CN105181435B - A kind of construction method of rock material plasto-elasticity constitutive model - Google Patents

Abstract

The invention discloses a kind of construction method of rock material plasto-elasticity constitutive model, comprise the following steps: measure and record axial, the lateral strain changing value with stress of rock sample, calculating the bulk strain of rock sample; According to the rock sample of record, axially omnidistance and lateral strain change, draws stress-axis, lateral strain relation curve, determines yield failure criterion and the sclerosis criterion of rock material belonging to test specimen respectively; According to the bulk strain of the rock sample calculated, draw stress-bulk strain relation curve, determine the unlinkability flowing criterion of rock material belonging to test specimen; Utilize thermodynamics elastic plastic theory, in conjunction with stress-strain curve of rock, peak stress, surrender initial stress and boundary intensity, determine constitutive model.The present invention has considered yield criteria, the unlinkability flow rule of rock material and criterion of hardening, and the behavior of good reflection rock material plasto-elasticity, ensure that uniqueness and the accuracy of constitutive model.

Description

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

Technical field

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

Background technology

Rock is as the basic composition material of rock mass, and the analysis and research of large-scale rock engineering, energy extraction, underground storage and geological phenomenon all need to carry out deep understanding to its mechanical characteristic.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 nonlinear plasto-elasticity constitutive model is study of rocks mechanical characteristic is built.

Rock type materials 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.Constantly perfect in recent years along with testing equipment and theory of mechanics, structure rock mechanics constitutive model obtains and develops rapidly, many scholars based on measured test data and binding isotherm mechanics principle, propose some elasto-plastic Constitutive Model, but all have some limitations;

Application number is disclose a kind of method building material or soil body elasto-plastic Constitutive Model based on lateral loading test result in the patent of invention " a kind of method setting up material or soil body elasto-plastic Constitutive Model " of 201310140844.1; Due to lateral loading test be hole at the scene in a kind of level of carrying out to loading test, be only applicable to cohesive soil, powder scholar, sand, gravelly soil, residual soil, ultimate soft rock and soft rock deformation, therefore for presenting the hard rock of brittle rupture and inapplicable, the method has some limitations; Secondly the method calculates the relational matrix of described material stress and the strain increment obtained, Main Basis is the matched curve of soil body body strain, do not consider the mechanical mechanism that material deformation destroys, the mechanical characteristics such as its surrender, sclerosis, destruction can not be reflected, therefore exist certain error.

" a kind of soil body of practicality is unified bullet and moulded-Visco-Plastic Constitutive Model " (Wang Xiangyu, Liu Huabei, Song Erxiang. a kind of soil body of practicality is unified bullet and is moulded-Visco-Plastic Constitutive Model [J]. Hohai University's journal (natural science edition), 2009,37 (2): 166-170.) non-linear graceful pungent criterion is used in, establish a kind of soil body to unify bullet and mould-Visco-Plastic Constitutive Model, this model is simple and practical and reasonably can consider soil counterforce, power hysteresis and rheological characteristics; But the flow rule in rock material mechanical deformation do not considered by this model, namely do not specify the size and Orientation of plastic strain increment, cause its analog side to exist to deformation result certain error.

In sum, still there is certain defect in the method for existing structure rock material plasto-elasticity constitutive model, is mainly reflected in:

(1) adopt relevance flow rule, do not consider the otherness of axis and lateral deformation;

(2) mostly be ideal elastoplastic model, do not consider the hardening characteristics of material;

(3) yield failure face is single, do not consider the otherness of deformation failure, and extendability is poor.

Therefore need badly provide a kind of consider material yield criterion, unlinkability flow rule and sclerosis criterion and the method for structure rock material plasto-elasticity constitutive model applied widely, accuracy is high.

Summary of the invention

The present invention is in order to solve the problem, propose a kind of construction method of rock material plasto-elasticity constitutive model, this method considers yield criteria, non-associated flow law and sclerosis criterion, build the strain increment in elastic-plastic deformation stage and the relational matrix of stress increment, and then obtain rock material plasto-elasticity constitutive model, the model expression constructed is unique, parameter is less and all can obtain based on test findings, ensure that and ask uniqueness of solution and accuracy that also there is applicability widely thus.

