CN106769482B - Static transverse isotropic rock mechanics experiment and analysis method - Google Patents
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- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0001—Type of application of the stress
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- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/06—Indicating or recording means; Sensing means
- G01N2203/067—Parameter measured for estimating the property
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Abstract
The invention provides a static transverse isotropic rock mechanics experiment and analysis method. The method comprises the steps of preparing at least 2 samples in a horizontal sample, a vertical sample and an included angle sample in the same vertical plane, conducting a triaxial compression failure experiment on each sample, recording axial deformation and lateral deformation in two directions of each sample in the experiment process, substituting experiment data into a deduced stress-strain equation set, and solving the equation set in a combined manner to obtain 5 independent rock mechanical parameters, namely horizontal Young modulus, horizontal Poisson ratio in the horizontal plane, vertical Young modulus, vertical Poisson ratio in the vertical plane and vertical in-plane shear modulus. The analysis result of the method gives 5 independent parameters of the rigidity matrix instead of 2 independent parameters of isotropic rock mechanics, so that the method is more in line with the actual situation, more accurately and reasonably describes the anisotropic behavior of the rock mechanics, and is suitable for rock mechanics test and analysis of sedimentary rock and shale.
Description
Technical field
The invention belongs to Rock Mechanics Test method and technology fields, and in particular to a kind of static state transverse isotropy rock power
Experiment and analysis method.
Background technique
Existing rock mechanics test method is mainly isotropism Rock Mechanics Test and analytical technology, that is, thinks rock
The mechanical properties of rock of all directions is identical.Laboratory test only needs to obtain two rock mechanics parameters: Young's modulus and pool
Loose ratio；Laboratory sample only needs one piece of core sample, and core sample is prepared as any direction coring；Experimental method is first to rock
Heart sample loads confining pressure to a numerical value, then keeps confining pressure constant, reloads axis pressure (i.e. deviatoric stress), until core sample is broken
It is bad, the sample axial strain and radial strain of record axis pressure loading procedure, according to two independent bullets of ess-strain equation calculation
Property parameter, formula are as follows:
In formula: E is Young's modulus；V is Poisson's ratio；σaFor axis pressure (i.e. deviatoric stress)；εrAnd εaRespectively radial strain and axis
To strain.
Existing isotropism Rock Mechanics Test method is suitable for the rock that all directions mechanical properties of rock is not much different
Stone, such as sandstone；But the stratum that all directions mechanical properties of rock has significant difference is not suitable for, such as sedimentary rock and shale
Deng.
Summary of the invention
To solve problems of the prior art, the purpose of the present invention is to provide a kind of static transverse isotropy rocks
The experiment and analysis method of stone mechanics.The analysis result of this method provides 5 independent parameters of stiffness matrix, rather than respectively to same
Property rock mechanics 2 independent parameters, it is suitable for the rock mechanics of sedimentary rock and shale test and analysis.
In order to achieve the above objectives, the present invention provides a kind of experiment of static transverse isotropy rock mechanics and analysis sides
Method comprising following steps:
(1) bed plane (also referred to as horizontal plane) of certain core sample to be analyzed is set as X/Y plane, by the bed plane
Normal direction (also referred to as vertical) is set as Z-direction, and the intersection point of X, Y, Z are set as O, then OZ is bed plane normal direction；With the rock to be analyzed
The OX axis of heart sample is that the cylindric rock sample that axis takes is denoted as horizontal sample；It is with the OZ axis of certain core sample to be analyzed
The cylindric rock sample that axis takes is denoted as vertical sample；It is the line of θ with the angle of the OZ axis of the core sample to be analyzed with this
It is denoted as angle sample for the cylindric rock sample that axis takes, and the axis of horizontal sample, vertical sample, angle sample is same
In one vertical plane OXZ；Angle sample described in taking at least one, and described in horizontal sample described at least one and/or one
Vertical sample；
(2) confining pressure is loaded to certain numerical value at least two pieces of samples that step (1) obtains respectively, then keeps confining pressure not
Become, then gradually loading axis pressure, until sample is destroyed, and records the axial strain, OXZ of every piece of sample in axis pressure loading procedure
The lateral strain of lateral strain and OXZ plane normal direction in plane；
(3) horizontal direction Young's modulus E is calculated using least square methodh, Poisson's ratio v in horizontal planeh, vertical Young mould
Measure Ev, Poisson's ratio v in vertical planevAnd shear modulus G in vertical plane.
In the above-mentioned methods, it is preferable that the sample that step (1) obtains is angle sample and horizontal sample, or is angle
Sample and vertical sample.
