dissipation, thermodynamic entropy increase, therefore, based on the short test of long duration data in indoor, in conjunction with rational yield function, plastic potential function and structural damage function, proposing a kind of simple to operate, applied widely and method that the is constitutive model of structure rock material timeliness-elastoplastic mechanical performance that accuracy is high is a problem in the urgent need to address.

Summary of the invention

The present invention is in order to solve the problem, propose the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model, this method with the short long-term test results of rock three axle for foundation, consider the yield criteria of rock, non-associated flow law and sclerosis criterion, on the basis building elastic and plastic mechanics model, bond material microscopic damage decay timeliness Evolution dynamics balance, construct the timeliness-strain increment in elastic-plastic deformation stage and the relational matrix of stress increment, obtain rock material timeliness-plasto-elasticity constitutive model, this model mechanics meaning is clear and definite, expression formula is unique, parameter is less and all can obtain based on test findings, ensure that thus and ask uniqueness of solution and accuracy, also there is applicability and extendability widely.

To achieve these goals, the present invention adopts following technical scheme:

A construction method for rock material timeliness-plasto-elasticity constitutive model, comprises the following steps:

(1) the conventional Rock Mechanics Tests of three axle short-terms are carried out to rock sample to be measured, measure and record axial, the lateral strain changing value with stress of rock sample; Three axial length phases streams are carried out to rock sample to be measured and becomes Rock Mechanics Test, to measure and axial, the lateral strain of recording rock sample are worth over time, calculate the short-term of rock sample and the bulk strain of test of long duration respectively;

(2) and lateral strain change axially omnidistance according to the rock sample of the conventional Rock Mechanics Test record of three axle short-terms, draw stress-axis, lateral strain relation curve, obtain the surrender starting point stress that peak stress under different confined pressure effect and rock are transformed to plasticity by elasticity;

(3) determine deviatoric stress q respectively according to the peak stress obtained and surrender starting point stress, in conjunction with the mean stress p of rock sample, build p-q curve respectively, determine yield failure criterion and the sclerosis criterion of rock material belonging to test specimen;

(4) according to the bulk strain of the rock sample of the conventional Rock Mechanics Test calculating of three axle short-terms, draw stress-bulk strain relation curve, under obtaining different confined pressure effect, rock volume is by compressing the boundary intensity transformed to dilatation, deviatoric stress q is determined according to it, in conjunction with the mean stress p of rock sample, build p-q curve, determine the unlinkability flowing criterion of rock material belonging to test specimen;

(5) according to thermodynamics elastic plastic theory, in conjunction with the conventional stress-strain curve of rock of short-term, peak stress, surrender initial stress and boundary intensity, select the mechanics parameter value of rock Elastic-plastic Constitutive equation, determine elasto-plastic Constitutive Model;

(6) the omnidistance axial and lateral strain change of rock sample of Rock Mechanics Test record is become according to three axial length phase streams, m-axial, lateral strain relation curve during drafting, the stage is become according to its decay stream change stage and steady state flow, introduce material structure damage variable, determine material microscopic damage decay evolution criterion;

(7) theoretical according to microscopic damage, in conjunction with m-strain curve during long-term stream change rock, select the mechanics parameter value of rock aging characteristic constitutive equation, the damage of rock secular distortion decay evolution criterion is extended in the elasto-plastic Constitutive Model obtained, determines timeliness-elasto-plastic Constitutive Model.

In described method, also comprise step (8) and utilize controller to carry out rock mechanics experiment emulation, simulated experiment effect, verify and improve timeliness-elasto-plastic Constitutive Model.

In described step (1), rock sample is cylindrical.

Preferably, the height of rock sample and diameter are than being 2:1.

In described step (1), the concrete grammar of the conventional Rock Mechanics Test of three axle short-terms is: under constant temperature and humidity condition, apply confined pressure σ to rock sample ₃to stable, secondly keep confined pressure constant, deviatoric stress σ is carried out to test specimen ₁-σ ₃the rock mechanics experiment progressively loaded, test is omnidistance measures axial strain ε ₁with lateral strain ε ₂change, finally calculate bulk strain ε _v.

In described step (1), apply deviatoric stress mode in three axial length phases stream change Rock Mechanics Test and be divided into single-stage to load and hierarchical loading, wherein, single-stage deviatoric stress loading method is: keep confined pressure σ ₃constant, a deviatoric stress σ is applied to test specimen ₁-σ ₃to stable, axial strain stress under measuring this deviatoric stress ₁with lateral strain ε ₂over time, bulk strain ε is finally calculated _v;

Classification deviatoric stress loading method is: keep confined pressure σ ₃constant, first apply initial deviator stress (σ ₁-σ ₃) ₁to stable, axial strain stress under measuring this deviatoric stress ₁with lateral strain ε ₂over time, to be deformed stable after carry out second level stress (σ ₁-σ ₃) ₂load; And then apply third level stress (σ ₁-σ ₃) ₃, by that analogy until test specimen generation rheodestruction.

Preferably, in classification deviatoric stress loading method, initial deviator stress (σ ₁-σ ₃) ₁get short-term normal experiment rock peak value deviatoric stress (σ ₁-σ ₃) _p10%-25%, second level stress (σ ₁-σ ₃) ₂get short-term normal experiment rock peak value deviatoric stress (σ ₁-σ ₃) _p35%-50%, third level stress (σ ₁-σ ₃) ₃get short-term normal experiment rock peak value deviatoric stress (σ ₁-σ ₃) _p60%-75%.

Preferably, the deviatoric stress numerical value of single-stage deviatoric stress loading method gets short-term normal experiment rock peak value deviatoric stress (σ ₁-σ ₃) _p75%.

In described step (3), the confirmation method of yield failure criterion is: based on the different confined pressure σ of short-term conventional test ₃under rock peak stress σ _1p, with rock sample now mean stress p, deviatoric stress q=σ _1p-σ ₃for condition, make peak stress p-q relation curve, according to the shape of this p-q curve, determine the yield failure criterion of this rock applicable.

In described step (3), the defining method of sclerosis criterion is: based on the different confined pressure σ of short-term conventional test ₃under rock plasticity surrender starting point stress σ _1y, with the mean stress p of rock sample, deviatoric stress q=σ _1y-σ ₃for condition, make surrender initial stress p-q relation curve, according to the shape of this p-q curve, determine the hardening Plastic criterion of this rock applicable.

In described step (4), the defining method of flow rule is: based on the different confined pressure σ of short-term conventional test ₃the boundary intensity σ of lower rock compressed and dilatation _1v, with the mean stress p of rock sample, deviatoric stress q=σ _1v-σ ₃for condition, make boundary intensity p-q relation curve, according to the shape of this p-q curve, determine the nonassociated plasticity flowing criterion of this rock applicable.

In described step (5), determine that the concrete grammar of Elastic-plastic Constitutive equation is: ε is by elastic strain ε in rock overall strain _ewith plastic strain ε _pcomposition, in conjunction with elastic-plastic mechanics theory, derives rock Elastic-plastic Constitutive equation; And based on the conventional stress-strain curve of rock of short-term, peak stress p-q curve, surrender initial stress p-q curve and boundary intensity p-q relation curve, determine the mechanics parameter value of equation.

