CN102183410A - Brazilian split method for measuring elastic parameter of rock under extension condition - Google Patents

Abstract

The invention discloses a Brazilian split method for measuring an elastic parameter of a rock under an extension condition, which comprises the steps of: A. horizontally putting a machined disc-shaped sample between the load bearing plates of a press machine by using a Brazilian disc split method, placing a hard steel wire respectively between the upper load bearing plate and the sample and between the lower load bearing plate and the sample, arranging a filler strip perpendicular to the symmetrical surfaces of the sample, and applying pressure on the upper load bearing plate and the lower load bearing plate to make the sample generate tension perpendicular to the action directions of an upper load and a lower load; B. carrying out analysis by using the Hooke's law in classical elasticity mechanics by combining specific conditions of the Brazilian split method; C. analyzing the stress condition of the rock and the measurement principle in the Brazilian disc split method; and D. obtaining the strain in the stress direction according to the Hooke's law from the stress condition, measuring a sum, obtaining the elastic parameter of the rock sample, and arranging a strain gauge in the center position of the rock sample for measurement. The method has the advantages of easiness for operation and use, clear principle, low material consumption, and the like. The method is suitable for wide popularization and application.

Description

A kind of Brazilian splitting method of measuring rock elasticity parameter under the stretching condition

Technical field

The tensile strength that the present invention relates to Brazilian split the law measurement rock more specifically relates to the Brazilian splitting method that rock elasticity parameter under the ill-condition is pulled open in a kind of measurement, this method is simple, principle is clear, can reflect that when obtaining to pull open bad intensity rock is pulling open the elastic property under going bad.As everyone knows, the tension character and the resistance to compression character of rock material have very big otherness, and in present rock mechanics hot issue, more and more pay close attention to the bad special nature that is showed of pulling open of rock.Patent of the present invention is bad at pulling open of rock, Brazilian split the law is simply improved, thereby the tensile strength and elastic modulus E and the Bai Song under pulling open badly that obtain rock compares μ.

Background technology

At present, along with Chinese large-sized water conservancy and hydropower and mining engineering constantly develop to the deep, rock mechanics is constantly in the face of new problem.The tensile strength of rock is the mechanics parameter of an important rock, and it not only reflects rock mechanics properties, still analyzes the important indicator of rock stability.In the new hot issue such as the rock burst that faces in engineering reality, core cakeization, particularly in deep rock mass engineering project, the failure mode of rock is broken bad development towards complicated more pulling open bad or draw, and the tensile strength of rock seems more important.In existing test, the elastic parameter of rock is generally determined by uniaxial compression test or triaxial compression test, have the bad characteristics that significantly crush in the rock elasticity parameter that crushes under bad, explain that with such elastic parameter the destruction that produces and engineering phenomenon obviously are not enough science under the tension condition.For this reason, patent of the present invention is improved by simple on the basis of original Brazilian split the law, under the theoretical direction of classical elasticity, obtains the elastic parameter of rock under pulling open badly.

In present laboratory experiment, the method for testing of Tensile Strength of Rock adopts direct pulling method and Brazilian disc split the law (Brazilian test) usually.The Brazilian disc split the law is owing to the restriction that is not subjected to anchor clamps, and is simple and reliable, so use comparatively extensive at present.The Brazilian disc split the law can obtain the tensile strength of rock, and the elastic parameter of rock need be tested by other shop experiment or on-the-spot original position and obtained.This test method is improved on the basis of Brazilian disc split the law, obtains the elastic parameter of rock simultaneously by the simple mechanics-based analysis, have be easy to carry out, practical economic characteristics.

Summary of the invention

The objective of the invention is to be to provide a kind of Brazilian splitting method of measuring rock elasticity parameter under the stretching condition, easy to implement the method, easy and simple to handle, this method utilizes traditional Brazilian split the law test can obtain the tensile strength and the elastic parameter (elastic modulus E under pulling open of rock sample is bad of rock simultaneously, Bai Song is than μ), it is clear to have principle, easy to use, material consumption waits a bit less, is fit to wide popularization and application.