In the above-mentioned methods, it is preferable that the sample that step (1) obtains is the angle sample and horizontal sample of θ=45 °, or
Person is the angle sample and vertical sample of θ=45 °.
In the above-mentioned methods, it is preferable that when the angle sample and horizontal sample that the sample that step (1) obtains is θ=45 °
When, following formula 1 is solved using least square method, horizontal direction Young's modulus E is calculatedh, Poisson's ratio v in horizontal planeh, vertical Young
Modulus Ev, Poisson's ratio v in vertical planevAnd shear modulus G in vertical plane:
In formula,The axial strain variable quantity in loading procedure is pressed in axis for horizontal sample,Exist for horizontal sample
Axis presses the lateral strain variable quantity in the OXZ plane in loading procedure,It is pressed in loading procedure for horizontal sample in axis
The lateral strain variable quantity of OXZ plane normal direction,The axial strain variable quantity in loading procedure is pressed in axis for angle sample,The lateral strain variable quantity in the OXZ plane in loading procedure is pressed in axis for angle sample,Exist for angle sample
Axis presses the lateral strain variable quantity of the OXZ plane normal direction in loading procedure,It is pressed in loading procedure for horizontal sample in axis
Axial stress (i.e. axis pressure) variable quantity,Axial stress (the i.e. axis pressure) variation in loading procedure is pressed in axis for angle sample
Amount.
In the above-mentioned methods, it is preferable that when the angle sample and vertical sample that the sample that step (1) obtains is θ=45 °
When, following formula 2 is solved using least square method, horizontal direction Young's modulus E is calculatedh, Poisson's ratio v in horizontal planeh, vertical Young
Modulus Ev, Poisson's ratio v in vertical planevAnd shear modulus G in vertical plane:
In formula,The axial strain variable quantity in loading procedure is pressed in axis for vertical sample,Exist for vertical sample
Axis presses the lateral strain variable quantity in the OXZ plane in loading procedure,It is pressed in loading procedure for vertical sample in axis
The lateral strain variable quantity of OXZ plane normal direction,The axial strain variable quantity in loading procedure is pressed in axis for angle sample,The lateral strain variable quantity in the OXZ plane in loading procedure is pressed in axis for angle sample,Exist for angle sample
Axis presses the lateral strain variable quantity of the OXZ plane normal direction in loading procedure,It is pressed in loading procedure for vertical sample in axis
Axial stress (i.e. axis pressure) variable quantity,Axial stress (the i.e. axis pressure) variation in loading procedure is pressed in axis for angle sample
Amount.
In above-mentioned formula 1 and formula 2, each strain of the sample in axis pressure loading procedure, stress variable quantity be not necessarily sample
Numerical value when product are destroyed subtracts the numerical value of starting loading axis pressure, can make and answer to three strain parameters of each sample respectively
Then stress-strain curve takes the random length of the straight line portion of every stress-strain diagram to calculate variable quantity (as long as with end
The numerical value in point direction subtracts the numerical value of prime direction), such as with the midpoint of the straightway of every stress-strain diagram be
Point respectively chooses certain length up and down, and length can flexibly be determined according to personal preference, such as optional 40%- for being rounded a straightway
60%, the also optional 30%-70% etc. for being rounded straightway.
In the present invention, it is desirable that obtain 5 independent variables of static transverse isotropy rock mechanics, at least 2 need to be prepared
Block laboratory sample；As shown in Figure 1, the bed plane (also referred to as horizontal plane) of certain core sample to be analyzed is set as X/Y plane, it will
The normal direction (also referred to as vertical) of the bed plane is set as Z-direction, and the intersection point of X, Y, Z are set as O, then OZ is bed plane normal direction；With this
The OX axis of core sample to be analyzed is that the cylindric rock sample that axis takes is denoted as horizontal sample；With certain core sample to be analyzed
The OZ axis of product is that the cylindric rock sample that axis takes is denoted as vertical sample；With the angle of the OZ axis of the core sample to be analyzed with this
The line that degree is θ is that cylindric rock sample that axis takes is denoted as angle sample, and horizontal sample, vertical sample, angle sample
Axis is in same vertical plane OXZ；Wherein 1 piece of angle sample that must be described in 2 pieces of required samples, another 1 piece can
To be the horizontal sample, it is also possible to the vertical sample.Fig. 2 is the preparation method schematic diagram of straight well core sample,
The horizontal sample, vertical sample, angle sample axis in same vertical plane.Fig. 3 is inclined shaft core sample
Preparation method schematic diagram, the horizontal sample, vertical sample, angle sample axis also in same vertical plane.?
