METHOD FOR DETERMINING WHOLE MACRO-MICRO PROCESS OF ROCK DEFORMATION AND FAILURE BASED ON FOUR-PARAMETER TEST

Abstract

Disclosed is a method for determining a whole macro-micro process of rock deformation and failure based on a four-parameter test, including following steps: firstly, obtaining acoustic emission data and deformation data of a sample in a compression test, and then calculating the deformation data according to a finite deformation theory to obtain a mean rotation angle θ at each stress level; using Grassberger-Procaccia (G-P) algorithm to calculate the acoustic emission data, and obtaining a fractal dimension of a temporal distribution D.sub.T of an acoustic emission signal and calculating a fractal dimension of a spatial distribution D.sub.S; obtaining a microscopic morphology of a fracture surface by scanning electron microscope (SEM) test after the compression test, and calculating a fractal dimension D.sub.A of the fracture surface; finally, obtaining a mathematical trend relationship between θ and D.sub.T, D.sub.S and D.sub.A according to a comprehensive analysis of D.sub.T, D.sub.S, D.sub.A and θ.

Claims

1. A method for determining a whole macro-micro process of rock deformation and failure based on a four-parameter test, wherein specific steps comprise: A: firstly sampling an engineering rock mass to be tested, and processing a sampled rock mass into a cylindrical specimen; B: placing the cylindrical specimen on a testing machine in a compression test system, sticking a deformation sensor and an acoustic emission probe on a surface of the cylindrical specimen, then starting a compression test, and collecting acoustic emission data through the acoustic emission probe and deformation data on the surface of the cylindrical specimen through the deformation sensor while the compression test is being carried out; C: calculating the deformation data collected in step B according to a finite deformation theory, and obtaining a parameter-mean rotation angle θ, wherein the parameter-mean rotation angle θ characterizes a macroscopic deformation characteristic of materials at each stress level below:
F.sub.j.sup.i=S.sub.j.sup.i+R.sub.j.sup.i  (1), wherein F.sub.j.sup.i is a deformation gradient, orthogonal transformation R.sub.j.sup.i is a rotation tensor and symmetric transformation S.sub.j.sup.i is a strain tensor, and an expression of S.sub.j.sup.i is as follows: $\begin{array}{cc}{S}_j^i=\frac{1}{2}\left(u^i{.Math.{ }_j+u^j.Math.}_i\right)-\left(1-\cos \theta \right)L_k^i{L}_j^k,& \left(2\right)\end{array}$ during a test measurement, calculating out a strain component based on a small deformation theory: $\begin{array}{cc}{\epsilon }_j^i=\frac{1}{2}\left(u^i{.Math. { }_j+u^j.Math.}_i\right),& \left(3\right)\end{array}$ wherein u.sup.i|.sub.j is a covariant derivative of displacement and ε.sub.j.sup.i is a small deformation strain; combined a small deformation strain component with a finite deformation strain component to get:
S.sub.j.sup.i=ε.sub.j.sup.i−(1−cos θ)L.sub.k.sup.iL.sub.j.sup.k  (4), wherein L.sub.j.sup.k is azimuth tensor of a rotation axis; wherein according to Hooke's law, a one-dimensional elastic lossless constitutive formula is
σ=ES  (5), from formula (4) and formula (5), getting
σ=Eε.sub.j.sup.i−E(1−cos θ)L.sub.k.sup.iL.sub.j.sup.k  (6), wherein a is a stress; extending formula (6) to a three-dimensional state and writing formula (6) as $\begin{array}{cc}\{\begin{array}{c}{\sigma }_1^1=E{\epsilon }_1^1-E\left(1-\cos \theta \right)L_k^i{L}_j^k+\mu \left({\sigma }_2^2+{\sigma }_3^3\right)\\ {\sigma }_2^2=E{\epsilon }_2^2-E\left(1-\cos \theta \right)L_k^i{L}_j^k+\mu \left({\sigma }_1^1+{\sigma }_3^3\right)\\ {\sigma }_3^3=E{\epsilon }_3^3-E\left(1-\cos \theta \right)L_k^i{L}_j^k+\mu \left({\sigma }_2^2+{\sigma }_1^1\right)\end{array},& \left(7\right)\end{array}$ in a triaxial test, σ.sub.2.sup.2=σ.sub.3.sup.3=σ.sub.con, combined with formula (10), getting: $\begin{array}{cc}\frac{{\sigma }_1^1-2{\mathrm{\mu \sigma }}_{\mathrm{con}}}{E}={\epsilon }_1^1-\left(1-\cos \theta \right)L_k^1{L}_1^k,& \left(8\right)\end{array}$ in a triaxial compression test, there being an assumption as follows:
(L.sub.2.sup.1).sup.2=(L.sub.3.sup.2).sup.2=(L.sub.1.sup.3).sup.2  (9), writing formula (8) as $\begin{array}{cc}\frac{{\sigma }_1^1-2{\mathrm{\mu \sigma }}_{\mathrm{con}}}{E}={\epsilon }_1^1+\frac{2}{3}\left(1-\cos \theta \right),& \left(10\right)\end{array}$ obtaining a formula for calculating the mean rotation angle θ from formula (12): $\begin{array}{cc}\theta =\arccos \left(1-\frac{3}{2}\left(\frac{{\sigma }_1^1-2{\mathrm{\mu \sigma }}_{\mathrm{con}}}{E}-{\epsilon }_1^1\right)\right),& \left(11\right)\end{array}$ so as to calculate the mean rotation angle θ; D: using Grassberger-Procaccia (G-P) algorithm on the acoustic emission data collected in step B to calculate a fractal dimension of a temporal distribution D.sub.T of an acoustic emission signal and calculating a fractal dimension a spatial distribution D.sub.S according to a spatial projection method; specifically: taking time series of the acoustic emission signal as a research object, and then corresponding each time series to a series set with a capacity of n:
X={x.sub.1,x.sub.2, . . . ,x.sub.n}  (12), constructing the formula (12) as a m-dimensional phase space (m<n), firstly, taking m numbers as a vector of m-dimensional space
X={x.sub.1,x.sub.2,x.sub.3, . . . ,x.sub.m}  (13), then shifting one data to the right and taking m numbers again to form another vector, and so on to form N=n−m+1 vectors, wherein a corresponding correlation function is: $\begin{array}{cc}W\left(r\right)=\frac{1}{N^2}\underset{i=1}{\overset{N}{.Math.}}\underset{j=1}{\overset{N}{.Math.}}H\left[r-.Math.X_i-X_j.Math.\right],& \left(14\right)\end{array}$ wherein H is a Heaviside function, r is a given scale; when assigning a value to scale r, making r=kr.sub.0 in order to avoid dispersion, where k is taken as a scale coefficient and $r_0=\frac{1}{N^2}\underset{i=1}{\overset{N}{.Math.}}\underset{j=1}{\overset{N}{.Math.}}.Math.X_i-X_j.Math.;$  obtaining n points in a double logarithmic coordinate system, and performing data fitting on n points; wherein if a result is a straight line, the result means that the acoustic emission series has fractal characteristics in a given scale range, and a slope of the straight line is the fractal dimension of the temporal distribution D.sub.T of the acoustic emission parameter,
D.sub.T=1 gW(r)/1 g(r)  (15), for D.sub.S, using a space box dimension to cover it, with the box dimension defined as:
N(r)=Cr.sup.−D.sup.S  (16), wherein N(r) is the number of discrete bodies whose characteristic size is greater than, C is a material constant, and the other form of the above formula is the number-radius relation as follows:
M(r)=Cr.sup.−D.sup.S  (17), wherein r is different radii covering natural discrete bodies, and M(r) is the number of discrete bodies covered in a circle with a radius of r; taking the logarithm on both sides to get:
1 gM(r)=1 gC+D.sub.S1 g(r)  (18), wherein D.sub.S is the fractal dimension of the spatial distribution; E: carrying out a scanning electron microscope (SEM) test on a fracture surface of the specimen after the compression test is completed, to obtain a microscopic morphology of the fracture surface, observing the morphology of the fracture surface and calculating the fractal dimension D.sub.A of the fracture surface; wherein the number of units needed to cover an image in units of δ is N(δ), D.sub.A=−log(N(δ))/log δ; F: because of a correspondence of a change of the mean rotation angle θ to each process of rock deformation, including a compaction stage, a linear stage and a plastic yield stage in a compression process, finally obtaining a mathematical trend relationship between θ and D.sub.T, D.sub.S and D.sub.A through comprehensively analyzing the obtained fractal dimension of the temporal distribution D.sub.T of the acoustic emission, the fractal dimension of the spatial distribution D.sub.S of the acoustic emission and the fractal dimension D.sub.A of the fracture surface at each stress level prior to a peak strength and the mean rotation angle θ at a same stress level, as shown in a following formula,
θ=a*D.sub.T+b*D.sub.S+c*D.sub.A  (19), lastly obtaining values of a, b and c, so as to establish a quantitative relationship between macro and micro in a whole process of rock deformation and failure.

2. The method for determining a whole macro-micro process of rock deformation and failure based on a four-parameter test according to claim 1, wherein a height of the cylindrical specimen is 100 mm and a diameter of the cylindrical specimen is 50 mm.