A kind of Brazilian splitting method of measuring rock elasticity parameter under the stretching condition, its theoretical foundation are classical theory of elastic mechanics, and its step is as follows:

A, Brazilian disc split the law (Brazilian test) will be through the discoid test specimens of processing, be horizontally placed between the bearing plate of pressing machine, and the hard steel wire that respectively to place a diameter between the upper and lower bearing plate of test specimen be 2mm is as filler strip, and filler strip is vertical with the plane of symmetry of test specimen.Upper and lower bearing plate is exerted pressure, make test specimen produce stretching force vertical and upper and lower load action direction, destroy until test specimen.By the mechanics feature of this test method, the tensile strength of rock can be expressed as:

${\mathrm{\σ}}_1=-\frac{2P}{\mathrm{\πD}}---\left(1\right)$

σ in the formula ₁---the tensile strength (being first principal stress) of rock

P---splitting payload values

The diameter of D---rock sample

π---circular constant

Simultaneously:

${\mathrm{\σ}}_2=\frac{6P}{\mathrm{\πD}}---\left(2\right)$

σ in the formula ₂---the second principal stress of rock sample

P---splitting payload values

The diameter of D---rock sample

π---circular constant

B, quote classical theory of mechanics and be updated in the Brazilian splitting model Hooke's law in the classical elasticity:

${\mathrm{\ϵ}}_1=\frac{1}{E}[{\mathrm{\σ}}_1-\mathrm{\μ}({\mathrm{\σ}}_2+{\mathrm{\σ}}_3)]---\left(3\right)$

${\mathrm{\ϵ}}_2=\frac{1}{E}[{\mathrm{\σ}}_2-\mathrm{\μ}({\mathrm{\σ}}_2+{\mathrm{\σ}}_3)]---\left(4\right)$

${\mathrm{\ϵ}}_3=\frac{1}{E}[{\mathrm{\σ}}_3-\mathrm{\μ}({\mathrm{\σ}}_1+{\mathrm{\σ}}_2)]---\left(5\right)$

σ in the formula ₁, σ ₂, σ ₃---be respectively first principal stress, second principal stress, the third principal stress of rock sample;

ε ₁, ε ₂, ε ₃---be respectively first principal strain, second principal strain, the 3rd principal strain of rock sample;

The Young modulus of E---rock sample;

The Poisson ratio of μ---rock sample;

Can obtain strain value by Hooke's law is formula (3), (4), in conjunction with Brazilian split the law be actual conditions as can be known, the first principal stress of rock sample, second principal stress direction should be on the circular sections, third principal stress is zero, the direction of corresponding first principal stress, second principal stress, corresponding first principal strain of third principal stress direction, second principal strain, the 3rd principal strain, and strain is non-vanishing on the direction of the 3rd principal strain.Because ε ₃Irrelevant with conclusion of the present invention, therefore ignore ε ₃

Rock sample can be analyzed by stress and obtain σ in C, the Brazilian disc split the law ₃=0, promptly the stress at the axis direction of cylindric rock sample is zero.On the circle of the cross section of rock sample, on any one cross section, be plane stress state, the direction of two principle stresses is respectively to be parallel to the direction of anchor clamps and perpendicular to the direction of anchor clamps.

On any one cross section, be easy to obtain that rock sample is out of shape situation accordingly in Brazilian diametral compression test, owing to be plane stress problem, in the strain stress of columniform hole axis direction ₃Can not consider two principal strain ε in the cross section ₁, ε ₂Direction strain and principal direction of stress σ ₁, σ ₂Consistent.The position of pasting foil gauge so in the accompanying drawings then can obtain on this cross section of end face at principal strain ε ₁, ε ₂The distortion of direction.

