CN106644680A - Quantitative classification method for rock sample crushing degree based on grid density and crack density - Google Patents
Quantitative classification method for rock sample crushing degree based on grid density and crack density Download PDFInfo
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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- G—PHYSICS
- 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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Abstract
The invention aims to provide a quantitative classification method for rock sample crushing degree based on grid density and crack density, wherein the method can meet quantitative analysis requirements of destroy characteristics and crushing degree of rock samples. The method includes the steps: firstly, acquiring crack expansion diagrams; secondly, making '360 grids'; thirdly, drawing relationship diagrams among 360 grid density gamma W subsections and corresponding number of rock samples; fourthly, drawing relationship diagrams among the number of cracks and 360 grid density gamma W according to the relationship diagrams obtained in the step 2 and the step 3; fifthly, building classification standards describing the rock sample crushing degree by the 360 grid density gamma W; sixthly, calculating crack density gamma J of the rock samples corresponding to the number of the cracks counted in the step 2; seventhly, building classification standards describing the rock sample crushing degree by the crack density gamma J of the rock samples; eighthly, performing quantitative classification for the rock sample crushing degree by the aid of the gamma W and the gamma J.
Description
Technical field
The present invention relates to the rock mechanics experiment field in Geotechnical Engineering, especially a kind of close based on mesh-density and crackle
The rock sample degree of crushing Quantitative Classification Method of degree.
Background technology
Rock mechanics experiment is the basis of rock mechanics, is one of important means of study of rocks mechanics and engineering.Although
Now scientific algorithm and theory analysis have reached suitable height, but rock mechanics experiment as in directly solution Practical Project
Mechanics problem still have irreplaceable effect, with research go deep into, for the analysis of result of the test propose it is higher
Requirement.
After the mechanical tests such as single shaft, three axles, rock sample can produce the destruction of macroscopic view to rock sample, and rock sample surface occurs
Several even tens of Cracks, corresponding rock sample can be broken down into block not of uniform size, in irregular shape, and the destruction of rock sample is special
Levy and degree of crushing be with rock type and add unloading stress paths it is closely related, probe into the failure mode of rock sample for assurance
Failure mechanism of the rock under the effect of various stress paths has very important significance, and is that rock mechanics analysis must
One of few content, thus accurate quantitative analysis judge rock sample degree of crushing be particularly important.
At present, in document, report and books with regard to the collapse state description after rock sample mechanical test, generally only
It is that qualitatively address is " relatively more broken ", " broken " etc., the crackle of rock sample is carried out and degree of crushing lacks quantitative target description,
The collapse state of the rock sample of identical or different types of rock or different plus unloading stress paths cannot quantitative comparison, be
The description of rock mechanics brings larger difficulty.
The content of the invention
The technical problem to be solved is to provide a kind of broken journey of rock sample based on mesh-density and crack density
Degree Quantitative Classification Method, can meet the requirement of rock sample destructive characteristics and degree of crushing quantitative analysis, and analysis process is simple,
Accurately, explicit physical meaning, result of calculation is directly perceived for value, is easy to practice operation.