3. The method for determining a whole macro-micro process of rock deformation and failure based on a four-parameter test according to claim 1, wherein the deformation data comprises axial deformation and circumferential deformation.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0040] FIG. 1 is a flow chart of a method for determining a whole macro-micro process of rock deformation and failure based on a four-parameter test according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0041] The technical solutions in the embodiments of the present disclosure will be clearly and completely described below. Obviously, the described embodiments are only part of the embodiments in this disclosure, but not all of them. Based on the embodiment in this disclosure, all other embodiments obtained by ordinary technicians in this field without creative effort are within the scope of protection in this disclosure.

[0042] As shown in FIG. 1, specific steps of this embodiment are as follows:

[0043] S1: firstly, sampling an engineering rock mass to be tested, and processing a sampled rock mass into a cylindrical specimen whose height is 100 mm high and diameter is 50 mm.

[0044] S2: placing the cylindrical specimen on a testing machine in a compression test system, sticking a deformation sensor and an acoustic emission probe on a surface of the cylindrical specimen, then starting a compression test, and collecting acoustic emission data through the acoustic emission probe and deformation data on the surface of the cylindrical specimen through the deformation sensor while the compression test is being carried out; with the deformation data comprising axial deformation and circumferential deformation.

[0045] S3: calculating the deformation data collected in S2 according to a finite deformation theory, and obtaining a parameter—mean rotation angle θ, which characterizes a macroscopic deformation characteristic of materials at each stress level and is specifically:

F.sub.j.sup.i=S.sub.j.sup.i+R.sub.j.sup.i  (1),

[0046] where F.sub.j.sup.i is a deformation gradient, orthogonal transformation R.sub.j.sup.i is a rotation tensor while symmetric transformation S.sub.j.sup.i is a strain tensor, and an expression of S.sub.j.sup.i is as follows:

[00009]$\begin{array}{cc}{S}_j^i=\frac{1}{2}\left(u^i{.Math.}_j+u^j{.Math.}_i\right)-\left(1-\cos \theta \right)L_k^i{L}_j^k,& \left(2\right)\end{array}$

[0047] during a test measurement, calculating out a strain component based on a small deformation theory below:

[00010]$\begin{array}{cc}{\epsilon }_j^i=\frac{1}{2}\left(u^i{.Math. { }_j+u^j.Math.}_i\right),& \left(3\right)\end{array}$

[0048] where u.sup.i|.sub.j is a covariant derivative of displacement and ε.sub.j.sup.i is a small deformation strain;

[0049] combined a small deformation strain component with a finite deformation strain component, getting:

S.sub.j.sup.i=ε.sub.j.sup.i−(1−cos θ)L.sub.k.sup.iL.sub.j.sup.i  (4),

[0050] where L.sub.j.sup.k, is an azimuth tensor of a rotation axis;

[0051] according to Hooke's law, one-dimensional elastic lossless constitutive formula is

σ=ES  (5),

[0052] from formula (4) and formula (5), getting

σ=Eε.sub.j.sup.i−E(1−cos θ)L.sub.k.sup.iL.sub.j.sup.k  (6),

[0053] where σ is a stress;

[0054] extending formula (6) to a three-dimensional state and writing formula (6) as

[00011]$\begin{array}{cc}\{\begin{array}{c}{\sigma }_1^1=E{\epsilon }_1^1-E\left(1-\cos \theta \right)L_k^i{L}_j^k+\mu \left({\sigma }_2^2+{\sigma }_3^3\right)\\ {\sigma }_2^2=E{\epsilon }_2^2-E\left(1-\cos \theta \right)L_k^i{L}_j^k+\mu \left({\sigma }_1^1+{\sigma }_3^3\right)\\ {\sigma }_3^3=E{\epsilon }_3^3-E\left(1-\cos \theta \right)L_k^i{L}_j^k+\mu \left({\sigma }_2^2+{\sigma }_1^1\right)\end{array},& \left(7\right)\end{array}$

[0055] in a triaxial test, σ.sub.2.sup.2=σ.sub.3.sup.3=σ.sub.con, combined with formula (10), getting:

[00012]$\begin{array}{cc}\frac{{\sigma }_1^1-2{\mathrm{\mu \sigma }}_{\mathrm{con}}}{E}={\epsilon }_1^1-\left(1-\cos \theta \right)L_k^1{L}_1^k,& \left(8\right)\end{array}$

[0056] in a triaxial compression test, there being an assumption as follows:

(L.sub.2.sup.1).sup.2=(L.sub.3.sup.2).sup.2=(L.sub.1.sup.3).sup.2  (9),

[0057] writing formula (8) as

[00013]$\begin{array}{cc}\frac{{\sigma }_1^1-2{\mathrm{\mu \sigma }}_{\mathrm{con}}}{E}={\epsilon }_1^1+\frac{2}{3}\left(1-\cos \theta \right),& \left(10\right)\end{array}$