D, Hooke's law (3), (4), (5) listed according to preamble can obtain can directly converting in the strain computing formula of figure shown in (2) becomes following formula:

${\mathrm{\ϵ}}_1=-\frac{2P}{\mathrm{\πDE}}(1+3\mathrm{\μ})---\left(6\right)$

${\mathrm{\ϵ}}_2=\frac{2P}{\mathrm{\πDE}}(3+\mathrm{\μ})---\left(7\right)$

The elastic modulus E that fortran just can directly obtain rock sample is carried out in (6), (7), and Bai Song is than μ:

$E=\frac{16P}{\mathrm{\πD}({3\mathrm{\ϵ}}_2+{\mathrm{\ϵ}}_1)}---\left(8\right)$

$\mathrm{\μ}=-\frac{{3\mathrm{\ϵ}}_1+{\mathrm{\ϵ}}_2}{{3\mathrm{\ϵ}}_2+{\mathrm{\ϵ}}_1}---\left(9\right)$

Therefore, as long as record ε ₁And ε ₂, can obtain the elastic parameter of this rock sample according to formula (8) and (9).Reaching this purpose only needs to measure ε at the center of rock sample placement foil gauge ₁, ε ₂Get final product.This method is simple and practical, economical and effective, only need original test method is improved slightly, just can obtain the mechanics parameter of rock by the knowledge of Elasticity, be fit to wide popularization and application, not only can obtain the tensile strength of rock sample after this test improves by Mechanics Calculation, can also obtain the elastic modulus E of rock sample under pulling open badly, Bai Song compares μ.

The present invention compares with other test methods that obtain rock mechanics parameter or Tensile Strength of Rock and has the following advantages:

(1) the present invention is simple and practical, and economical and effective is improved on the basis of the Brazilian disc split the law of original widespread use slightly, just can obtain the tensile strength of rock simultaneously, and, wherein specifically referring to elastic modulus E in the elastic parameter of pulling open rock sample under the evil idea, Bai Song compares μ.

(2) method of traditional mechanics parameter at indoor acquisition rock generally is that uniaxial compressive strength or three compressive strength test results by several groups of rock samples analyze acquisition, in actual engineering, the rock mass unstability of many complexity is not that crushing of rock is bad, but pulls open bad.So the rock elasticity parameter that obtains under pulling open bad prerequisite can reflect the practical problems in the rock mechanics engineering to a certain extent more.

Description of drawings:

Fig. 1 is that a kind of Brazilian split the law is measured ε ₁The resistance strain gage arrangenent diagram

Fig. 2 is that a kind of Brazilian split the law is measured ε ₂The resistance strain gage arrangenent diagram

Wherein: the diameter of P one splitting payload values, D one rock sample.

Embodiment

Embodiment 1:

A kind of Brazilian splitting method of measuring rock elasticity parameter under the stretching condition, its step is as follows:

A, Brazilian disc split the law (Brazilian test) will be through the discoid test specimens of processing, be horizontally placed between the bearing plate of pressing machine, and the hard steel wire that respectively to place a diameter between the upper and lower bearing plate of test specimen be 2mm is as filler strip, and filler strip is vertical with the plane of symmetry of test specimen.Upper and lower bearing plate is exerted pressure, make test specimen produce stretching force vertical and upper and lower load action direction, destroy until test specimen.By the mechanics feature of this test method, the tensile strength of rock can be expressed as:

${\mathrm{\σ}}_1=-\frac{2P}{\mathrm{\πD}}---\left(1\right)$

σ in the formula ₁---the tensile strength (being first principal stress) of rock

P---splitting payload values

The diameter of D---rock sample

π---circular constant

Simultaneously:

${\mathrm{\σ}}_2=\frac{6P}{\mathrm{\πD}}---\left(2\right)$

σ in the formula ₂---the second principal stress of rock sample

P---splitting payload values

The diameter of D---rock sample

π---circular constant

B, quote classical theory of mechanics and be updated in the Brazilian splitting model Hooke's law in the classical elasticity:

${\mathrm{\ϵ}}_1=\frac{1}{E}[{\mathrm{\σ}}_1-\mathrm{\μ}({\mathrm{\σ}}_2+{\mathrm{\σ}}_3)]---\left(3\right)$