In described step (6), aging characteristic is that the macroscopic view of damage decay Evolution dynamics equilibrium process on the micro-meso-scale of rock interior structure embodies, the shape of change and steady state flow varied curve is flowed based on decay, introducing can the characteristic of material mechanics damage variable of qualitative description micro-microscopical structure timeliness Damage Evolution, determine the microscopic damage decay evolution criterion that can describe rock secular distortion according to this damage variable, think that material deformation destruction characteristic produces change based on this damage criterion.

In described step (7), determine that the concrete grammar of timeliness-Elastic-plastic Constitutive equation is: be embodied in material ages deformation process by the damage of rock secular distortion decay evolution criterion, and extend to Elastic-plastic Constitutive equation, derive rock timeliness-Elastic-plastic Constitutive equation; And based on time the decay of m-strain curve and steady state flow become the stage, determine the timeliness parameter value of equation.

In the present invention, being meant to of popularization, by the characteristic of material mechanics that this timeliness changes, brings in the short-term elastic-plastic model originally not thought and consider that the time damages; Deriving is exactly utilize the same procedure building short-term elasto-plastic Constitutive Model, obtains the elastic and plastic mechanics model considering timeliness damage development, i.e. rock timeliness-Elastic-plastic Constitutive equation; For the determination of timeliness parameter, based on rheological test curve, it is exactly the relation curve of strain and time.

Short, the long-term mechanical test instrument of a kind of rock three axle, comprises confined pressure loader, bias voltage loader, axial strain measuring appliance, lateral strain measuring appliance, specimen holder and data transducer, and wherein, confined pressure loader is used for the applying of confined pressure and keeps constant; Bias voltage loader is used for the applying of bias voltage; Confined pressure loader, bias voltage loader all connect specimen holder; Axial strain measuring appliance is for measuring sample axial strain; Lateral strain measuring appliance is for measuring sample lateral strain; Both are all arranged at outside specimen holder; Specimen holder is for installing test specimen and being fixed, and data transducer connects specimen holder device, for gathering and transmitting test specimen axially and the change of lateral strain.

Beneficial effect of the present invention is:

(1) the present invention provides a kind of new method for accurately building rock material timeliness-plasto-elasticity constitutive model, this model is based on short, the long-term mechanical test of rock three axle, can build simple clear and definite and consider nonlinear strain and the stress increment relational matrix of timeliness damage, there is higher accuracy and applicability widely;

(2) yield criteria of rock material, unlinkability flow rule, sclerosis criterion and timeliness damage decay evolution criterion has been considered, well can reflect the short long-term plasto-elasticity behavior of rock material, think that its mechanical meaning is clear and definite, ensure that uniqueness and the accuracy of constitutive model;

(3) the present invention adopts unified theoretical logic method, first constructs rock Elastic-plastic Constitutive equation, and next is promoted this model in conjunction with fine sight timeliness defect theory, constructs rock timeliness-Elastic-plastic Constitutive equation; The method has certain novelty, and gained model has good extendability and applicability widely.

(4) model parameter set up is less, and all obtain by laboratory test results, simple and convenient, accuracy is higher, is easy to be applied to actual rock engineering and calculates and analyze.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the embodiment of the present invention;

Fig. 2 is short, the long-term mechanical test instrument of rock three axle required for the present invention;

Fig. 3 (a) is typical fragmented rock sample;

Fig. 3 (b) is typical fragmented rock sample;

Fig. 3 (c) is typical fragmented rock sample;

Fig. 4 fragmented rock triaxial stress-axis, lateral strain relation curve;

Fig. 5 fragmented rock initial yield surface, compression dilatation interphase and plastic yielding failure mechanics;

Fig. 6 (a) confined pressure 1.0MPa effect is fragmented rock axis, side direction and the time dependent creep curve of bulk strain down;

Fig. 6 (b) confined pressure 1.5MPa effect is fragmented rock axis, side direction and the time dependent creep curve of bulk strain down;

Fig. 6 (c) confined pressure 2.0MPa effect is fragmented rock axis, side direction and the time dependent creep curve of bulk strain down;

Fig. 7 fragmented rock hardening function and generalized plasticity shearing strain relation curve;

Fig. 8 fragmented rock short-term conventional elasto-plastic Constitutive Model analog result schematic diagram;

The lower fragmented rock of Fig. 9 (a) confined pressure 1.0MPa effect flows change timeliness-elasto-plastic Constitutive Model analog result schematic diagram for a long time;

The lower fragmented rock of Fig. 9 (b) confined pressure 1.5MPa effect flows change timeliness-elasto-plastic Constitutive Model analog result schematic diagram for a long time;

The lower fragmented rock of Fig. 9 (c) confined pressure 2.0MPa effect flows change timeliness-elasto-plastic Constitutive Model analog result schematic diagram for a long time;

Figure 10 sandstone initial yield surface, compression dilatation interphase and plastic yielding failure mechanics;

Figure 11 sandstone short-term elasto-plastic Constitutive Model analog result schematic diagram.

The lower sandstone of Figure 12 confined pressure 12.0MPa effect flows change timeliness-elasto-plastic Constitutive Model analog result schematic diagram for a long time.

Wherein, 1, constant confining pressure loader, 2, constant bias loader, 3, axial strain measuring appliance, 4, hoop strain measuring appliance, 5, specimen holder, 6, data transducer.

Embodiment:

Below in conjunction with accompanying drawing and embodiment, the invention will be further described.

As shown in Figure 1, a kind of construction method of rock material timeliness-plasto-elasticity constitutive model, comprises the following steps successively:

Step S1: rock engineering spot sampling, makes height with diameter than the cylinder specimen for 2:1; Test specimen is mounted in short, the long-term mechanical test instrument of rock three axle, and adjustment axis and lateral strain are to initial value;

Step S2: carry out the conventional rock mechanics experiment of three axle short-terms to test specimen, test is omnidistance measures axial strain ε ₁with lateral strain ε ₂with deviatoric stress σ ₁-σ ₃change; Calculation testing piece bulk strain thus; For cylinder specimen, bulk strain ε _v=ε ₁+ 2 ε ₂;

Step S3: carry out three axial length phase streams to test specimen and become rock mechanics experiment, test is omnidistance measures axial strain ε ₁with lateral strain ε ₂the change of t in time; Calculation testing piece bulk strain thus; For cylinder specimen, bulk strain ε _v=ε ₁+ 2 ε ₂;

Step S4: based on the conventional rock mechanics experiment of three axle short-terms, draw stress-axis, lateral strain relation curve, obtain different confined pressure σ ₃the peak stress σ of the lower rock of effect _1p, make peak stress p-q relation curve; For cylinder specimen, q=σ _1p-σ ₃, based on the shape of p-q curve, determine the yield failure criterion of rock;

Step S5: based on stress-axis, the lateral strain relation curve of step s4, obtain different confined pressure σ ₃the surrender starting point stress σ that the lower rock of effect is transformed to plasticity by elasticity _1y, make surrender initial stress p-q relation curve; For cylinder specimen, q=σ _1y-σ ₃, according to the shape of p-q curve, determine the hardening Plastic criterion of rock;

Step S6: based on the conventional rock mechanics experiment of three axle short-terms, draw stress-bulk strain relation curve, obtain different confined pressure σ ₃the lower rock volume of effect is by compressing the stress σ transformed to dilatation _1v, make boundary intensity p-q relation curve; For cylinder specimen, q=σ _1y-σ ₃, according to the shape of p-q curve, determine the nonassociated plasticity flowing criterion of rock;

Step S7: become rock mechanics experiment, m-axial, lateral strain relation curve during drafting based on three axial length phase streams, judges that the decay of this curve and steady state flow become the stage, introduces material time damage variable thus determine material microscopic damage decay evolution criterion;

Step S8: based on thermodynamics elastic plastic theory, in short-term conventional test process, ε is by elastic strain ε in rock overall strain _ewith plastic strain ε _pcomposition, derives rock Elastic-plastic Constitutive equation; And in conjunction with indoor short-term conventional test data, identification model parameter, checking and improved model.

