CN102183410A

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

Info

Publication number: CN102183410A
Application number: CN2011100311986A
Authority: CN
Inventors: 周辉; 杨艳霜; 张占荣; 徐速超; 李震
Original assignee: Wuhan Institute of Rock and Soil Mechanics of CAS
Current assignee: Wuhan Institute of Rock and Soil Mechanics of CAS
Priority date: 2011-01-27
Filing date: 2011-01-27
Publication date: 2011-09-14
Anticipated expiration: 2031-01-27
Also published as: CN102183410B

Abstract

本发明公开了一种测量拉伸条件下岩石弹性参数的巴西劈裂方法，其步骤：A、巴西圆盘劈裂法将经加工的圆盘状试件，横置于压力机的承压板间，在试件的上、下承压板间各放置硬质钢丝，垫条与试件的对称面垂直，对上、下承压板施加压力，使试件产生垂直与上、下荷载作用方向的张拉力；B、结合巴西劈裂法的具体情况，用经典弹性力学中的虎克定律进行分析；C、分析巴西圆盘劈裂法中岩样的受力情况及测量的原理；D、由受力状态得到

，根据虎克定律得到应力方向对应的应变，测得

和

，获得该岩样的弹性参数，达到在岩样的中心位置放置应变片来测量

、

。方法易行，操作简便，具有原理清晰，使用简便，材料消耗少等优点，适合广泛推广应用。The invention discloses a Brazilian splitting method for measuring elastic parameters of rocks under tensile conditions. The steps are: A. Brazilian disc splitting method, the processed disc-shaped test piece is placed horizontally on the pressure bearing plate of a press Place hard steel wires between the upper and lower bearing plates of the test piece, and the pads are perpendicular to the symmetrical plane of the test piece, and apply pressure to the upper and lower bearing plates to make the test piece produce vertical and upper and lower loads. B. Combining with the specific situation of the Brazilian splitting method, using Hooke's law in classical elastic mechanics to analyze; C. Analyzing the force of the rock sample in the Brazilian disc splitting method and the principle of measurement; D. , obtained from the state of stress

, the strain corresponding to the stress direction is obtained according to Hooke's law, and the measured

and

, to obtain the elastic parameters of the rock sample, to measure by placing a strain gauge at the center of the rock sample

,

. The method is easy to operate, easy to operate, clear in principle, easy to use, less in material consumption, etc., and is suitable for wide popularization and application.

Description

A Brazilian Split Method for Measuring Rock Elastic Parameters Under Tensile Conditions

技术领域technical field

本发明涉及巴西劈裂法测量岩石的抗拉强度更具体涉及一种测量拉破坏条件下岩石弹性参数的巴西劈裂方法，该方法简单，原理清晰，在获得拉破坏强度的同时能够反映岩石在拉破坏下的弹性性质。众所周知，岩石材料的抗拉性质和抗压性质有着很大的差异性，而在目前的岩石力学热点问题中，越来越关注岩石的拉破坏所表现出来的特殊性质。本发明专利针对岩石的拉破坏，对巴西劈裂法进行简单的改进，从而获得岩石的抗拉强度以及在拉破坏下的弹性模量E和柏松比μ。The present invention relates to the Brazilian splitting method for measuring the tensile strength of rocks, and more specifically relates to a Brazilian splitting method for measuring rock elastic parameters under tensile failure conditions. Elastic properties under tension failure. It is well known that the tensile properties and compressive properties of rock materials are very different, and in the current hot issues of rock mechanics, more and more attention is paid to the special properties of rocks exhibited by tensile failure. The patent of the present invention aims at the tensile failure of the rock, and simply improves the Brazilian splitting method, so as to obtain the tensile strength of the rock, the elastic modulus E and the Poisson's ratio μ under the tensile failure.