To solve above-mentioned technical problem, the technical solution adopted in the present invention is:One kind is close based on mesh-density and crackle
The rock sample degree of crushing Quantitative Classification Method of degree, the method is comprised the following steps:
Step 1:Obtain the crackle expanded view after the rock sample destruction of multiple same sizes;
Step 2:" 360 grid " of each rock sample is made, each crackle obtained to step 1 by " 360 grid " is launched
Crack number in figure is counted, and draws the graph of a relation of crack number and corresponding rock sample quantity;
Step 3:By the number of grid Q containing crackle in each crackle expanded view that " 360 grid " is obtained to step 1W
Counted, calculating each rock sample there are 360 mesh-density Γ of crackleW, computing formula is
In formula, QWFor the number of grid that each rock sample contains crackle, 0≤Qw≤ 360,
Draw 360 mesh-density ΓWIt is segmented the graph of a relation with corresponding rock sample quantity;
Step 4:According to the graph of a relation that step 2 and 3 are obtained, crack number and 360 mesh-density Γ are drawnWGraph of a relation,
Graph of a relation is analyzed and is learnt:With the increase of crack number, 360 mesh-densities increase in power function form, in crackle number
When amount reaches more than 20,360 mesh-density growth trends are intended to steadily;
Step 5:According to the result of step 4 statistical analysis, refer to regard to rock crushing degree with reference to rock mechanics related specifications
Mark criteria for classification, the actual degree of crushing of decohesion rock sample and its 360 mesh-density values, set up with 360 mesh-density ΓWDescription
The criteria for classification of rock sample degree of crushing is as follows:
0≤ΓW<0.1:It is slight broken;
0.1≤ΓW<0.3:Relatively crush;
0.3≤ΓW<0.5:It is broken;
0.5≤ΓW<0.8:Crush very much;
0.8≤ΓW≤1.0:Crush completely;
Step 6:The rock sample crack density Γ corresponding to each crack number counted in calculation procedure 2J, computing formula is
In formula, QJFor crack number;S is rock sample lateral area, and K is regulation coefficient;
Step 7:According to the result of step 6 statistical analysis, refer to regard to rock crushing degree with reference to rock mechanics related specifications
Mark criteria for classification, the actual degree of crushing of decohesion rock sample and its crack density value, set up and use rock sample crack density ΓJDescription
The criteria for classification of rock sample degree of crushing is as follows:
0≤ΓJ<0.3:Thin crackle;
0.3≤ΓJ<0.5:Closeer crackle;
0.5≤ΓJ<0.8:Intensive crackle;
0.8≤ΓJ<1.0:Very intensive crackle;
ΓJ≥1.0:Fragmentation;
Step 8:The mesh-density Γ of use 360 that step 5 is set upWThe criteria for classification and step 7 of description rock sample degree of crushing
The use rock sample crack density Γ of foundationJThe criteria for classification of description rock sample degree of crushing combines, and it is fixed that rock sample degree of crushing is carried out
Amount classification, is defined as follows:
(1) it is more complete:0≤ΓW<0.1,0≤ΓJ<0.5;
(2) relatively crush:0.1≤ΓW<0.3,0.5≤ΓJ<0.8;
(3) crush:0.3≤ΓW<0.5,0.8≤ΓJ<1.0;
(4) crush very much:0.5≤ΓW<0.8, ΓJ≥1.0;
(5) fragmentation completely:0.8≤ΓW≤ 1.0, ΓJ≥1.0。
In step 1, by " a kind of rock sample crackle drawing apparatus and retouching disclosed in Patent No. 201410068603.5
Paint method " obtain the crackle expanded view after rock sample destruction;Rock examination can also be obtained by way of rock sample photofit
Crackle expanded view after sample destruction.
In step 2, the preparation method of " 360 grid " is:The crackle exhibition figure that step 1 is obtained is put down in rock sample short transverse
10 lattice are divided into, in rock sample circumferential direction 36 lattice are equally divided into, formed " 360 grid " of totally 360 grids.
In step 2, crack number statistical method is:
A, for the independent crackle for occurring, directly count according to actual bar number;
B, for have in the middle of crackle intersection or bifurcated, according to rock sample destruction controlling crack advance direction, first count
Major control crackle, then count intersect therewith or bifurcated secondary crackle.
In step 3, the number of grid Q containing crackleWStatistical method be:
The crackle occurred in a, all grids is counted as 1;
B, same grid are still counted as 1 when there are many Cracks simultaneously, i.e., only statistics has the number of grid that crackle occurs,
The crackle in grid is not repeatedly counted.
The regulation coefficient K computational methods of step 6 are:
Find in statistic processes, destruction rock sample crackle bar number is crushed completely when being 20 or so, for the ease of splitting
The regularization statistics of line density, it is standard 1 to define corresponding crack density when crack number is 20, therefore K values areD is rock sample diameter.
It is a kind of based on mesh-density and the rock sample degree of crushing Quantitative Classification Method of crack density that the present invention is provided, big
On the basis of amount destruction rock sample face crack development degree and degree of crushing quantitative statistical analysis, the grid of rock sample crackle is considered
Two parameters of density and crack density, propose a kind of brand-new Quantitative Classification Method, can meet rock sample destructive characteristics and
The requirement of degree of crushing quantitative analysis, analysis process is simple, and accurately, explicit physical meaning, result of calculation is directly perceived, is easy to reality for value
Trample operation.