Before preparing laboratory sample, OXZ plane can be gone out in the surface marker of core sample to be analyzed, it is flat to draw OXZ on its surface
Lateral strain in OXZ plane is denoted as ε by the markings in facel1, the lateral strain of OXZ plane normal orientation is denoted as εl2, do reality
Installation lateral strain measuring device is more convenient when testing.Confining pressure is loaded to certain numerical value to every piece of sample, then keeps confining pressure constant,
Gradually loading axis pressure again, until sample broke, and record in axis pressure loading procedure sample axial deformation and two it is lateral
Deformation.
The constitutive relation of transversely isotropic layer is as shown in Equation 3；
In formula: [εx εy εz γxy γyz γzx]TFor the stain vector at any point, [σx σy σz τxy τyz τzx]T
For the stress vector at any point, EhAnd vhRespectively Poisson's ratio in horizontal direction Young's modulus and horizontal plane, EvAnd vvRespectively hang down
The Poisson's ratio into Young's modulus and vertical plane, G are vertical In-plane Shear Modulus.Therefore, the rock mechanics of transverse isotropy is real
Test 5 independent parameters that need to obtain stiffness matrix: Eh、vh、Ev、vvAnd G.
The strain calculation formula of every piece of sample is as shown in Equation 4:
In formula: εaFor axial strain, εl1For the lateral strain in OXZ plane, εl2For the lateral strain of OXZ plane normal direction,
σcAnd σaRespectively confining pressure and axis pressure.
The expression formula of stiffness coefficient is as shown in Equation 5:
It is vertical sample when θ=0 ° in formula 5, is horizontal sample when θ=90 °.Two pieces of core samples are selected to do rock power
5 independent variables can be found out by learning experiment, but one of must be angle sample.In a preferred embodiment of the invention,
The horizontal sample of the angle sample and θ=90 ° that take θ=45 ° is one group of sample, or takes angle sample and θ=0 ° of θ=45 °
Vertical sample be one group of sample, both of these case can find out 5 independent variables.
Confining pressure is to maintain constant during loading axis pressure, usually determines rock power according to the variable quantity of ess-strain
Elastic parameter is learned, so rewritable formula 4 is formula 6 in axis pressure loading procedure:
In formula: Δ εaThe axial strain variable quantity in loading procedure, Δ ε are pressed in axis for samplel1It presses and loads in axis for sample
The lateral strain variable quantity in OXZ plane in the process, Δ εl2The side of the OXZ plane normal direction in loading procedure is pressed in axis for sample
To strain variation amount, Δ σaAxial stress (i.e. axis pressure) variable quantity in loading procedure is pressed in axis for sample.
It is one group of sample when taking θ=45 ° angle sample and θ=90 ° horizontal sample, when determining 5 independent parameters, according to formula
6, have
It is one group of sample when taking θ=45 ° angle sample and θ=0 ° vertical sample, when determining 5 independent parameters, according to formula
6, have
In formula 1 and formula 2, subscript h, v and i respectively represent horizontal sample, vertical sample and 45 ° of angle samples；5 independences
Position quantity, 6 equations, solving this overdetermined equation using least square method can be obtained result.
Comparison expression 1 and formula 2, in formula 2Only last line has coefficient, and the relative error acquired is larger, therefore can use up
5 independent ginsengs that amount selects θ=45 ° angle sample and θ=90 ° horizontal sample that need to obtain for one group of sample to determine the present invention
Number.
The present invention provides a kind of test of the rock mechanics of transverse isotropy and analysis methods, that is, think parallel bedding face
Direction (i.e. horizontal direction) it is different from the mechanical properties of rock of bed plane normal direction (i.e. vertical direction).Transverse isotropy rock
The independent parameter that mechanical stress strains the flexibility matrix of constitutive relation is 5, i.e. horizontal direction Young's modulus, Poisson in horizontal plane
Than, Poisson's ratio and vertical In-plane Shear Modulus in vertical Young's modulus, vertical plane, therefore transverse isotropy Rock Mechanics Test
The task of test is also this 5 independent parameters.Based on Linear elastic mechanics principle, closed according to rock physics equations and coordinate transform
System derives the stress-strain relation of transverse isotropy rock mechanics different directions laboratory sample, forms equation group.Test sample
At least 2 pieces of samples of product being prepared as preparing in same vertical plane in horizontal sample, vertical sample and angle sample, to every
Block sample does triaxial compressions breaking test, and the axial deformation of every piece of sample and the lateral change of both direction are recorded in experimentation
Shape, experimental data are updated in the ess-strain equation group derived, combine solve system of equation, and 5 independent rocks can be obtained
Mechanics parameter, and then obtain the flexibility matrix and stiffness matrix of transverse isotropy rock mechanics stress-strain Constitutive Relationship.