背景技术Background technique

目前，随着我国大型水利水电以及采矿工程不断向深部发展，岩石力学不断面对新的问题。岩石的抗拉强度是一个重要岩石的力学参数，它不仅反映岩石的力学性质，还是分析岩体稳定性的重要指标。在工程实际中面临的岩爆、岩芯饼化等新的热点问题中，特别是在深部岩体工程中，岩石的破坏形式向着更加复杂的拉破坏或拉剪破坏发展，岩石的抗拉强度显得更加重要。在现有的试验中，岩石的弹性参数一般由单轴压缩试验或者三轴压缩试验来确定，在压破坏下的岩石弹性参数带有明显的压破坏特点，用这样的弹性参数来解释在拉应力条件下产生的破坏及工程现象显然是不够科学的。为此，本发明专利在原有的巴西劈裂法的基础上通过简单的改进，在经典弹性力学的理论指导下，获得岩石在拉破坏下的弹性参数。At present, with the continuous development of large-scale water conservancy, hydropower and mining projects in my country, rock mechanics is constantly facing new problems. The tensile strength of rock is an important mechanical parameter of rock. It not only reflects the mechanical properties of rock, but also is an important index for analyzing the stability of rock mass. In the new hot issues such as rockburst and core cake in engineering practice, especially in deep rock mass engineering, the failure form of rock is developing towards more complex tensile failure or tensile shear failure, and the tensile strength of rock appear more important. In the existing tests, the elastic parameters of rock are generally determined by uniaxial compression test or triaxial compression test. The elastic parameters of rock under compression failure have obvious characteristics of compression failure. The damage and engineering phenomena produced under stress conditions are obviously not scientific enough. For this reason, the patent of the present invention obtains the elastic parameters of the rock under tensile failure by simple improvement on the basis of the original Brazilian splitting method and under the guidance of the theory of classical elastic mechanics.

在目前的室内实验中，岩石抗拉强度的测试方法通常采用直接拉伸法和巴西圆盘劈裂法(Brazilian test)。巴西圆盘劈裂法由于不受夹具的限制，简单可靠，故目前应用较为广泛。巴西圆盘劈裂法可以获得岩石的抗拉强度，而岩石的弹性参数需要由另外的室内试验或者现场原位实验来获得。本试验方法在巴西圆盘劈裂法的基础上进行改进，通过简单的力学分析同时获得岩石的弹性参数，具有易于开展、实用经济的特点。In the current laboratory experiments, the testing method of rock tensile strength usually adopts direct tension method and Brazilian disc splitting method (Brazilian test). The Brazilian disc splitting method is widely used because it is simple and reliable without the limitation of fixtures. The Brazilian disc splitting method can obtain the tensile strength of the rock, while the elastic parameters of the rock need to be obtained by another laboratory test or in-situ experiment. This test method is improved on the basis of the Brazilian disc splitting method, and the elastic parameters of the rock are obtained through simple mechanical analysis, which is easy to carry out, practical and economical.

发明内容Contents of the invention

本发明的目的是在于提供了一种测量拉伸条件下岩石弹性参数的巴西劈裂方法，方法易行，操作简便，该方法利用传统的巴西劈裂法试验可以同时获得岩石的抗拉强度和在岩样的拉破坏下的弹性参数(弹性模量E，柏松比μ)，具有原理清晰，使用简便，材料消耗少等有点，适合广泛推广应用。The object of the present invention is to provide a kind of Brazilian splitting method of rock elastic parameter under the measuring tensile condition, method is easy to implement, easy to operate, this method utilizes traditional Brazilian splitting method test and can obtain the tensile strength and the tensile strength of rock simultaneously The elastic parameters (elastic modulus E, Poisson's ratio μ) under the tensile failure of rock samples have the advantages of clear principle, easy to use, and less material consumption, and are suitable for wide application.