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

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

(1) three axle Rock Mechanics Tests are carried out to rock sample to be measured, measure and record axial, the lateral strain changing value with stress of rock sample, calculating the bulk strain of rock sample;

(2) and lateral strain change axially omnidistance according to the rock sample of record, 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, determine yield failure criterion and the sclerosis criterion of rock material belonging to test specimen respectively;

(3) according to the bulk strain of the rock sample calculated, draw stress-bulk strain relation curve, under obtaining different confined pressure effect, rock volume is by compressing the boundary intensity transformed to dilatation, determines the unlinkability flowing criterion of rock material belonging to test specimen;

(4) utilize thermodynamics elastic plastic theory, in conjunction with stress-strain curve of rock, peak stress, surrender initial stress and boundary intensity, select the mechanics parameter value of rock constitutive equation, determine constitutive model.

Further, also comprise step (5), utilize controller to emulate, simulated experiment effect, checking is improved model also.

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

Preferably, the height of described rock sample is 2:1 with diameter ratio.

In described step (1), the concrete preparation method of described rock sample is: to original sillar boring and coring, obtains cylindric long core, carries out cutting and obtains the smooth test specimen of end face, polish test specimen end face long core end face.

In described step (1), the concrete grammar of three axle Rock Mechanics Tests is: under constant temperature and humidity condition, applies 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 loaded, test is omnidistance measures axial strain ε ₁with lateral strain ε ₂change, finally calculate bulk strain ε _v, for cylinder specimen, bulk strain ε _v=ε ₁+ 2 ε ₂.

In described step (2), the confirmation method of yield failure criterion is: based on different confined pressure σ ₃under rock peak stress σ _1p, with rock sample now mean stress 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 hardening Plastic criterion of this rock applicable.

In described step (2), the defining method of sclerosis criterion is: based on different confined pressure σ ₃under rock plasticity surrender starting point stress σ _1y, with the mean stress 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 (3), the defining method of flow rule is: based on different confined pressure σ ₃the boundary intensity σ of lower rock compressed and dilatation _1v, with the mean stress 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 (4), concrete grammar 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 constitutive equation; And based on stress-strain curve of rock, 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.

A kind of rock three-axis force test instrument, comprises confined pressure loader, bias voltage loader, axial strain measuring appliance, lateral strain measuring appliance, specimen holder and data transducer; 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 plasto-elasticity constitutive model, this model is based on the conventional mechanical test of rock three axle, simply clear and definite nonlinear strain and stress increment relational matrix can be built, there is higher accuracy and applicability widely;

(2) considered the yield criteria of rock material, unlinkability flow rule and sclerosis criterion, well can reflect the behavior of rock material plasto-elasticity, thought that its mechanical meaning is clear and definite, ensure that uniqueness and the accuracy of constitutive model;

(3) model parameter set up is less, all obtains by laboratory test results; And the embedded program of finite element software can be compiled as, think that the method is simple and convenient thus, 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 the conventional 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 fragmented rock hardening function and generalized plasticity shearing strain relation curve;

Fig. 7 fragmented rock elasto-plastic Constitutive Model analog result schematic diagram;

Fig. 8 sandstone initial yield surface, compression dilatation interphase and plastic yielding failure mechanics;

Fig. 9 sandstone elasto-plastic Constitutive Model analog result schematic diagram.

Embodiment:

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

As shown in Figure 1, a kind of method building rock material 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 the conventional 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 axles 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: 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 S4: based on stress-axis, lateral strain relation curve, 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 S5: 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 S6: based on thermodynamics elastic plastic theory, ε is by elastic strain ε in rock overall strain _ewith plastic strain ε _pcomposition, derives rock constitutive equation; And in conjunction with indoor experimental data, identification model parameter, finally adopts computerese to be achieved, checking and improved model.