[0058] obtaining a formula for calculating the mean rotation angle θ from formula (12):

[00014]$\begin{array}{cc}\theta =\arccos \left(1-\frac{3}{2}\left(\frac{{\sigma }_1^1-2{\mathrm{\mu \sigma }}_{\mathrm{con}}}{E}-{\epsilon }_1^1\right)\right),& \left(11\right)\end{array}$

[0059] so as to calculate the mean rotation angle θ;

[0060] S4: using Grassberger-Procaccia (G-P) algorithm on the acoustic emission data collected in S2 to calculate a fractal dimension of a temporal distribution D.sub.T of an acoustic emission signal and calculating a fractal dimension of a spatial distribution D.sub.S according to a spatial projection method; specifically:

[0061] taking time series of the acoustic emission signal as a research object, then corresponding each time series to a series set with a capacity of n:

X={x.sub.1,x.sub.2, . . . ,x.sub.n}  (12),

[0062] constructing formula (12) as a m-dimensional phase space (m<n), firstly, taking m numbers as a vector of m-dimensional space

X.sub.1={x.sub.1,x.sub.2,x.sub.3, . . . ,x.sub.m}  (13),

[0063] then shifting one data to the right and taking m numbers again to form another vector, and so on to form N=n−m+1 vectors; the corresponding correlation function is:

[00015]$\begin{array}{cc}W\left(r\right)=\frac{1}{N^2}\underset{i=1}{\overset{N}{.Math.}}\underset{j=1}{\overset{N}{.Math.}}H\left[r-.Math.X_i-X_j.Math.\right],& \left(14\right)\end{array}$

[0064] where H is Heaviside function; r is a given scale; when assigning a value to scale r, making r=kr.sub.0 in order to avoid dispersion, where k is taken as a scale coefficient and

[00016]$r_0=\frac{1}{N^2}\underset{i=1}{\overset{N}{.Math.}}\underset{j=1}{\overset{N}{.Math.}}.Math.X_i-X_j.Math.;$

obtaining n points in a double logarithmic coordinate system, and performing data fitting on n points. If the result is a straight line, it shows that the acoustic emission series has fractal characteristics in a given scale range, and a slope of the straight line is the fractal dimension of the temporal distribution D.sub.T of the acoustic emission parameter, namely

D.sub.T=1 gW(r)/1 g(r)  (15).

[0065] For D.sub.S, the space box dimension is used. The box dimension is defined as:

N(r)=Cr.sup.−D.sup.S  (16),

[0066] where N(r) is the number of discrete bodies whose characteristic size is greater than r, C is a material constant, and the other form of the above formula is the number-radius relation as follows:

M(r)=Cr.sup.−D.sup.S  (17),

[0067] where r is different radii covering natural discrete bodies, and M(r) is the number of discrete bodies covered in a circle with radius of r. Taking the logarithm on both sides to get:

1 gM(r)=1 gC+D.sub.S1 g(r)  (18),

[0068] where D.sub.S is the fractal dimension of the spatial distribution;

[0069] S5: carrying out a scanning electron microscope (SEM) test on a fracture surface of the sample after the compression test is completed, to obtain a microscopic morphology of the fracture surface, observing the morphology of the fracture surface and calculating the fractal dimension D.sub.A of the fracture surface.

[0070] The number of units needed to cover an image in units of δ is N(δ), D.sub.A=−log(N(δ))/log δ.

[0071] S6: because of a correspondence of a change of the mean rotation angle θ to each process of rock deformation, including a compaction stage, a linear stage and a plastic yield stage in a compression process, finally obtaining a mathematical trend relationship between θ and D.sub.T, D.sub.S and D.sub.A through comprehensively analyzing the obtained the fractal dimension of the temporal distribution D.sub.T of the acoustic emission, the fractal dimension of the spatial distribution D.sub.S of the acoustic emission and the fractal dimension D.sub.A of the fracture surface at each stress level (prior to a peak strength) and the mean rotation angle θ at a same stress level, as shown in a following formula,

θ=a*D.sub.T+b*D.sub.S+c*D.sub.A  (19),

[0072] eventually obtaining values of a, b and c, so as to establish the quantitative relationship between macro and micro in the whole process of rock deformation and failure.

[0073] In this application, specific examples are used to explain the principle and implementation of this application. The explanations of the above examples are only used to help understand the methods and core ideas of this application. At the same time, according to the ideas in this application, there will be some changes in the specific implementation and application scope for ordinary technicians in this field. To sum up, the contents of this specification should not be construed as a limitation to this application.