一种测量拉伸条件下岩石弹性参数的巴西劈裂方法，其理论基础是经典的弹性力学理论，其步骤如下：A Brazilian splitting method for measuring elastic parameters of rocks under tensile conditions, the theoretical basis of which is the classical elastic mechanics theory, and the steps are as follows:

A、巴西圆盘劈裂法(Brazilian test)将经加工的圆盘状试件，横置于压力机的承压板间，并且在试件的上、下承压板间各放置一根直径为2mm的硬质钢丝作为垫条，垫条与试件的对称面垂直。对上、下承压板施加压力，使试件产生垂直与上、下荷载作用方向的张拉力，直至试件破坏。由该试验方法的力学特点，岩石的抗拉强度可表示为：A. The Brazilian disc splitting method (Brazilian test) places the processed disc-shaped test piece horizontally between the pressure plates of the press, and places a diameter between the upper and lower pressure plates of the test piece. The hard steel wire with a diameter of 2 mm is used as a pad, and the pad is perpendicular to the symmetry plane of the test piece. Apply pressure to the upper and lower bearing plates, so that the specimen produces a tensile force perpendicular to the direction of the upper and lower loads until the specimen is destroyed. According to the mechanical characteristics of this test method, the tensile strength of rock can be expressed as:

${σ σ}_{11} = = - - \frac{22 P P}{πD πD} - - - - - - ((11))$

式中σ₁——岩石的抗拉强度(即第一主应力)In the formula σ ₁ ——the tensile strength of the rock (namely the first principal stress)

P——劈裂荷载值P——Splitting load value

D——岩样的直径D - the diameter of the rock sample

π——圆周率π - pi

同时：at the same time:

${σ σ}_{22} = = \frac{66 P P}{πD πD} - - - - - - ((22))$

式中σ₂——岩样的第二主应力In the formula, σ ₂ ——the second principal stress of the rock sample

P——劈裂荷载值P——Splitting load value

D——岩样的直径D - the diameter of the rock sample

π——圆周率π - pi

B、引用经典的力学理论代入到巴西劈裂模型中，经典弹性力学中的虎克定律：B. Citing the classical mechanical theory and substituting it into the Brazilian splitting model, Hooke's law in classical elastic mechanics:

${ϵ ϵ}_{11} = = \frac{11}{E E.} [[{σ σ}_{11} - - μ μ (({σ σ}_{22} + + {σ σ}_{33}))]] - - - - - - ((33))$

${ϵ ϵ}_{22} = = \frac{11}{E E.} [[{σ σ}_{22} - - μ μ (({σ σ}_{22} + + {σ σ}_{33}))]] - - - - - - ((44))$

${ϵ ϵ}_{33} = = \frac{11}{E E.} [[{σ σ}_{33} - - μ μ (({σ σ}_{11} + + {σ σ}_{22}))]] - - - - - - ((55))$

式中σ₁、σ₂、σ₃——分别为岩样的第一主应力、第二主应力、第三主应力；In the formula, σ ₁ , σ ₂ , σ ₃ ——respectively, the first principal stress, the second principal stress, and the third principal stress of the rock sample;

ε₁、ε₂、ε₃——分别为岩样的第一主应变、第二主应变、第三主应变；ε ₁ , ε ₂ , ε ₃ ——respectively, the first principal strain, the second principal strain, and the third principal strain of the rock sample;

E——岩样的杨氏模量；E——Young's modulus of the rock sample;

μ——岩样的泊松比；μ - Poisson's ratio of the rock sample;

由虎克定律可以得到应变值为公式(3)、(4)，结合巴西劈裂法是实际情况可知，岩样的第一主应力、第二主应力方向应在圆截面上，第三主应力为零，相应的第一主应力、第二主应力、第三主应力方向对应第一主应变、第二主应变、第三主应变的方向，且在第三主应变的方向上应变不为零。由于ε₃与本发明的结论无关，因此忽略ε₃。According to Hooke's law, the strain values can be obtained from the formulas (3) and (4). Combined with the actual situation of the Brazilian splitting method, it can be seen that the directions of the first principal stress and the second principal stress of the rock sample should be on the circular section, and the directions of the third principal stress should be on the circular section. The stress is zero, and the corresponding directions of the first principal stress, the second principal stress and the third principal stress correspond to the directions of the first principal strain, the second principal strain and the third principal strain, and the strain in the direction of the third principal strain is not to zero. Since ε ₃ is irrelevant to the conclusions of the present invention, ε ₃ is ignored.