This structure of transversely isotropic layer can be obtained using transverse isotropy static state rock mechanics test method of the invention
5 independent parameters of flexibility matrix in relationship, rather than 2 independent parameters of isotropism rock mechanics.5 independences acquired
Parameter can portray the property of transverse isotropy rock mechanics comprehensively, compared with isotropism rock mechanics 2 independent parameters more
It tallies with the actual situation, it is also more acurrate and reasonably describe the anisotropy behavior of rock mechanics.Horizontal sight of the invention is each to same
Property rock mechanics test and analysis method be suitable for the vertical rock different with horizontal direction mechanical properties of rock (i.e. with relatively showing
The anisotropic rock write), such as shale and sedimentary rock, but both rocks are not limited only to, it is all to have horizontal sight each to same
The rock of property mechanical properties of rock feature can use test method of the invention.
Detailed description of the invention
Fig. 1 is static transverse isotropy Rock Mechanics Test sample preparation schematic diagram；
Fig. 2 is the preparation method schematic diagram of straight well core sample；
Fig. 3 is the preparation method schematic diagram of inclined shaft core sample；
Fig. 4 is the stress-strain diagram of the horizontal sample of embodiment 1；
Fig. 5 is the stress-strain diagram of 45 ° of angle samples of embodiment 1.
Specific embodiment
In order to which technical characteristic of the invention, purpose and beneficial effect are more clearly understood, now to skill of the invention
Art scheme carries out described further below, but should not be understood as that limiting the scope of the invention.
Embodiment 1
Present embodiments provide the experiment and analysis method of a kind of static transverse isotropy rock mechanics comprising following
Step:
(1) it is put down as shown in Figure 1, the bed plane (also referred to as horizontal plane) of certain straight well core sample to be analyzed is set as XY
The normal direction (also referred to as vertical) of the bed plane is set as Z-direction, and the intersection point of X, Y, Z is set as O by face, then OZ is bed plane normal direction；
Horizontal sample is denoted as using the cylindric rock sample that the OX axis of the core sample to be analyzed takes as axis；With certain rock to be analyzed
The OZ axis of heart sample is that the cylindric rock sample that axis takes is denoted as vertical sample；With the OZ axis of the core sample to be analyzed with this
Angle be θ line be that the cylindric rock sample that axis takes is denoted as angle sample, and horizontal sample, vertical sample, angle sample
The axis of product is in same vertical plane OXZ；As shown in Fig. 2, taking the angle sample and a horizontal sample of θ=45 °；
(2) confining pressure is loaded to two pieces of samples that step (1) obtains respectively, then keeps confining pressure constant, then gradually loading axis
Pressure until sample is destroyed, and records in axis pressure loading procedure the axial strain ε of every piece of samplea, it is lateral in OXZ plane
Strain stressl1And the lateral strain ε of OXZ plane normal directionl2；Fig. 4 is the stress-strain diagram of horizontal sample, and Fig. 5 is 45 ° of angle samples
The stress-strain diagram of product, ordinate are axis pressure, and abscissa is three-dimensional strain；According to Fig. 4 and Fig. 5 respectively obtain horizontal sample and
The axial strain converted quantity of angle sample, two lateral strain variable quantities and axial stress variable quantity, i.e.,Determine that these ess-strains become in Fig. 4,5
When the amount of changing, it is not necessarily numerical value when numerical value when sample is destroyed subtracts starting loading axis pressure, Fig. 4, answering in 5 can be chosen
The random length of the straight line portion of stress-strain curve calculates variable quantity, such as in the straightway of every stress-strain diagram
Point is midpoint, respectively chooses certain length up and down, and length can flexibly be determined according to personal preference, such as optional rounding straightway
40%-60%, the also optional 30%-70% etc. for being rounded straightway；
(3) sample that the present embodiment uses is the combination of horizontal sample and angle sample, according to formula 1:
Formula 7 can be obtained:
Formula 7 is solved using least square method, 5 independent parameters are calculated --- horizontal direction Young's modulus Eh, horizontal plane
Interior Poisson's ratio vh, vertical Young's modulus Ev, Poisson's ratio v in vertical planevAnd shear modulus G in vertical plane:
Ev=14.79E9, vv=0.1864, Eh=28.82E9, vh=0.1729, G=6.83E9.