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

Embodiment one:

For certain rock engineering fragmented rock, based on the conventional mechanical test of three axles, build fragmented rock 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 conventional 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 axles 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) 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:

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

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;

(4) 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 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:

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

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;

(5) draw stress-bulk strain relation curve, as shown in Figure 5, 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:

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

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

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

(6) based on thermodynamics elastic plastic theory, think that the overall strain ε of rock is by elastic strain ε _ewith plastic strain ε _pcomposition, obtaining its stress increment is:

${\mathrm{d\σ}}_{ij}=C_{ijkl}^0\left({\mathrm{d\ϵ}}_{kl}-d\mathrm{\λ}\frac{\∂g}{\∂{\mathrm{\σ}}_{kl}}\right)---\left(5\right)$

And based on agreement principle:

$\begin{array}{c}df=\frac{\∂f}{\∂{\mathrm{\σ}}_{ij}}{\mathrm{d\σ}}_{ij}+\frac{\∂f}{\∂{\mathrm{\α}}_p}{\mathrm{d\α}}_p\\ =\frac{3}{2q}\frac{{\mathrm{\σ}}_{ij}^d}{{\mathrm{\σ}}_{eq}}{\mathrm{d\σ}}_{ij}+\frac{1}{3}{\mathrm{A\α}}_p{\mathrm{\δ}}_{ij}{\mathrm{d\σ}}_{ij}+Ab\left(p-C_0\right)\left(1-{\mathrm{\α}}_p^0\right)e^{-{\mathrm{b\γ}}_p}{\mathrm{d\γ}}_p=0\end{array}---\left(6\right)$

Based on plastic flow rule, plastic strain is defined:

${\mathrm{d\ϵ}}_{ij}^p=d\mathrm{\λ}\frac{\∂g}{\∂{\mathrm{\σ}}_{ij}}---\left(7\right)$

$\frac{\∂g}{\∂{\mathrm{\σ}}_{ij}}=\frac{\∂g}{\∂q}\frac{dq}{{\mathrm{d\σ}}_{ij}}+\frac{\∂g}{\∂p}\frac{dp}{{\mathrm{d\σ}}_{ij}}=\frac{3}{2q}\frac{{\mathrm{\σ}}_{ij}^d}{{\mathrm{\σ}}_{ep}}-\frac{\mathrm{\η}}{3}{\mathrm{\δ}}_{ij}-\frac{q}{3I}{\mathrm{\δ}}_{ij}---\left(8\right)$

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(9\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 (9) 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 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. 6 generalized plasticity shearing strain γ _pchange obtain; Flow rule parameter η compresses dilatation interphase by Fig. 5 and is determined; Therefore, fragmented rock elasto-plastic Constitutive Model parameter is obtained as shown in table 1.

Table 1 fragmented rock elasto-plastic Constitutive Model parameter value

Above-mentioned constitutive modeling and parameter is adopted to carry out simulation to fragmented rock elastoplastic mechanical performance, as shown in Figure 7; Analog result and test findings present rule and have consistance, illustrate that this model can be described the basic mechanical characteristic that fragmented rock triaxial test is observed accurately.Think that the methods and results based on three axle conventional tests structure rock elastic and plastic mechanics models that the present invention proposes is accurate, easy to operate thus, and mechanical meaning is clear and definite.

The method with the mechanical characteristic of rock deformation and failure for foundation, the yield criteria of rock material, non-associated flow law and sclerosis criterion are considered, construct the rock material 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 conventional mechanical test 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 conventional mechanical test 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 axles 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 2.0,6.0 and 10.0MPa; 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) 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 8, determine that the yield failure criterion of this rock applicable is quadratic function:

$\left.\begin{array}{c}f=q^2+{\mathrm{A\&alpha;}}_p\left(p-C_0\right)=0\\ p=\frac{{\mathrm{\&sigma;}}_{kk}}{3},q=\sqrt{3J_2}\\ J_2=\frac{1}{2}{S}_{ij}{S}_{ij},S_{ij}={\mathrm{\&sigma;}}_{ij}-\frac{{\mathrm{\&sigma;}}_{kk}}{3}{\mathrm{\&delta;}}_{ij}\end{array}\right\}---\left(10\right)$