C、巴西圆盘劈裂法中岩样由受力状态可以分析得到σ₃＝0，即在圆柱状岩样的轴线方向的应力为零。在岩样的截面圆上，在任意一个截面上是平面应力状态，两个主应力的方向分别是平行于夹具的方向和垂直于夹具的方向。C. In the Brazilian disc splitting method, the rock sample can be analyzed from the stress state to get σ ₃ =0, that is, the stress in the axial direction of the cylindrical rock sample is zero. On the cross-sectional circle of the rock sample, any cross-section is in a plane stress state, and the directions of the two principal stresses are parallel to the clamp and perpendicular to the clamp, respectively.

在任意一个截面上，很容易获得了在巴西劈裂试验中岩样相应的变形情况，由于是平面应力问题，在圆柱形的洞轴线方向的应变ε₃可以不考虑，在截面的两个主应变ε₁、ε₂方向应变与主应力方向σ₁、σ₂一致。那么在附图中贴应变片的位置则可以获得在端面这个截面上在主应变ε₁、ε₂方向的变形。On any section, it is easy to obtain the corresponding deformation of the rock sample in the Brazilian splitting test. Since it is a plane stress problem, the strain ε ₃ in the axial direction of the cylindrical hole can be ignored. The strains in the directions ε ₁ and ε ₂ are consistent with the principal stress directions σ ₁ and σ ₂ . Then, the position where the strain gauge is pasted in the attached drawing can obtain the deformation in the direction of the principal strain ε ₁ and ε ₂ on the section of the end face.

D、根据前文所列的虎克定律(3)、(4)、(5)可以得到在图(2)中所示的应变计算公式可直接换算成为下式：D. According to Hooke's law (3), (4) and (5) listed above, the strain calculation formula shown in Figure (2) can be directly converted into the following formula:

${ϵ ϵ}_{11} = = - - \frac{22 P P}{πDE πDE} ((11 + + 33 μ μ)) - - - - - - ((66))$

${ϵ ϵ}_{22} = = \frac{22 P P}{πDE πDE} ((33 + + μ μ)) - - - - - - ((77))$

对(6)、(7)进行公式变换就可以直接得到岩样的弹性模量E，柏松比μ：By transforming formulas (6) and (7), the elastic modulus E and Poisson's ratio μ of the rock sample can be obtained directly:

$E E. = = \frac{1616 P P}{πD πD (({33 ϵ ϵ}_{22} + + {ϵ ϵ}_{11}))} - - - - - - ((88))$

$μ μ = = - - \frac{{33 ϵ ϵ}_{11} + + {ϵ ϵ}_{22}}{{33 ϵ ϵ}_{22} + + {ϵ ϵ}_{11}} - - - - - - ((99))$

因此，只要测得ε₁和ε₂，即可根据式(8)和(9)获得该岩样的弹性参数。达到该目的只需在岩样的中心位置放置应变片来测量ε₁、ε₂即可。该方法简单实用，经济有效，只需将原有的试验方法略加改进，通过弹性力学的知识便可获得岩石的力学参数，适合广泛推广应用，该试验改进后通过力学计算不仅可以获得岩样的抗拉强度，还可以获得在拉破坏下岩样的弹性模量E，柏松比μ。Therefore, as long as ε ₁ and ε ₂ are measured, the elastic parameters of the rock sample can be obtained according to formulas (8) and (9). To achieve this purpose, it is only necessary to place a strain gauge at the center of the rock sample to measure ε ₁ and ε ₂ . This method is simple, practical, economical and effective. It only needs to slightly improve the original test method, and the mechanical parameters of the rock can be obtained through the knowledge of elastic mechanics, which is suitable for wide application. The elastic modulus E and Poisson's ratio μ of the rock sample under tensile failure can also be obtained.

本发明与其他获得岩石力学参数或岩石抗拉强度的试验方法相比具有以下优点：Compared with other test methods for obtaining rock mechanical parameters or rock tensile strength, the present invention has the following advantages:

(1)本发明简便实用，经济有效，在原有的已经广泛应用的巴西圆盘劈裂法的基础上略加改进，便可同时获得岩石的抗拉强度，以及在拉破坏下岩样的弹性参数，其中具体指弹性模量E，柏松比μ。(1) The present invention is simple and practical, economical and effective, slightly improved on the basis of the original widely used Brazilian disc splitting method, and can simultaneously obtain the tensile strength of the rock and the elasticity of the rock sample under tensile failure Parameters, which specifically refer to the elastic modulus E, Poisson's ratio μ.