Description of the drawings
With reference to the accompanying drawings and examples the invention will be further described:
Fig. 1 is the rock sample crackle expanded view that the step 1 of the embodiment of the present invention one is obtained;
Fig. 2 is " 360 grid " schematic diagram that the step 2 of the embodiment of the present invention one makes;
Fig. 3 be the step 2 of the embodiment of the present invention one refer to can be used to be fixed on rock sample be easy to count the net containing crackle
" 360 graph paper " of lattice quantity;
Fig. 4 is the graph of a relation of the crack number with corresponding rock sample quantity of the step 2 of the embodiment of the present invention one drafting;
Fig. 5 is the 360 mesh-density Γ that the step 3 of the embodiment of the present invention one is drawnWIt is segmented the pass with corresponding rock sample quantity
System's figure;
Fig. 6 is the crack number and 360 mesh-density Γ that the step 4 of the embodiment of the present invention one is drawnWGraph of a relation;
Fig. 7 is 360 mesh-density Γ different in the step 5 of the embodiment of the present invention oneWCorresponding rock sample degree of crushing shows
It is intended to;
Fig. 8 is rock sample crack density Γ different in the step 7 of the embodiment of the present invention oneJCorresponding rock sample degree of crushing shows
It is intended to;
Fig. 9 is the compares figure evaluated the standard that the present invention sets up in the embodiment of the present invention two, and now rock sample is crushed
Degree classification is more complete;
Figure 10 is the compares figure evaluated the standard that the present invention sets up in the embodiment of the present invention two, and now rock sample is crushed
Degree classification is more broken;
Figure 11 is the compares figure evaluated the standard that the present invention sets up in the embodiment of the present invention two, and now rock sample is crushed
Degree classification is broken;
Figure 12 is the compares figure evaluated the standard that the present invention sets up in the embodiment of the present invention two, and now rock sample is crushed
Degree classification is to crush very much;
Figure 13 is the compares figure evaluated the standard that the present invention sets up in the embodiment of the present invention two, and now rock sample is crushed
Degree classification is to crush completely.
Specific embodiment
Embodiment one
It is a kind of based on mesh-density and the rock sample degree of crushing Quantitative Classification Method of crack density, the method includes following step
Suddenly:
Step 1:A large amount of sandstone, limestone, granite, sand slate, the piece fiber crops completed with reference to documents and materials and laboratory early stage
The all kinds such as rock rock destroys rock sample under different plus unloading stress paths, 200 groups altogether;Obtain 200 same sizes
Crackle expanded view after rock sample destruction, as shown in Figure 1;
Step 2:" 360 grid " of each rock sample is made, each crackle obtained to step 1 by " 360 grid " is launched
Crack number in figure is counted.Statistics is as shown in table 1:
The rock sample crack number statistical form of table 1
The graph of a relation of crack number and corresponding rock sample quantity is drawn, as shown in Figure 4;
Step 3:By the number of grid Q containing crackle in each crackle expanded view that " 360 grid " is obtained to step 1W
Counted,
Calculating each rock sample has 360 mesh-density Γ of crackleW, computing formula is
In formula, QWFor the number of grid that each rock sample contains crackle, 0≤Qw≤ 360, the result of calculation such as institute of table 2
Show:
The mesh-density statistical form of table 2 360
Draw 360 mesh-density ΓWThe graph of a relation with corresponding rock sample quantity is segmented, as shown in Figure 5;
Step 4:According to the graph of a relation that step 2 and 3 are obtained, crack number and 360 mesh-density Γ are drawnWGraph of a relation,
As shown in fig. 6, graph of a relation is analyzed learning:With the increase of crack number, 360 mesh-densities increase in power function form
Long, when crack number reaches more than 20,360 mesh-density growth trends are intended to steadily;
Step 5:According to the result of step 4 statistical analysis, refer to regard to rock crushing degree with reference to rock mechanics related specifications
Mark criteria for classification, the actual degree of crushing of decohesion rock sample and its 360 mesh-density values, set up with 360 mesh-density ΓWDescription