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;

(4) 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 8, 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:

$\left.\begin{array}{c}{\mathrm{\&alpha;}}_p={\mathrm{\&alpha;}}_p^0-\left({\mathrm{\&alpha;}}_p^0-1\right)\frac{{\mathrm{\&gamma;}}_p}{B+{\mathrm{\&gamma;}}_p}\\ {\mathrm{\&gamma;}}_p=\&Integral;\sqrt{\frac{2}{2}{\mathrm{de}}_{ij}^p{d}_{ij}^p,}{e}^p={\mathrm{\&epsiv;}}^p-\frac{1}{3}{\mathrm{tr\&epsiv;}}^p{\mathrm{\&delta;}}_{ij}\end{array}\right\}---\left(13\right)$

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;

(5) 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(11)

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

$g=q+A\mathrm{\&eta;}(p-C_0)ln\left(\frac{p-C_0}{I_0}\right)=0---\left(12\right)$

(6) based on thermodynamics elastic plastic theory, think that the overall strain ε of rock is by elastic strain ε _ewith plastic strain ε _pcomposition, obtaining its stress increment is:

${\mathrm{d\&sigma;}}_{ij}=C_{ijkl}^0\left({\mathrm{d\&epsiv;}}_{kl}-d\mathrm{\&lambda;}\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{kl}}\right)---\left(14\right)$

And based on agreement principle:

$\left.\begin{array}{c}df=\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{ij}}{\mathrm{d\&sigma;}}_{ij}+\frac{\&part;f}{\&part;{\mathrm{\&alpha;}}_p}\frac{\&part;{\mathrm{\&alpha;}}_p}{\&part;{\mathrm{\&lambda;}}_p}{\mathrm{d\&gamma;}}_p=0\\ \frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{ij}}=\frac{\&part;f}{\&part;q}\frac{\&part;q}{\&part;{\mathrm{\&sigma;}}_{ij}}+\frac{\&part;f}{\&part;p}\frac{\&part;p}{\&part;{\mathrm{\&sigma;}}_{ij}}=3\frac{{\mathrm{\&sigma;}}_{ij}^d}{{\mathrm{\&sigma;}}_{eq}}+\frac{1}{3}{\mathrm{A\&alpha;}}_p{\mathrm{\&delta;}}_{ij}\\ \frac{\&part;f}{\&part;{\mathrm{\&lambda;}}_p}=Ah\left(\mathrm{\&theta;}\right)\left(p-C_0\right)\left({\mathrm{\&alpha;}}_p^0-1\right)\frac{B}{{\left(B+{\mathrm{\&gamma;}}_P\right)}^2}\end{array}\right\}---\left(15\right)$

Based on plastic flow rule, plastic strain is defined:

${\mathrm{d\&epsiv;}}_{ij}^p=d\mathrm{\&lambda;}\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{ij}}---\left(16\right)$

$\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{ij}}=\frac{\&part;g}{\&part;q}\frac{dq}{{\mathrm{d\&sigma;}}_{ij}}+\frac{\&part;g}{\&part;p}\frac{dp}{{\mathrm{d\&sigma;}}_{ij}}=\frac{3}{2q}\frac{{\mathrm{\&sigma;}}_{ij}^d}{{\mathrm{\&sigma;}}_{ep}}+\frac{1}{3}A\mathrm{\&eta;}\&lsqb;1-\frac{q}{A\mathrm{\&eta;}h\left(\mathrm{\&theta;}\right)\left(p-C_0\right)}\&rsqb;{\mathrm{\&delta;}}_{ij}---\left(17\right)$

Obtaining plastic factory d λ is thus:

$\left.\begin{array}{c}d\mathrm{\&lambda;}=\frac{\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{ij}}{C}_{ijkl}^0{\mathrm{d\&epsiv;}}_{kl}}{H_{\mathrm{\&epsiv;}d}}\\ H_{\mathrm{\&epsiv;}d}=\frac{\&part;f}{\&part;{\mathrm{\&sigma;}}_{pq}}{C}_{pqrs}^0\frac{\&part;g}{\&part;{\mathrm{\&sigma;}}_{rs}}-\frac{\&part;f}{\&part;{\mathrm{\&alpha;}}_p}\frac{\&part;{\mathrm{\&alpha;}}_p}{\&part;{\mathrm{\&gamma;}}_p}\&times;{\&lsqb;\frac{2}{3}{\left(dev\frac{\&part;g}{\&part;\mathrm{\&sigma;}}\right)}_{ij}{\left(dev\frac{\&part;g}{\&part;\mathrm{\&sigma;}}\right)}_{ij}\&rsqb;}^{1/2}\\ dev=\frac{1}{2}\left({\mathrm{\&delta;}}_{ik}{\mathrm{\&delta;}}_{jl}+{\mathrm{\&delta;}}_{il}{\mathrm{\&delta;}}_{jk}\right)-\frac{1}{3}{\mathrm{\&delta;}}_{ij}{\mathrm{\&delta;}}_{kl}\end{array}\right\}---\left(18\right)$

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 (18) 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 Fig. 8 plastic yielding failure mechanics with A; Sclerosis Initial Hurdle parameter determined by Fig. 8 initial yield surface; Hardening parameter B is by generalized plasticity shearing strain γ _pchange obtain; Flow rule parameter η compresses dilatation interphase by Fig. 5 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 elastoplastic mechanical performance, as shown in Figure 9; Analog result and test findings present rule and have consistance, illustrate that this model can be described the basic mechanical characteristic that sandstone triaxial test is observed accurately.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 plasto-elasticity constitutive model, is characterized in that: comprise the following steps:

(1) three axle Rock Mechanics Tests are carried out to rock sample to be measured, measure and record axial, the lateral strain changing value with stress of rock sample, calculating the bulk strain of rock sample;

(2) and lateral strain change axially omnidistance according to the rock sample of record, 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, determine yield failure criterion and the sclerosis criterion of rock material belonging to test specimen respectively;

(3) according to the bulk strain of the rock sample calculated, draw stress-bulk strain relation curve, under obtaining different confined pressure effect, rock volume is by compressing the boundary intensity transformed to dilatation, determines the unlinkability flowing criterion of rock material belonging to test specimen;

(4) utilize thermodynamics elastic plastic theory, in conjunction with stress-strain curve of rock, peak stress, surrender initial stress and boundary intensity, select the mechanics parameter value of rock constitutive equation, determine constitutive model.

2. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 1, is characterized in that: also comprise step (5), utilize controller to emulate, simulated experiment effect, and checking is improved model also.

3. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (1), rock sample is cylindrical.

4. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 3, is characterized in that: the height of described rock sample is 2:1 with diameter ratio.

5. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (1), the concrete preparation method of described rock sample is: to original sillar boring and coring, obtain cylindric long core, cutting is carried out to long core end face and obtains the smooth test specimen of end face, test specimen end face is polished.

6. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (1), the concrete grammar of three axle Rock Mechanics Tests is: under constant temperature and humidity condition, applies 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 loaded, test is omnidistance measures axial strain ε ₁with lateral strain ε ₂change, finally calculate bulk strain ε _v.

7. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 1, it is characterized in that: in described step (2), the defining method of yield failure criterion is: based on different confined pressure σ ₃under rock peak stress σ _1p, with rock sample now mean stress 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.

8. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 1, is characterized in that: in described step (2), and the defining method of sclerosis criterion is: based on different confined pressure σ ₃under rock plasticity surrender starting point stress σ _1y, with the mean stress 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.

9. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 1, is characterized in that: in described step (3), and the defining method of flowing criterion is: based on different confined pressure σ ₃the boundary intensity σ of lower rock compressed and dilatation _1v, with the mean stress 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 unlinkability flowing criterion of this rock applicable.

10. the construction method of a kind of rock material plasto-elasticity constitutive model as claimed in claim 1, is characterized in that: in described step (4), concrete grammar 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 constitutive equation; And based on stress-strain curve of rock, 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.