(2)传统的在室内获得岩石的力学参数的方法一般是通过几组岩样的单轴抗压强度或者三轴抗压强度试验结果来分析获得，在实际工程中，许多复杂的岩体失稳并不是岩石的压破坏，而是拉破坏。故在拉破坏的前提下获得的岩石弹性参数在一定程度上更加能够反映岩石力学工程中的实际问题。(2) The traditional method of obtaining rock mechanical parameters indoors is generally obtained through the analysis of uniaxial compressive strength or triaxial compressive strength test results of several groups of rock samples. In actual engineering, many complex rock mass failures Stability is not the compressive failure of rocks, but the tensile failure. Therefore, the rock elastic parameters obtained under the premise of tensile failure can better reflect the practical problems in rock mechanics engineering to a certain extent.

附图说明：Description of drawings:

图1为一种巴西劈裂法测量ε₁的电阻应变片布置图Figure 1 is a layout diagram of resistance strain gauges for measuring _ε1 by Brazilian split method

图2为一种巴西劈裂法测量ε₂的电阻应变片布置图Figure 2 is a layout diagram of resistance strain gauges for measuring _ε2 by Brazilian split method

其中：P一劈裂荷载值、D一岩样的直径。Among them: P—split load value, D—diameter of rock sample.

具体实施方式Detailed ways

实施例1：Example 1:

一种测量拉伸条件下岩石弹性参数的巴西劈裂方法，其步骤如下：A Brazilian splitting method for measuring elastic parameters of rock under tensile conditions, the steps are as follows:

${σ σ}_{11} = = - - \frac{22 P P}{πD πD} - - - - - - ((11))$

P——劈裂荷载值P——Splitting load value

D——岩样的直径D - the diameter of the rock sample

π——圆周率π - pi

同时：at the same time:

${σ σ}_{22} = = \frac{66 P P}{πD πD} - - - - - - ((22))$

P——劈裂荷载值P——Splitting load value

D——岩样的直径D - the diameter of the rock sample

π——圆周率π - pi

${ϵ ϵ}_{22} = = \frac{11}{E E.} [[{σ σ}_{22} - - μ μ (({σ σ}_{11} + + {σ σ}_{33}))]] - - - - - - ((44))$

式中σ₁、σ₂、ε₃——分别为岩样的第一主应力、第二主应力、第三主应力；In the formula, σ ₁ , σ ₂ , ε ₃ ——respectively, the first principal stress, the second principal stress, and the third principal stress of the rock sample;

E——岩样的杨氏模量；E——Young's modulus of the rock sample;

μ——岩样的泊松比；μ - Poisson's ratio of the rock sample;

${ϵ ϵ}_{22} = = - - \frac{22 P P}{πDE πDE} ((33 + + μ μ)) - - - - - - ((77))$

Claims

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:

σ_{1} = - \frac{2 P}{πD} - - - (1)

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

P---splitting payload values

The diameter of D---rock sample

π---circular constant

σ_{2} = \frac{6 P}{πD} - - - (2)

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:

ϵ_{1} = \frac{1}{E} [σ_{1} - μ (σ_{2} + σ_{3})] - - - (3)

ϵ_{2} = \frac{1}{E} [σ_{2} - μ (σ_{2} + σ_{3})] - - - (4)

ϵ_{3} = \frac{1}{E} [σ_{3} - μ (σ_{1} + σ_{2})] - - - (5)

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:

ϵ_{1} = - \frac{2 P}{πDE} (1 + 3 μ) - - - (6)

ϵ_{2} = \frac{2 P}{πDE} (3 + μ) - - - (7)

And then obtain the elastic parameter of rock sample:

E = \frac{16 P}{πD ({3 ϵ}_{2} + ϵ_{1})} - - - (8)

μ = - \frac{{3 ϵ}_{1} + ϵ_{2}}{{3 ϵ}_{2} + ϵ_{1}} - - - (9)

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