Step S9: theoretical based on microscopic damage, in long-term rheological test process, ε is by elastic strain ε in rock overall strain _e, plastic strain ε _pwith timeliness strain stress _tcomposition, wherein elastic strain ε _ewith plastic strain ε _pfor instantaneous short-term strains, ε _tfor Long-term Aging strain; The damage of rock secular distortion decay evolution criterion is extended in the Elastic-plastic Constitutive equation in step S7, derives rock timeliness-Elastic-plastic Constitutive equation; And combine indoor long-term rheological test data, identification model parameter, finally adopt computerese to be achieved, checking and improved model.

Constitutive equation is exactly the relation obtaining stress and strain in rock, rock overall strain is strained by elastic strain, plastic strain and timeliness and forms, elastic strain can directly be obtained by Hooke's law (Hooke'slaw), and plastic strain and timeliness strain can be derived acquisition based on the criterion of above-mentioned acquisition.

Embodiment one:

For certain rock engineering fragmented rock, based on the short long-term rock mechanics experiment of three axles, build fragmented rock timeliness-plasto-elasticity constitutive model, carry out following operation:

(1) based on the on-the-spot core-drilling of China's certain engineering fragmented rock western, according to ISRM's proposed standard, height is prepared into diameter than the cylindric test specimen for 2:1; This routine fragmented rock test specimen diameter is 50mm, and height is 100mm, as shown in Fig. 3 (a), Fig. 3 (b) He Fig. 3 (c); Test specimen is mounted in the short long-term mechanical test instrument of rock three axle, as shown in Figure 2; And adjustment axis and lateral strain are to initial value, initial value is similar to 0;

(2) carry out the conventional rock mechanics experiment of three axle short-terms to test specimen, all tests are all carried out under constant temperature and humidity condition; First confined pressure is applied to predetermined value with loading speed 0.375MPa/min; Based on on-the-spot terrestrial stress condition, test confined pressure value is 1.0,1.5 and 2.0MPa; Secondly apply deviatoric stress with loading speed 0.375MPa/min to destroy to test specimen; Test is omnidistance measures axial strain ε ₁with lateral strain ε ₂with deviatoric stress σ ₁-σ ₃change; Finally, calculation testing piece bulk strain ε _v, bulk strain ε _v=ε ₁+ 2 ε ₂, ε ₁for on the occasion of, ε ₂for negative value.

(3) adopt stress load control model to carry out multistage stress grading to test specimen and load Creep Mechanics test, creep test is the one of rheological test; All tests are all carried out under constant temperature and humidity condition, belong to the triaxial creepage mechanical test of the confined pressures such as single sample, axial deviatoric stress hierarchical loading; First confined pressure is applied to predetermined value with loading speed 0.375MPa/min; Based on on-the-spot terrestrial stress condition, test confined pressure value is 1.0,1.5 and 2.0MPa; Secondly keep confined pressure constant, apply deviatoric stress to σ with loading speed 0.375MPa/min ₁=1.0MPa, and keep constant deviatoric stress 48 hours, measure stress σ ₁the lower axial strain stress of effect ₁with lateral strain ε ₂the change of t in time; To be deformed stable after carry out second level deviatoric stress σ ₂=1.75MPa stress loading; Repetitive operation; And then apply third level deviatoric stress σ ₃=2.5MPa; By that analogy until test specimen generation creep rupture; Test is omnidistance measures axial strain ε ₁with lateral strain ε ₂the change of t in time; Finally, calculation testing piece bulk strain ε _v, bulk strain ε _v=ε ₁+ 2 ε ₂, ε ₁for on the occasion of, ε ₂for negative value.

(4) based on the conventional rock mechanics experiment of three axle short-terms, stress-axis, lateral strain relation curve is drawn, as shown in Figure 4; Obtain different confined pressure σ ₃the lower rock peak stress σ of effect _1p, make rock peak stress p-q relation curve; For cylinder specimen, q=σ _1p-σ ₃.According to p-q curve plastic yielding face shape, as shown in Figure 5, determine that the yield failure criterion of this rock applicable is linear function:

$\left.\begin{array}{c}f=q+{\mathrm{A\α}}_p(p-C_0)=0\\ p=\frac{{\mathrm{\σ}}_{kk}}{3},q=\sqrt{3J_2}\\ J_2=\frac{1}{2}{S}_{ij}{S}_{ij},S_{ij}={\mathrm{\σ}}_{ij}-\frac{{\mathrm{\σ}}_{kk}}{3}{\mathrm{\δ}}_{ij}\end{array}\right\}---\left(1\right)$

Parameter p is mean stress, and q is deviatoric stress; Parameter C ₀initial cohesion and the angle of internal friction in material damage face is represented respectively, α with A _pfor material hardening function;

(5) based on Fig. 4 stress-axis, lateral strain relation curve, different confined pressure σ is obtained ₃the surrender starting point stress σ that the lower rock of effect is transformed to plasticity by elasticity _1y; Make rock yield stress p-q relation curve.For cylinder specimen, q=σ _1y-σ ₃.Surrender initial surface curve according to p-q, as shown in Figure 5, determine that the hardening Plastic criterion of this rock applicable is by generalized plasticity shearing strain γ _pchange in the power function that increases gradually:

$\left.\begin{array}{c}{\mathrm{\α}}_p=1-\left(1-{\mathrm{\α}}_p^0\right)e^{-{\mathrm{b\γ}}_p}\\ {\mathrm{\γ}}_p=\∫\sqrt{\frac{2}{3}{\mathrm{de}}_{ij}^p{\mathrm{de}}_{ij}^p},e^p={\mathrm{\ϵ}}^p-\frac{1}{3}{\mathrm{tr\ϵ}}^p{\mathrm{\δ}}_{ij}\end{array}\right\}---\left(2\right)$

Parameter for the initial plastic threshold values in shear yielding face; Parameter b determines material plasticity hardening ratio, controls the dynamic process of plasticity strengthening;