The criteria for classification of rock sample degree of crushing is as follows:
0≤ΓW<0.1:It is slight broken;
0.1≤ΓW<0.3:Relatively crush;
0.3≤ΓW<0.5:It is broken;
0.5≤ΓW<0.8:Crush very much;
0.8≤ΓW≤1.0:Crush completely;
360 different mesh-density ΓWCorresponding rock sample degree of crushing schematic diagram is as shown in Figure 7;
Step 6:The rock sample crack density Γ corresponding to each crack number counted in calculation procedure 2J, computing formula is
In formula, QJFor crack number, unit is (bar), and unit is (bar/cm2);S is rock sample lateral area, and unit is (cm2);
K is regulation coefficient;
According to the statistics of table 1, corresponding crack number is converted into into crack density, as shown in table 3:
The rock sample crack density statistical form of table 3
Step 7:According to the result of step 6 statistical analysis, refer to regard to rock crushing degree with reference to rock mechanics related specifications
Mark criteria for classification, the actual degree of crushing of decohesion rock sample and its crack density value, set up and use rock sample crack density ΓJDescription
The criteria for classification of rock sample degree of crushing is as follows:
0≤ΓJ<0.3:Thin crackle;
0.3≤ΓJ<0.5:Closeer crackle;
0.5≤ΓJ<0.8:Intensive crackle;
0.8≤ΓJ<1.0:Very intensive crackle;
ΓJ≥1.0:Fragmentation;
Different rock sample crack density ΓJCorresponding rock sample degree of crushing schematic diagram is as shown in Figure 8;
Step 8:If evaluated using 360 mesh-densities or crack density of rock sample merely, it is understood that there may be not enough
In terms of accurately, for example, when rock sample is based on penetrability long crack, crack density is less, and mesh-density is larger, is running through
Property short and small crackle it is more when, crack density is larger, and mesh-density is less, in order to it is more accurate, comprehensively pass judgment on out rock sample
Degree of crushing, it is considered to the actual degree of crushing of rock sample;
The mesh-density Γ of use 360 that step 5 is set upWWhat the criteria for classification and step 7 of description rock sample degree of crushing was set up
With rock sample crack density ΓJThe criteria for classification of description rock sample degree of crushing combines, and considers situation as shown in table 4:
The rock sample degree of crushing classification chart of table 4
(note:When the mesh-density value and crack density value of rock sample to be determined are unsatisfactory for the endpoint value of above-mentioned classification, nearby
Principle is chosen.)
According to table 4, quantitative classification is carried out to rock sample degree of crushing, be defined as follows:
(1) it is more complete:0≤ΓW<0.1,0≤ΓJ<0.5;
(2) relatively crush:0.1≤ΓW<0.3,0.5≤ΓJ<0.8;
(3) crush:0.3≤ΓW<0.5,0.8≤ΓJ<1.0;
(4) crush very much:0.5≤ΓW<0.8, ΓJ≥1.0;
(5) fragmentation completely:0.8≤ΓW≤ 1.0, ΓJ≥1.0。
In step 1, by " a kind of rock sample crackle drawing apparatus and retouching disclosed in Patent No. 201410068603.5
Paint method " obtain the crackle expanded view after rock sample destruction;Rock examination can also be obtained by way of rock sample photofit
Crackle expanded view after sample destruction.
In step 2, the preparation method of " 360 grid " is:The crackle exhibition figure that step 1 is obtained is put down in rock sample short transverse
10 lattice (spacing 1cm) are divided into, in rock sample circumferential direction 36 lattice (10 ° of spacing) are equally divided into, form " the 360 of totally 360 grids
Grid ", as shown in Figure 2;
Above-mentioned " 360 grid " also can be printed on the transparent plastic film of 15.7cm × 10cm (length × height) square
On, referred to as " 360 graph paper ", when crackle statistics is carried out, by " 360 graph paper ", circumferentially direction, around rock sample is destroyed one week, is covered
It is in rock sample side and fixed, by artificial counting, statistics crack number and mesh-density, " 360 graph paper " schematic diagram such as Fig. 3 institutes
Show, " 360 graph paper " right-hand member is provided with three pieces of adhesive sticker pasters in Fig. 3, for fixing.
In step 2, crack number statistical method is:
A, for the independent crackle for occurring, directly count according to actual bar number;
B, for have in the middle of crackle intersection or bifurcated, according to rock sample destruction controlling crack advance direction, first count
Major control crackle, then count intersect therewith or bifurcated secondary crackle.