${\mathrm{\ϵ}}_2=\frac{1}{E}[{\mathrm{\σ}}_2-\mathrm{\μ}({\mathrm{\σ}}_1+{\mathrm{\σ}}_3)]---\left(4\right)$

${\mathrm{\ϵ}}_3=\frac{1}{E}[{\mathrm{\σ}}_3-\mathrm{\μ}({\mathrm{\σ}}_1+{\mathrm{\σ}}_2)]---\left(5\right)$

σ in the formula ₁, σ ₂, ε ₃---be respectively first principal stress, second principal stress, the third principal stress of rock sample;

ε ₁, ε ₂, ε ₃---be respectively first principal strain, second principal strain, the 3rd principal strain of rock sample;

The Young modulus of E---rock sample;

The Poisson ratio of μ---rock sample;

Can obtain strain value by Hooke's law is formula (3), (4), in conjunction with Brazilian split the law be actual conditions as can be known, the first principal stress of rock sample, second principal stress direction should be on the circular sections, third principal stress is zero, the direction of corresponding first principal stress, second principal stress, corresponding first principal strain of third principal stress direction, second principal strain, the 3rd principal strain, and strain is non-vanishing on the direction of the 3rd principal strain.Because ε ₃Irrelevant with conclusion of the present invention, therefore ignore ε ₃

Rock sample can be analyzed by stress and obtain σ in C, the Brazilian disc split the law ₃=0, promptly the stress at the axis direction of cylindric rock sample is zero.On the circle of the cross section of rock sample, on any one cross section, be plane stress state, the direction of two principle stresses is respectively to be parallel to the direction of anchor clamps and perpendicular to the direction of anchor clamps.

On any one cross section, be easy to obtain that rock sample is out of shape situation accordingly in Brazilian diametral compression test, owing to be plane stress problem, in the strain stress of columniform hole axis direction ₃Can not consider two principal strain ε in the cross section ₁, ε ₂Direction strain and principal direction of stress σ ₁, σ ₂Consistent.The position of pasting foil gauge so in the accompanying drawings then can obtain on this cross section of end face at principal strain ε ₁, ε ₂The distortion of direction.

D, Hooke's law (3), (4), (5) listed according to preamble can obtain can directly converting in the strain computing formula of figure shown in (2) becomes following formula:

${\mathrm{\ϵ}}_1=-\frac{2P}{\mathrm{\πDE}}(1+3\mathrm{\μ})---\left(6\right)$

${\mathrm{\ϵ}}_2=-\frac{2P}{\mathrm{\πDE}}(3+\mathrm{\μ})---\left(7\right)$

The elastic modulus E that fortran just can directly obtain rock sample is carried out in (6), (7), and Bai Song is than μ:

$E=\frac{16P}{\mathrm{\πD}({3\mathrm{\ϵ}}_2+{\mathrm{\ϵ}}_1)}---\left(8\right)$

$\mathrm{\μ}=-\frac{{3\mathrm{\ϵ}}_1+{\mathrm{\ϵ}}_2}{{3\mathrm{\ϵ}}_2+{\mathrm{\ϵ}}_1}---\left(9\right)$

Therefore, as long as record ε ₁And ε ₂, can obtain the elastic parameter of this rock sample according to formula (8) and (9).Reaching this purpose only needs to measure ε at the center of rock sample placement foil gauge ₁, ε ₂Get final product.This method is simple and practical, economical and effective, only need original test method is improved slightly, just can obtain the mechanics parameter of rock by the knowledge of Elasticity, be fit to wide popularization and application, not only can obtain the tensile strength of rock sample after this test improves by Mechanics Calculation, can also obtain the elastic modulus E of rock sample under pulling open badly, Bai Song compares μ.