(6) based on the conventional rock mechanics experiment of three axle short-terms, draw stress-bulk strain relation curve, as shown in Figure 4, obtain different confined pressure σ ₃the lower rock volume strain of effect is converted into the stress σ of dilatation by compression _1v; Make rock boundary intensity p-q relation curve.For cylinder specimen, q=σ _1v-σ ₃.According to the curve that p-q compression transforms to dilatation, as shown in Figure 5, determine that this rock compressed applicable and dilatation separatrix are linear function:

$\stackrel{\‾}{f_s}=q+\mathrm{\η}I=0---\left(3\right)$

Parameter η is dilatancy and the interfacial slope of compression; Based on interphase, obtain the Plastic Flow criterion describing this rock:

$\left.\begin{array}{c}g=q-\mathrm{\η}Iln\left(\frac{I}{\stackrel{\‾}{I_0}}\right)=0\\ I=p+C_0\end{array}\right\}---\left(4\right)$

(7) become rock mechanics experiment based on three axial length phase streams, m-axial, side direction, volume flow change relation curve during drafting, as shown in such as Fig. 6 (a), Fig. 6 (b) He Fig. 6 (c); Obtain different confined pressure σ ₃decay and the steady state flow of the lower fragmented rock of effect become the stage, introduce time material time damage variable based on this:

$\mathrm{\ζ}\left(t\right)=\mathrm{\ζ}\left({\mathrm{\ϵ}}_{ij}^p\right(t),t)---\left(5\right)$

The soluble material volume unit of this variable is under effect of stress, and between solid particle, the relative damage change of fine sight surface of contact, also can reflect the dynamic process of material granule solubilizing reaction, belong to the standard value function depending on the description plastic yield of time variations.

Determine that material fine sight timeliness damage decay evolution criterion is thus:

$\frac{\∂\mathrm{\ζ}\left(t\right)}{\∂t}=\mathrm{\γ}(\stackrel{\‾}{\mathrm{\ζ}}-\mathrm{\ζ})---\left(6\right)$

the steady dissolution equilibrium state that between representative and material internal particle, the thermodynamic equilibrium state at fine sight surface of contact place is closely related, time t → ∞, suppose that material internal fine sight Structural Dynamics evolution process can describe according to internal balance state deviation, value namely by embody; γ represents the dissolution kinetics process of material granule plasticity shear polymer effect, is closely related with extraneous chemical physics factor, and the present invention ignores chemistry, temperature to the impact of mechanical characteristic, therefore γ is considered as constant; And sample equilibrium state can be by definition, depends on the stress intensity of applying, span and can damage the accurate side of decay evolution to timeliness by Laplace conversion and convolution theorem and carry out accurate definition, during time t=0, ζ (0)=0, obtains the accurate side of the decay evolution of timeliness damage accurately thus:

$({\mathrm{\ζ}}^{n+1}-{\mathrm{\ζ}}^n)=({\stackrel{\‾}{\mathrm{\ζ}}}^{n+1}-{\stackrel{\‾}{\mathrm{\ζ}}}^n)*(1-e^{-\mathrm{\γ}(t^{n+1}-t^n)})---\left(7\right)$

(8) based on thermodynamics elastic plastic theory, think that the overall strain ε of rock in short-term conventional test process is by elastic strain ε _ewith plastic strain ε _pcomposition, obtaining its stress increment is:

${\mathrm{d\σ}}_{ij}=C_{ijkl}^0({\mathrm{d\ϵ}}_{kl}-d\mathrm{\λ}\frac{\∂g}{\∂{\mathrm{\σ}}_{kl}})---\left(8\right)$

And based on agreement principle:

$\begin{array}{c}df=\frac{\∂f}{\∂{\mathrm{\σ}}_{ij}}{\mathrm{d\σ}}_{ij}+\frac{\∂f}{\∂{\mathrm{\α}}_p}{\mathrm{d\α}}_p\\ =\frac{3}{2q}\frac{{\mathrm{\σ}}_{ij}^d}{{\mathrm{\σ}}_{eq}}{\mathrm{d\σ}}_{ij}+\frac{1}{3}{\mathrm{A\α}}_p{\mathrm{\δ}}_{ij}{\mathrm{d\σ}}_{ij}+Ab\left(p-C_0\right)\left(1-{\mathrm{\α}}_p^0\right)e^{-{\mathrm{b\γ}}_p}{\mathrm{d\γ}}_p=0\end{array}---\left(9\right)$

Based on plastic flow rule, plastic strain is defined:

${\mathrm{d\ϵ}}_{ij}^p=d\mathrm{\λ}\frac{\∂g}{\∂{\mathrm{\σ}}_{ij}}---\left(10\right)$

$\frac{\∂g}{\∂{\mathrm{\σ}}_{ij}}=\frac{\∂g}{\∂q}\frac{dq}{{\mathrm{d\σ}}_{ij}}+\frac{\∂g}{\∂p}\frac{dp}{{\mathrm{d\σ}}_{ij}}=\frac{3}{2q}\frac{{\mathrm{\σ}}_{ij}^d}{{\mathrm{\σ}}_{ep}}-\frac{\mathrm{\η}}{3}{\mathrm{\δ}}_{ij}-\frac{q}{3I}{\mathrm{\δ}}_{ij}---\left(11\right)$

Obtaining plastic factory d λ is thus:

$d\mathrm{\λ}=\frac{\frac{\∂f}{\∂{\mathrm{\σ}}_{ij}}{C}_{ijkl}^0{\mathrm{d\ϵ}}_{kl}}{\frac{\∂f}{\∂{\mathrm{\σ}}_{pq}}{C}_{pqrs}^0\frac{\∂g}{\∂{\mathrm{\σ}}_{rs}}-\frac{\∂f}{\∂{\mathrm{\α}}_p}\frac{\∂{\mathrm{\α}}_p}{\∂{\mathrm{\γ}}_p}\×{\[\frac{2}{3}{\left(dev\frac{\∂g}{\∂\mathrm{\σ}}\right)}_{ij}{\left(dev\frac{\∂g}{\∂\mathrm{\σ}}\right)}_{ij}\]}^{1/2}}---\left(12\right)$

Adopt computerese to above-mentioned short-term elastic-plastic model programming realization; As f < 0, material is in Hookean region, there is not Plastic Flow, can directly utilize elasticity hooke law to be described; Otherwise represent that rock exists the effect of plasticity shear polymer, distortion exists Plastic Flow, plasticity Product-factor d λ > 0, and available formula (12) is determined, now need to adopt short-term elastic-plastic model to be described.

Analog parameter is all obtained by short-term conventional chambers threeaxis test results.Wherein, elastic modulus E and Poisson ratio υ are determined by the bullet linearity range of Fig. 4; Surrender parameter C ₀determined by Fig. 5 plastic yielding failure mechanics with A; Sclerosis Initial Hurdle parameter determined by Fig. 5 initial yield surface; Hardening parameter b is by Fig. 7 generalized plasticity shearing strain γ _pchange obtain; Flow rule parameter η compresses dilatation interphase by Fig. 5 and is determined; Therefore, fragmented rock short-term elasto-plastic Constitutive Model parameter is obtained as shown in table 1.