In step 3, the number of grid Q containing crackleWStatistical method be:
The crackle occurred in a, all grids is counted as 1;
B, same grid are still counted as 1 when there are many Cracks simultaneously, not crackle repeatedly in statistics grid.
The regulation coefficient K computational methods of step 6 are:
Find in statistic processes, destruction rock sample crackle bar number is crushed completely when being 20 or so, for the ease of splitting
The regularization statistics of line density, it is standard 1 to define corresponding crack density when crack number is 20,
Therefore K values areD be rock sample diameter, unit cm;For example, a diameter of 5cm of rock sample, K are 2.5 π.
Embodiment two
In order to verify the applicability and reasonability of sorting technique proposed by the present invention, typical damage rock sample is chosen, according to upper
The method of stating carries out rock sample degree of crushing Calculation Estimation;
As seen from Figure 9:360 mesh-density ΓWFor 0.08 (< 0.1 of 0 < 0.08), crack density ΓJFor 0.2 (0 <
0.2 < 0.5), rock sample degree of crushing classification:It is more complete.
As seen from Figure 10:360 mesh-density ΓWFor 0.19 (< 0.3 of 0.1 < 0.19), crack density ΓJFor 0.55
(< 0.8 of 0.5 < 0.55), rock sample degree of crushing classification:Relatively crush.
As seen from Figure 11:360 mesh-density ΓWFor 0.42 (< 0.5 of 0.3 < 0.42), crack density is ΓJ0.95
(< 1.0 of 0.8 < 0.95), rock sample degree of crushing classification:It is broken.
As seen from Figure 12:360 mesh-density ΓWFor 0.51 (< 0.8 of 0.5 < 0.51), crack density ΓJFor 1.2
(1.2>1), rock sample degree of crushing classification:Crush very much.
As seen from Figure 13:360 mesh-density ΓWFor 0.81 (< 1.0 of 0.8 < 0.81), crack density ΓJFor 2.8
(2.8>1), rock sample degree of crushing classification:Crush completely.
From embodiment two as can be seen that can quantitatively be commented to standard according to 360 mesh-densities and crack density of rock sample crackle
The degree of crushing of valency rock sample, can meet the requirement of rock sample destructive characteristics and degree of crushing quantitative analysis, analysis process letter
Single, accurately, explicit physical meaning, result of calculation is directly perceived for value, is easy to practice operation.
Claims (7)
1. it is a kind of based on mesh-density and the rock sample degree of crushing Quantitative Classification Method of crack density, it is characterised in that the method bag
Include following steps:
Step 1:Obtain the crackle expanded view after the rock sample destruction of multiple same sizes;
Step 2:" 360 grid " of each rock sample is made, by each crackle expanded view that " 360 grid " is obtained to step 1
Crack number counted, draw the graph of a relation of crack number and corresponding rock sample quantity;
Step 3:By the number of grid Q containing crackle in each crackle expanded view that " 360 grid " is obtained to step 1WUnited
Meter, calculating each rock sample has 360 mesh-density Γ of crackleW, computing formula is
In formula, QWFor the number of grid that each rock sample contains crackle, 0≤QW≤360。
Draw 360 mesh-density ΓWIt is segmented the graph of a relation with corresponding rock sample quantity;
Step 4:According to the graph of a relation that step 2 and 3 are obtained, crack number and 360 mesh-density Γ are drawnWGraph of a relation, to relation
Figure is analyzed to be learnt:With the increase of crack number, 360 mesh-densities increase in power function form, reach in crack number
When more than 20,360 mesh-density growth trends are intended to steadily;
Step 5:According to the result of step 4 statistical analysis, with reference to rock mechanics related specifications with regard to rock crushing level index point
Class standard, the actual degree of crushing of decohesion rock sample and its 360 mesh-density values, set up with 360 mesh-density ΓWDescription rock sample
The criteria for classification of degree of crushing is as follows:
0≤ΓW<0.1:It is slight broken;
0.1≤ΓW<0.3:Relatively crush;
0.3≤ΓW<0.5:It is broken;
0.5≤ΓW<0.8:Crush very much;
0.8≤ΓW≤1.0:Crush completely;
Step 6:The rock sample crack density Γ corresponding to each crack number counted in calculation procedure 2J, computing formula is