Claims (1)

1. a Brazilian splitting method of measuring rock elasticity parameter under the stretching condition the steps include:

A, Brazilian disc split the law will be through the discoid test specimens of processing, be horizontally placed between the bearing plate of pressing machine, between the upper and lower bearing plate of test specimen, respectively place a hard steel wire as filler strip, filler strip is vertical with the plane of symmetry of test specimen, upper and lower bearing plate is exerted pressure, test specimen produces stretching force vertical and upper and lower load action direction, destroys until test specimen, and the tensile strength of rock is:

${\mathrm{\σ}}_1=-\frac{2P}{\mathrm{\πD}}---\left(1\right)$

σ in the formula ₁---the tensile strength of rock

P---splitting payload values

The diameter of D---rock sample

π---circular constant

${\mathrm{\σ}}_2=\frac{6P}{\mathrm{\πD}}---\left(2\right)$

σ in the formula ₂---the second principal stress of rock sample

P---splitting payload values

The diameter of D---rock sample

π---circular constant;

B, according to the Hooke's law in the classical elasticity:

${\mathrm{\ϵ}}_1=\frac{1}{E}[{\mathrm{\σ}}_1-\mathrm{\μ}({\mathrm{\σ}}_2+{\mathrm{\σ}}_3)]---\left(3\right)$

${\mathrm{\ϵ}}_2=\frac{1}{E}[{\mathrm{\σ}}_2-\mathrm{\μ}({\mathrm{\σ}}_2+{\mathrm{\σ}}_3)]---\left(4\right)$

${\mathrm{\ϵ}}_3=\frac{1}{E}[{\mathrm{\σ}}_3-\mathrm{\μ}({\mathrm{\σ}}_1+{\mathrm{\σ}}_2)]---\left(5\right)$

σ in the formula ₁, σ ₂, σ ₃---be respectively first principal stress, second principal stress, the third principal stress of rock sample;

ε ₁, ε ₂, ε ₃---be respectively first principal strain, second principal strain, the 3rd principal strain of rock sample;

The Young modulus of E---rock sample;

The Poisson ratio of μ---rock sample;

In conjunction with Brazilian split the law, the first principal stress of rock sample, second principal stress direction should be on the circular sections, third principal stress is zero, the direction of corresponding first principal stress, second principal stress, corresponding first principal strain of third principal stress direction, second principal strain, the 3rd principal strain, strain is non-vanishing on the direction of the 3rd principal strain;

Rock sample obtains σ by the stress analysis in C, the Brazilian disc split the law ₃=0, be zero at the stress of the axis direction of cylindric rock sample, on the circle of the cross section of rock sample, on any one cross section, be plane stress state, the direction of two principle stresses is respectively to be parallel to the direction of anchor clamps and perpendicular to the direction of anchor clamps;

On any one cross section, be easy to obtain that rock sample is out of shape situation accordingly in Brazilian diametral compression test, in the strain stress of columniform hole axis direction ₃Do not consider two principal strain ε in the cross section ₁, ε ₂Direction strain and principal direction of stress σ ₁, σ ₂Unanimity obtains on this cross section of end face at principal strain ε in the position of pasting foil gauge ₁, ε ₂The distortion of direction;

D, stress obtain σ ₃=0, the strain that obtains the stress direction correspondence according to Hooke's law is:

${\mathrm{\ϵ}}_1=-\frac{2P}{\mathrm{\πDE}}(1+3\mathrm{\μ})---\left(6\right)$

${\mathrm{\ϵ}}_2=\frac{2P}{\mathrm{\πDE}}(3+\mathrm{\μ})---\left(7\right)$

And then obtain the elastic parameter of rock sample:

$E=\frac{16P}{\mathrm{\πD}({3\mathrm{\ϵ}}_2+{\mathrm{\ϵ}}_1)}---\left(8\right)$

$\mathrm{\μ}=-\frac{{3\mathrm{\ϵ}}_1+{\mathrm{\ϵ}}_2}{{3\mathrm{\ϵ}}_2+{\mathrm{\ϵ}}_1}---\left(9\right)$

In the formula: E is an elastic modulus, and μ is the Bai Song ratio;

Record ε ₁And ε ₂, obtain the elastic parameter of this rock sample according to formula (8) and (9), reach this purpose and place foil gauge in the center of rock sample and measure ε ₁, ε ₂

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