Table 1 fragmented rock elasto-plastic Constitutive Model parameter value

The simulation of above-mentioned Elastic-plastic Constitutive and parameter is adopted to carry out simulation to the conventional elastoplastic mechanical performance of fragmented rock short-term, as shown in Figure 8; Analog result and test findings present rule and have consistance, illustrate that this model can be described the elastoplastic mechanical performance that the ordinary triaxial test of fragmented rock short-term is observed accurately.

(9) theoretical based on microscopic damage, think that in long-term rheological test process, ε is by elastic strain ε in rock overall strain _e, plastic strain ε _pwith timeliness strain stress _tcomposition:

${\mathrm{\&epsiv;}}_{ij}={\mathrm{\&epsiv;}}_{ij}^e+{\mathrm{\&epsiv;}}_{ij}^p+{\mathrm{\&epsiv;}}_{ij}^t---\left(13\right)$

For creep test, stress loading path is determined, obtains based on time damage criterion strain stress relation:

${\mathrm{\&epsiv;}}_{ij}=\frac{1}{1-\mathrm{\&zeta;}}{D}_{ijkl}^0{\mathrm{\&sigma;}}_{kl}+{\mathrm{\&epsiv;}}_{ij}^p,$ D ⁰＝(C ⁰) ^-1(14)

Parameter D ⁰for the initial elasticity Flexibility tensor of material; And parameter E and A depends on material internal damage criterion and changes:

E(ζ)＝(1-ζ)E ₀；A(ζ)＝(1-ζ)A ₀(15)

And based on agreement principle:

$df=\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{ij}}{\mathrm{d\&sigma;}}_{ij}+\frac{\&part;f}{\&part;{\mathrm{\&alpha;}}_p}\frac{\&part;{\mathrm{\&alpha;}}_p}{\&part;{\mathrm{\&gamma;}}_p}{\mathrm{d\&gamma;}}_p+\frac{\&part;f}{\&part;A}dA=0---\left(16\right)$

Adopt the method building the conventional elastic and plastic mechanics model of short-term, obtain long-term flow time-elastic and plastic mechanics model:

$\begin{array}{c}{\mathrm{d\&epsiv;}}_{ij}=\frac{1}{1-\mathrm{\&zeta;}}{D}_{ijkl}^0{\mathrm{d\&sigma;}}_{kl}+\frac{1}{{\left(1-\mathrm{\&zeta;}\right)}^2}{D}_{ijkl}^0{\mathrm{\&sigma;}}_{kl}d\mathrm{\&zeta;}\\ +\frac{1}{H_{\mathrm{\&sigma;}d}}\left(\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{mn}}{\mathrm{d\&sigma;}}_{mn}\right)\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{ij}}-A_0\frac{1}{H_{\mathrm{\&sigma;}d}}\frac{\&part;f}{\&part;A}\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{ij}}d\mathrm{\&zeta;}\end{array}---\left(17\right)$

$H_{\mathrm{\&sigma;}d}=-\frac{\&part;f}{\&part;{\mathrm{\&alpha;}}_p}\frac{\&part;{\mathrm{\&alpha;}}_p}{\&part;{\mathrm{\&gamma;}}_p}{\&lsqb;\frac{2}{3}dev{\left(\frac{\&part;g}{\&part;\mathrm{\&sigma;}}\right)}_{ij}dev{\left(\frac{\&part;g}{\&part;\mathrm{\&sigma;}}\right)}_{ij}\&rsqb;}^{1/2}---\left(18\right)$

Adopt computerese to above-mentioned timeliness-elastic-plastic model programming realization; Material plastic flow is made up of two parts, and one is the instantaneous plastic yield that applying stress causes, and another part is the timeliness plastic flow distortion that under constant load long term, material internal particle damage decay evolution causes.When damage decay evolution does not occur material internal, this model can deteriorate to the conventional elastic-plastic model of short-term.

Analog parameter all turns indoor threeaxis test results obtained by flowing for a long time.Rheological parameter γ is determined by Fig. 6; Obtain long-term rheological parameter γ=0.00005 of fragmented rock.

Adopt above-mentioned timeliness-elasto-plastic Constitutive Model and parameter to flow change elastoplastic mechanical performance for a long time to fragmented rock and carry out simulation, as shown in Figure 9; Analog result and test findings present rule and have consistance, illustrate that this model can flow fragmented rock accurately for a long time and become the timeliness mechanical characteristic observed of triaxial test and described.Think that the methods and results based on three axles short test of long duration structure rock timeliness-elastic and plastic mechanics model that the present invention proposes is accurate, easy to operate thus, and mechanical meaning is clear and definite.

And the method with the mechanical characteristic of rock deformation and failure for foundation, the yield criteria of rock material, non-associated flow law, sclerosis criterion and microscopic damage evolution criterion are considered, construct the rock material timeliness-plasto-elasticity constitutive model based on threeaxis test results, eliminate artificial subjectivity, there is higher accuracy and applicability more widely, can be used for the research and analysis of rock mechanics in Practical Project.

Embodiment two:

For certain rock engineering sandstone, based on the short long-term rock mechanics experiment of three axles, build sandstone plasto-elasticity constitutive model, carry out following operation:

(1) get core based on China's sandstone engineering site, based on rock mechanics association proposed standard, be prepared into height with diameter than the cylinder specimen for 2:1; This routine sandstone test specimen diameter is 50mm, and height is 100mm; Test specimen is mounted in the short long-term rock mechanics experiment instrument of rock three axle; Adjustment axis and lateral strain are to initial value, and initial value is similar to 0;

(2) carry out the conventional rock mechanics experiment of three axle short-terms to test specimen, all tests are all carried out under constant temperature and humidity condition; First confined pressure is applied to predetermined value with loading speed 0.75MPa/min; Based on on-the-spot terrestrial stress condition, test confined pressure value is 2.0,6.0 and 10.0MPa; Secondly apply deviatoric stress with loading speed 0.75MPa/min to destroy to test specimen; Test is omnidistance measures axial strain ε ₁with lateral strain ε ₂with deviatoric stress σ ₁-σ ₃change; Finally, calculation testing piece bulk strain ε _v, bulk strain ε _v=ε ₁+ 2 ε ₂, ε ₁for on the occasion of, ε ₂for negative value.

(3) adopt stress load control model to carry out multistage stress grading to test specimen and add the test of unloading rheology; All tests are all carried out under constant temperature and humidity condition, belong to the triaxial rheology mechanical test of the confined pressures such as single sample, axial deviatoric stress step load and unload; First confined pressure is applied to predetermined value with loading speed 0.375MPa/min; Based on on-the-spot terrestrial stress condition, test confined pressure value is 12.0MPa; Secondly keep confined pressure constant, apply deviatoric stress to σ with loading speed 0.75MPa/min ₁=10.0MPa, and keep constant deviatoric stress 100 hours, measure stress σ ₁the lower axial strain stress of effect ₁with lateral strain ε ₂the change of t in time; To be deformed stable after carry out second level deviatoric stress σ ₂=14.6MPa stress loading; Repetitive operation; And then unloading third level deviatoric stress is to σ ₃=9.7MPa; Finally carry out most rear class deviatoric stress σ ₂=10.7MPa stress loading; Test is omnidistance measures axial strain ε ₁with lateral strain ε ₂the change of t in time; Finally, calculation testing piece bulk strain ε _v, bulk strain ε _v=ε ₁+ 2 ε ₂, ε ₁for on the occasion of, ε ₂for negative value.