In formula, QJFor crack number;S is rock sample lateral area, and K is regulation coefficient;
Step 7:According to the result of step 6 statistical analysis, with reference to rock mechanics related specifications with regard to rock crushing level index point
Class standard, the actual degree of crushing of decohesion rock sample and its crack density value, set up and use rock sample crack density ΓJDescription rock sample
The criteria for classification of degree of crushing is as follows:
0≤ΓJ<0.3:Thin crackle;
0.3≤ΓJ<0.5:Closeer crackle;
0.5≤ΓJ<0.8:Intensive crackle;
0.8≤ΓJ<1.0:Very intensive crackle;
ΓJ≥1.0:Fragmentation;
Step 8:The mesh-density Γ of use 360 that step 5 is set upWWhat the criteria for classification and step 7 of description rock sample degree of crushing was set up
With rock sample crack density ΓJThe criteria for classification of description rock sample degree of crushing combines, and to rock sample degree of crushing quantitative classification is carried out,
It is defined as follows:
(1) it is more complete:0≤ΓW<0.1,0≤ΓJ<0.5;
(2) relatively crush:0.1≤ΓW<0.3,0.5≤ΓJ<0.8;
(3) crush:0.3≤ΓW<0.5,0.8≤ΓJ<1.0;
(4) crush very much:0.5≤ΓW<0.8, ΓJ≥1.0;
(5) fragmentation completely:0.8≤ΓW≤ 1.0, ΓJ≥1.0。
2. a kind of rock sample degree of crushing quantitative classification for being based on 360 mesh-densities and crack density according to claim 1
Method, it is characterised in that:In step 1, by the way that " a kind of rock sample crackle is described disclosed in Patent No. 201410068603.5
Device and plotting method " obtains the crackle expanded view after rock sample destruction.
3. according to claim 1 a kind of based on mesh-density and the rock sample degree of crushing quantitative classification side of crack density
Method, it is characterised in that:In step 1, the crackle exhibition after rock sample destruction can also be obtained by way of rock sample photofit
Open figure.
4. according to claim 1 a kind of based on mesh-density and the rock sample degree of crushing quantitative classification side of crack density
Method, it is characterised in that in step 2, the preparation method of " 360 grid " is:The crackle exhibition figure that step 1 is obtained is in rock sample height side
10 lattice are equally divided into upwards, in rock sample circumferential direction 36 lattice are equally divided into, formed " 360 grid " of totally 360 grids.
5. according to claim 1 a kind of based on mesh-density and the rock sample degree of crushing quantitative classification side of crack density
Method, it is characterised in that in step 2, crack number statistical method is:
A, for the independent crackle for occurring, directly count according to actual bar number;
B, for having intersection or bifurcated in the middle of crackle, according to the controlling crack advance direction of rock sample destruction, first count main
Controlling crackle, then count intersect therewith or bifurcated secondary crackle.
6. according to claim 1 a kind of based on mesh-density and the rock sample degree of crushing quantitative classification side of crack density
Method, it is characterised in that in step 3, the number of grid Q containing crackleWStatistical method be:
The crackle occurred in a, all grids is counted as 1;
B, same grid are still counted as 1 when there are many Cracks simultaneously, i.e., only statistics has the number of grid that crackle occurs, and does not weigh
The crackle in grid is counted again.
7. according to claim 1 a kind of based on mesh-density and the rock sample degree of crushing quantitative classification side of crack density
Method, it is characterised in that the regulation coefficient K computational methods of step 6 are:
Find in statistic processes, destruction rock sample crackle bar number is crushed completely when being 20 or so, close for the ease of crackle
The regularization statistics of degree, it is standard 1 to define corresponding crack density when crack number is 20, therefore K values areD
For rock sample diameter.
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康天合 等: "煤体裂隙尺度分布的分形研究", 《煤炭学报》 * |
邱俊刚 等: "焦家金矿破碎岩体岩石力学分级稳定性研究", 《金属矿山》 * |
鄢泰宁: "《岩土钻掘工艺学》", 31 August 2013, 中南大学出版社 * |
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