According to the above results as can be seen that the Young's modulus of the core sample vertical direction of the present embodiment is much smaller than level side
To Young's modulus, and the Poisson's ratio of both direction is not much different, therefore for sedimentary rock and shale, it is necessary to using of the invention
Transverse isotropy rock mechanics measuring technology tests its mechanical properties of rock.
Claims (1)
1. a kind of experiment and analysis method of static state transverse isotropy rock mechanics comprising following steps:
(1) bed plane of certain core sample to be analyzed is set as X/Y plane, the normal direction of the bed plane is set as Z-direction, and by X,
Y, the intersection point of Z is set as O；Horizontal sample is denoted as using the cylindric rock sample that the OX axis of the core sample to be analyzed takes as axis
Product；Vertical sample is denoted as using the cylindric rock sample that the OZ axis of certain core sample to be analyzed takes as axis；To be waited for point with this
The line that the angle of the OZ axis of the core sample of analysis is θ is that the cylindric rock sample that axis takes is denoted as angle sample, and horizontal sample
Product, vertical sample, angle sample axis in same vertical plane OXZ；Angle sample, Yi Jizhi described in taking at least one
Vertical sample described in horizontal sample and/or one described in few one；
(2) confining pressure is loaded to certain numerical value at least two pieces of samples that step (1) obtains respectively, then keeps confining pressure constant, then
Gradually loading axis pressure until sample is destroyed, and records in axis pressure loading procedure the axial strain, OXZ plane of every piece of sample
The lateral strain of interior lateral strain and OXZ plane normal direction；
(3) horizontal direction Young's modulus E is calculated using least square methodh, Poisson's ratio ν in horizontal planeh, vertical Young's modulus Ev、
Poisson's ratio ν in vertical planevAnd shear modulus G in vertical plane；
Wherein, the sample that step (1) obtains is the angle sample and horizontal sample of θ=45 °, or the angle sample for θ=45 °
With vertical sample；
When the sample that step (1) obtains is the angle sample and horizontal sample of θ=45 °, following formula is solved using least square method
1, horizontal direction Young's modulus E is calculatedh, Poisson's ratio ν in horizontal planeh, vertical Young's modulus Ev, Poisson's ratio ν in vertical planevWith
And shear modulus G in vertical plane:
In formula,The axial strain variable quantity in loading procedure is pressed in axis for horizontal sample,It is horizontal sample in axis pressure
The lateral strain variable quantity in OXZ plane in loading procedure,Press the OXZ in loading procedure flat in axis for horizontal sample
The lateral strain variable quantity of face normal direction,The axial strain variable quantity in loading procedure is pressed in axis for angle sample,For
Lateral strain variable quantity of the angle sample in the OXZ plane in axis pressure loading procedure,It presses and loads in axis for angle sample
The lateral strain variable quantity of OXZ plane normal direction in the process,The axial stress in loading procedure is pressed in axis for horizontal sample
Variable quantity,The axial stress variable quantity in loading procedure is pressed in axis for angle sample；
When the sample that step (1) obtains is the angle sample and vertical sample of θ=45 °, following formula is solved using least square method
2, horizontal direction Young's modulus E is calculatedh, Poisson's ratio ν in horizontal planeh, vertical Young's modulus Ev, Poisson's ratio ν in vertical planevWith
And shear modulus G in vertical plane:
In formula,The axial strain variable quantity in loading procedure is pressed in axis for vertical sample,It is vertical sample in axis pressure
The lateral strain variable quantity in OXZ plane in loading procedure,Press the OXZ in loading procedure flat in axis for vertical sample
The lateral strain variable quantity of face normal direction,The axial strain variable quantity in loading procedure is pressed in axis for angle sample,For
Lateral strain variable quantity of the angle sample in the OXZ plane in axis pressure loading procedure,It presses and loads in axis for angle sample
The lateral strain variable quantity of OXZ plane normal direction in the process,The axial stress in loading procedure is pressed in axis for vertical sample
Variable quantity,The axial stress variable quantity in loading procedure is pressed in axis for angle sample.
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| CN110174307B (en) * | 2019-04-25 | 2021-06-22 | 华北水利水电大学 | Parameter identification method based on transverse isotropic rock mass three-dimensional creep model |
| CN111366452B (en) * | 2020-03-26 | 2021-01-29 | 北京科技大学 | Method for measuring energy storage level of self-energy-storage rock mass |
| CN114076710A (en) * | 2020-08-21 | 2022-02-22 | 中国石油化工股份有限公司 | Method and system for measuring rock crushing energy |
| CN115950765B (en) * | 2023-03-10 | 2023-05-26 | 国网山西省电力公司电力科学研究院 | System and method for detecting shear stress intensity of epoxy part of GIS basin-type insulator |
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