(4) based on the conventional rock mechanics experiment of three axle short-terms, stress-axis, lateral strain relation curve is drawn; Obtain different confined pressure σ ₃the lower rock peak stress σ of effect _1p, make rock peak stress p-q relation curve; For cylinder specimen, q=σ _1p-σ ₃.According to p-q curve plastic yielding face shape, as shown in Figure 10, determine that the yield failure criterion of this rock applicable is quadratic function:

$\left.\begin{array}{c}f=q^2+{\mathrm{A\&alpha;}}_p(p-C_0)=0\\ p=\frac{{\mathrm{\&sigma;}}_{kk}}{3},q=\sqrt{3J_2}\\ J_2=\frac{1}{2}{S}_{ij}{S}_{ij},S_{ij}={\mathrm{\&sigma;}}_{ij}-\frac{{\mathrm{\&sigma;}}_{kk}}{3}{\mathrm{\&delta;}}_{ij}\end{array}\right\}---\left(19\right)$

Parameter p is mean stress, and q is deviatoric stress; Parameter C ₀initial cohesion and the angle of internal friction in material damage face is represented respectively, α with A _pfor relevant hardening function;

(5) based on stress-axis, lateral strain relation curve, different confined pressure σ is obtained ₃the surrender starting point stress σ that the lower rock of effect is transformed to plasticity by elasticity _1y, make rock yield initial stress p-q relation curve.For cylinder specimen, q=σ _1y-σ ₃.Surrender initial surface curve according to p-q, as shown in Figure 10, determine that the hardening Plastic criterion of this rock applicable is by generalized plasticity shearing strain γ _pchange in the reciprocal function that increases gradually:

$\left.\begin{array}{c}{\mathrm{\&alpha;}}_p={\mathrm{\&alpha;}}_p^0-\left({\mathrm{\&alpha;}}_p^0-1\right)\frac{{\mathrm{\&gamma;}}_p}{B+{\mathrm{\&gamma;}}_p}\\ {\mathrm{\&gamma;}}_p=\&Integral;\sqrt{\frac{2}{3}{\mathrm{de}}_{ij}^p{\mathrm{de}}_{ij}^p},e^p={\mathrm{\&epsiv;}}^p-\frac{1}{3}{\mathrm{tr\&epsiv;}}^p{\mathrm{\&delta;}}_{ij}\end{array}\right\}---\left(20\right)$

Parameter for the initial plastic threshold values in shear yielding face; Parameter B determines material plasticity hardening ratio, controls the dynamic process of plasticity strengthening;

(6) draw stress-bulk strain relation curve, obtain different confined pressure σ ₃the lower rock volume strain of effect is converted into the stress σ of dilatation by compression _1v; Make rock boundary intensity p-q relation curve.For cylinder specimen, q=σ _1v-σ ₃.According to the curve that p-q compression transforms to dilatation, determine that this rock compressed applicable and dilatation separatrix are linear function:

f _b＝q-Aη(p-C ₀)＝0(21)

Parameter η is dilatancy and the interfacial slope of compression; Based on interphase, obtain the Plastic Flow criterion describing this rock:

$g=q+A\mathrm{\&eta;}(p-C_0)ln\left(\frac{p-C_0}{I_0}\right)=0---\left(22\right)$

(7) rock mechanics experiment is become based on three axial length phase streams, m-axial, side direction, volume flow change relation curve during drafting; Obtain different confined pressure σ ₃decay and the steady state flow of the lower fragmented rock of effect become the stage, introduce time material time damage variable based on this:

$\mathrm{\&zeta;}\left(t\right)=\mathrm{\&zeta;}\left({\mathrm{\&epsiv;}}_{ij}^p\right(t),t)---\left(23\right)$

The soluble material volume unit of this variable is under effect of stress, and between solid particle, the relative damage change of fine sight surface of contact, also can reflect the dynamic process of material granule solubilizing reaction, belong to the standard value function depending on the description plastic yield of time variations.

Determine that the accurate side of material fine sight timeliness damage decay evolution is thus:

$\mathrm{\&zeta;}\left(t\right)={\&Integral;}_0^t\mathrm{\&gamma;}\stackrel{\&OverBar;}{\mathrm{\&zeta;}}\left(\mathrm{\&tau;}\right)e^{-\mathrm{\&gamma;}(t-\mathrm{\&tau;})}d\mathrm{\&tau;}---\left(24\right)$

the steady dissolution equilibrium state that between representative and material internal particle, the thermodynamic equilibrium state at fine sight surface of contact place is closely related, time t → ∞, suppose that material internal fine sight Structural Dynamics evolution process can describe according to internal balance state deviation, value namely by embody; γ represents the dissolution kinetics process of material granule plasticity shear polymer effect, is closely related with extraneous chemical physics factor, and the present invention ignores chemistry, temperature to the impact of mechanical characteristic, therefore γ is considered as constant; And sample equilibrium state can be by definition, depends on the stress intensity of applying, span and as time t=0, ζ (0)=0, obtains the accurate side of the decay evolution of timeliness damage accurately thus:

$\mathrm{\&zeta;}\left(t\right)=\stackrel{\&OverBar;}{\mathrm{\&zeta;}}\left(t\right)-{\&Integral;}_o^t\frac{\&part;\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}{\&part;\mathrm{\&tau;}}{e}^{-\mathrm{\&gamma;}(t-\mathrm{\&tau;})}d\mathrm{\&tau;}---\left(25\right)$

(8) based on thermodynamics elastic plastic theory, think that the overall strain ε of rock in short-term conventional test process is by elastic strain ε _ewith plastic strain ε _pcomposition, obtaining its stress increment is::

${\mathrm{d\&sigma;}}_{ij}=C_{ijkl}^0({\mathrm{d\&epsiv;}}_{kl}-d\mathrm{\&lambda;}\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{kl}})---\left(26\right)$

And based on agreement principle:

$\left.\begin{array}{c}df=\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{ij}}{\mathrm{d\&sigma;}}_{ij}+\frac{\&part;f}{\&part;{\mathrm{\&alpha;}}_p}\frac{\&part;{\mathrm{\&alpha;}}_p}{\&part;{\mathrm{\&gamma;}}_p}{\mathrm{d\&gamma;}}_p=0\\ \frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{ij}}=\frac{\&part;f}{\&part;q}\frac{\&part;p}{\&part;{\mathrm{\&sigma;}}_{ij}}+\frac{\&part;f}{\&part;p}\frac{\&part;p}{\&part;{\mathrm{\&sigma;}}_{ij}}=3\frac{{\mathrm{\&sigma;}}_{ij}^d}{{\mathrm{\&sigma;}}_{eq}}+\frac{1}{3}{\mathrm{A\&alpha;}}_p{\mathrm{\&delta;}}_{ij}\\ \frac{\&part;f}{\&part;{\mathrm{\&gamma;}}_p}=Ah\left(\mathrm{\&theta;}\right)\left(p-C_0\right)({\mathrm{\&alpha;}}_p^0-1)\frac{B}{{(B+{\mathrm{\&gamma;}}_P)}^2}\end{array}\right\}---\left(27\right)$

Based on plastic flow rule, plastic strain is defined:

${\mathrm{d\&epsiv;}}_{ij}^p=d\mathrm{\&lambda;}\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{ij}}---\left(28\right)$

$\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{ij}}=\frac{\&part;g}{\&part;q}\frac{dq}{{\mathrm{d\&sigma;}}_{ij}}+\frac{\&part;g}{\&part;p}\frac{dp}{{\mathrm{d\&sigma;}}_{ij}}=\frac{3}{2q}\frac{{\mathrm{\&sigma;}}_{ij}^d}{{\mathrm{\&sigma;}}_{ep}}+\frac{1}{3}A\mathrm{\&eta;}\&lsqb;1-\frac{q}{A\mathrm{\&eta;}h\left(\mathrm{\&theta;}\right)(p-C_0)}\&rsqb;{\mathrm{\&delta;}}_{ij}---\left(29\right)$

Obtaining plastic factory d λ is thus:

$\left.\begin{array}{c}d\mathrm{\&lambda;}=\frac{\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{ij}}{C}_{ijkl}^0{\mathrm{d\&epsiv;}}_{kl}}{H_{\mathrm{\&epsiv;}d}}\\ H_{\mathrm{\&epsiv;}d}=\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{pq}}{C}_{pqrs}^0\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{rs}}-\frac{\&part;f}{\&part;{\mathrm{\&alpha;}}_p}\frac{\&part;{\mathrm{\&alpha;}}_p}{\&part;{\mathrm{\&gamma;}}_p}\&times;{\&lsqb;\frac{2}{3}{\left(dev\frac{\&part;g}{\&part;\mathrm{\&sigma;}}\right)}_{ij}{\left(dev\frac{\&part;g}{\&part;\mathrm{\&sigma;}}\right)}_{ij}\&rsqb;}^{1/2}\\ dev=\frac{1}{3}\left({\mathrm{\&delta;}}_{ik}{\mathrm{\&delta;}}_{jl}+{\mathrm{\&delta;}}_{il}{\mathrm{\&delta;}}_{jk}\right)-\frac{1}{3}{\mathrm{\&delta;}}_{ij}{\mathrm{\&delta;}}_{kl}\end{array}\right\}---\left(30\right)$

Adopt computerese to above-mentioned formula programming realization; As f < 0, material is in Hookean region, there is not Plastic Flow, can directly utilize elasticity hooke law to be described; Otherwise represent that rock exists the effect of plasticity shear polymer, distortion exists Plastic Flow, plasticity Product-factor d λ > 0, and available formula (30) is determined, now need to adopt elastic-plastic model to be described.

Analog parameter is all obtained by indoor threeaxis test results.Wherein, elastic modulus E and Poisson ratio υ are determined by the bullet linearity range of stress-axis, lateral strain relation curve; Surrender parameter C ₀determined by Figure 10 plastic yielding failure mechanics with A; Sclerosis Initial Hurdle parameter determined by Figure 10 initial yield surface; Hardening parameter B is by generalized plasticity shearing strain γ _pchange obtain; Flow rule parameter η compresses dilatation interphase by Figure 10 and is determined; Therefore, the parameter obtaining sandstone elasto-plastic Constitutive Model is as shown in table 2.

Table 2 sandstone elasto-plastic Constitutive Model parameter value

Above-mentioned constitutive modeling and parameter is adopted to carry out simulation to sandstone short-term elastoplastic mechanical performance, as shown in figure 11; Analog result and test findings present rule and have consistance, illustrate that this model can be described the basic mechanical characteristic that the ordinary triaxial test of sandstone short-term is observed accurately.

(9) theoretical based on microscopic damage, think that in long-term rheological test process, ε is by elastic strain ε in rock overall strain _e, plastic strain ε _pwith timeliness strain stress _tcomposition:

${\mathrm{\&epsiv;}}_{ij}={\mathrm{\&epsiv;}}_{ij}^e+{\mathrm{\&epsiv;}}_{ij}^p+{\mathrm{\&epsiv;}}_{ij}^t---\left(31\right)$

For creep test, stress loading path is determined, obtains based on time damage criterion strain stress relation:

${\mathrm{\&epsiv;}}_{ij}=\frac{1}{1-\mathrm{\&zeta;}}{D}_{ijkl}^0{\mathrm{\&sigma;}}_{kl}+{\mathrm{\&epsiv;}}_{ij}^p,$ D ⁰＝(C ⁰) ^-1(32)

Parameter D ⁰for the initial elasticity Flexibility tensor of material; And parameter E and A depends on material internal damage criterion and changes:

E(ζ)＝(1-ζ)E ₀；A(ζ)＝(1-ζ)A ₀(15)

And based on agreement principle:

$df=\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{ij}}{\mathrm{d\&sigma;}}_{ij}+\frac{\&part;f}{\&part;{\mathrm{\&alpha;}}_p}{\mathrm{d\&alpha;}}_p+\frac{\&part;f}{\&part;\mathrm{\&zeta;}}d\mathrm{\&zeta;}---\left(33\right)$

Adopt the method building the conventional elastic and plastic mechanics model of short-term, obtain long-term flow time-elastic and plastic mechanics model:

$\begin{array}{c}{\mathrm{d\&epsiv;}}_{ij}=\frac{1}{1-\mathrm{\&zeta;}}{D}_{ijkl}^0{\mathrm{d\&sigma;}}_{kl}+\frac{1}{{\left(1-\mathrm{\&zeta;}\right)}^2}{D}_{ijkl}^0{\mathrm{\&sigma;}}_{kl}d\mathrm{\&zeta;}\\ +\frac{1}{H_{\mathrm{\&sigma;}d}}\left(\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{mn}}{\mathrm{d\&sigma;}}_{mn}\right)\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{ij}}-A_0\frac{1}{H_{\mathrm{\&sigma;}d}}\frac{\&part;f}{\&part;A}\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{ij}}d\mathrm{\&zeta;}\end{array}---\left(34\right)$

$H_{\mathrm{\&sigma;}d}=-\frac{\&part;f}{\&part;{\mathrm{\&alpha;}}_p}\frac{\&part;{\mathrm{\&alpha;}}_p}{\&part;{\mathrm{\&gamma;}}_p}{\&lsqb;\frac{2}{3}dev{\left(\frac{\&part;g}{\&part;\mathrm{\&sigma;}}\right)}_{ij}dev{\left(\frac{\&part;g}{\&part;\mathrm{\&sigma;}}\right)}_{ij}\&rsqb;}^{1/2}---\left(35\right)$

Adopt computerese to above-mentioned timeliness-elastic-plastic model programming realization; Material plastic flow is made up of two parts, and one is the instantaneous plastic yield that applying stress causes, and another part is the timeliness plastic flow distortion that under constant load long term, material internal particle damage decay evolution causes.When damage decay evolution does not occur material internal, this model can deteriorate to the conventional elastic-plastic model of short-term.

Analog parameter all turns indoor threeaxis test results obtained by flowing for a long time.Rheological parameter γ is determined by indoor rheological curve; Obtain long-term rheological parameter γ=0.00001 of sandstone.

Adopt above-mentioned timeliness-elasto-plastic Constitutive Model and parameter to flow change elastoplastic mechanical performance for a long time to fragmented rock and carry out simulation, as shown in figure 12; Analog result and test findings present rule and have consistance, illustrate that this model can flow sandstone accurately for a long time and become the timeliness mechanical characteristic observed of triaxial test and described.Accuracy and the rationality of the method for rock elastic and plastic mechanics model that builds based on three axle conventional tests that the present invention proposes are confirmed.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (10)

1. a construction method for rock material timeliness-plasto-elasticity constitutive model, is characterized in that: comprise the following steps:

(1) the conventional Rock Mechanics Tests of three axle short-terms are carried out to rock sample to be measured, measure and record axial, the lateral strain changing value with stress of rock sample; Three axial length phases streams are carried out to rock sample to be measured and becomes Rock Mechanics Test, to measure and axial, the lateral strain of recording rock sample are worth over time; Calculate the short-term of rock sample and the bulk strain of test of long duration respectively;

(2) and lateral strain change axially omnidistance according to the rock sample of the conventional Rock Mechanics Test record of three axle short-terms, draw stress-axis, lateral strain relation curve, obtain the surrender starting point stress that peak stress under different confined pressure effect and rock are transformed to plasticity by elasticity;

(3) determine deviatoric stress q respectively according to the peak stress obtained and surrender starting point stress, in conjunction with the mean stress p of rock sample, build p-q curve respectively, determine yield failure criterion and the sclerosis criterion of rock material belonging to test specimen;

(4) according to the bulk strain of the rock sample of the conventional Rock Mechanics Test calculating of three axle short-terms, draw stress-bulk strain relation curve, under obtaining different confined pressure effect, rock volume is by compressing the boundary intensity transformed to dilatation, deviatoric stress q is determined according to it, in conjunction with the mean stress p of rock sample, build p-q curve, determine the unlinkability flowing criterion of rock material belonging to test specimen;

(5) according to thermodynamics elastic plastic theory, in conjunction with the conventional stress-strain curve of rock of short-term, peak stress, surrender initial stress and boundary intensity, select the mechanics parameter value of rock Elastic-plastic Constitutive equation, determine elasto-plastic Constitutive Model;

(6) the omnidistance axial and lateral strain change of rock sample of Rock Mechanics Test record is become according to three axial length phase streams, m-axial, lateral strain relation curve during drafting, the stage is become according to its decay stream change stage and steady state flow, introduce material structure damage variable, determine material microscopic damage decay evolution criterion;

(7) theoretical according to microscopic damage, in conjunction with m-strain curve during long-term stream change rock, select the mechanics parameter value of rock aging characteristic constitutive equation, the damage of rock secular distortion decay evolution criterion is extended in the elasto-plastic Constitutive Model obtained, determines timeliness-elasto-plastic Constitutive Model.

2. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described method, also comprising step (8) utilizes controller to carry out rock mechanics experiment emulation, simulated experiment effect, verifies and improves timeliness-elasto-plastic Constitutive Model.

3. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (1), the concrete grammar of the conventional Rock Mechanics Test of three axle short-terms is: under constant temperature and humidity condition, apply confined pressure σ to rock sample ₃to stable, secondly keep confined pressure constant, deviatoric stress σ is carried out to test specimen ₁-σ ₃the rock mechanics experiment progressively loaded, test is omnidistance measures axial strain ε ₁with lateral strain ε ₂change, finally calculate bulk strain ε _v.

4. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (1), applying deviatoric stress mode in three axial length phases stream change Rock Mechanics Test is divided into single-stage to load and hierarchical loading, wherein, single-stage deviatoric stress loading method is: keep confined pressure σ ₃constant, a deviatoric stress σ is applied to test specimen ₁-σ ₃to stable, axial strain stress under measuring this deviatoric stress ₁with lateral strain ε ₂over time, bulk strain ε is finally calculated _v;

Classification deviatoric stress loading method is: keep confined pressure σ ₃constant, first apply initial deviator stress (σ ₁-σ ₃) ₁to stable, axial strain stress under measuring this deviatoric stress ₁with lateral strain ε ₂over time, to be deformed stable after carry out second level stress (σ ₁-σ ₃) ₂load; And then apply third level stress (σ ₁-σ ₃) ₃, by that analogy until test specimen generation rheodestruction.

5. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (3), the confirmation method of yield failure criterion is: based on the different confined pressure σ of short-term conventional test ₃under rock peak stress σ _1p, with rock sample now mean stress p, deviatoric stress q=σ _1p-σ ₃for condition, make peak stress p-q relation curve, according to the shape of this p-q curve, determine the yield failure criterion of this rock applicable.

6. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, is characterized in that: in described step (3), and the defining method of sclerosis criterion is: based on the different confined pressure σ of short-term conventional test ₃under rock plasticity surrender starting point stress σ _1y, with the mean stress p of rock sample, deviatoric stress q=σ _1y-σ ₃for condition, make surrender initial stress p-q relation curve, according to the shape of this p-q curve, determine the hardening Plastic criterion of this rock applicable.

7. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (4), the defining method of flow rule is: based on the different confined pressure σ of short-term conventional test ₃the boundary intensity σ of lower rock compressed and dilatation _1v, with the mean stress p of rock sample, deviatoric stress q=σ _1v-σ ₃for condition, make boundary intensity p-q relation curve, according to the shape of this p-q curve, determine the nonassociated plasticity flowing criterion of this rock applicable.

8. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, is characterized in that: in described step (5), determines that the concrete grammar of Elastic-plastic Constitutive equation is: ε is by elastic strain ε in rock overall strain _ewith plastic strain ε _pcomposition, in conjunction with elastic-plastic mechanics theory, derives rock Elastic-plastic Constitutive equation; And based on the conventional stress-strain curve of rock of short-term, peak stress p-q curve, surrender initial stress p-q curve and boundary intensity p-q relation curve, determine the mechanics parameter value of equation.

9. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (6), aging characteristic is that the macroscopic view of damage decay Evolution dynamics equilibrium process on the micro-meso-scale of rock interior structure embodies, the shape of change and steady state flow varied curve is flowed based on decay, introducing can the characteristic of material mechanics damage variable of qualitative description micro-microscopical structure timeliness Damage Evolution, the microscopic damage decay evolution criterion that can describe rock secular distortion is determined according to this damage variable, think that material deformation destruction characteristic produces change based on this damage criterion.

10. the construction method of a kind of rock material timeliness-plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (7), determine that the concrete grammar of timeliness-Elastic-plastic Constitutive equation is: be embodied in material ages deformation process by the damage of rock secular distortion decay evolution criterion, and extend to Elastic-plastic Constitutive equation, derive rock timeliness-Elastic-plastic Constitutive equation; And based on time the decay of m-strain curve and steady state flow become the stage, determine the timeliness parameter value of equation.