小断层

Research on Development Character of Middle and Small Size Fault Structure in DongPang Mine Field on Fractal Theory

Sun Xue-yang

School of Geology and Environment Xi’an University of Science and Technology

Xi’an, China

sunxy02211@https://www.360docs.net/doc/4d13873609.html,

Xia Yu-cheng

School of Geology and Environment Xi’an University of Science and Technology

Xi’an China

xiayc@https://www.360docs.net/doc/4d13873609.html,

Abstract—Middle and small size fault structure is the key geological factor affecting the safety production of DongPang mine field.Finding out development character of middle and small fault structure in DongPang mine field is to provide the geological premise for mining design of coal mine and working face layout. Based on the analysis of real data, 20 factors affecting the development of middle and small fault structure are summarized. And on the fractal theory, the fault fractal dimension value is worked out ;and then the key factors affecting the development of middle and small fault structure are filtrated by means of regression analysis, finally the relation of fault fractal dimension and the key factors affecting fault structure development is analyzed by using the grey relational analysis method. The results showed that fault fractal dimension can be used as comprehensive index of quantity, scale, combination form, horizontal extending length and inhomogeneity of distribution of fault structure. And the bigger its value is, the more fault structure is developed. Hence, fault fractal dimension is a reliable index denoting development degree of middle and small fault structure in DongPang mine field.

Keywords: fault fractal dimension; middle and small size fault structure; fractal theory; DongPang mine field of China

I.I NTRODUCTION

A lot of researches have indicated that the distribution of fault structure and geometric shape have the fractal structures[1-2]. Fractal feature of fault structure with different scales of crust has been studied respectively by Turcotte, Li Ben-liang, Lu Xin-wei, Shen Zhong-min etc, it was pointed out that the spatial distribution characteristics and self-similarity of fault structure can be described quantitatively by fractal value, Berry and Lewis hold that the size of fractal value of fault system is a comprehensive embodiment of quantity, scale, combination form of fault and dynamic mechanism.[3-6] Fault structure in DongPang mine field developed very well, according to statistics there are nearly 200 faults. Middle and small fault structure is the key geological factor affecting coal production. According to the data of the districts where the middle and small fault structure had been disclosed, influencing factors of fault development are analyzed and summarized; in unmined districts, the degree of medium feature. And so analyzing the feature of middle and small fault structure development is very important and basic work. Based on Fractal Theory in the paper, research shows that fault reference cone is reliable index denoting development degree of middle and small fault structure.

II.T HE FACTORS BEING

fault development will be forecast by structural

LIKELY TO AFFECT THE

S

ng mine

itions of the factors affecting the

d ture

easures(Mxhd):the total

ormality of the thickness of coal mea

Mxhd_pjz ?In the equation

of co

ness of main mine

of the thickness of coal seam

Mchd_pjz ?In the equat

of co

overlying strata (Jyh

DEVELOPMENT OF MIDDLE AND SMALL FAULT

TRUCTURE AND QUANTIZATION OF ITS INDEXES

Proceed from the actual conditions of DongPa

field, the factors which are likely to affect middle and small fault structure development are fined for 14 indexes, and the features of fault development are fined to 6 indexes.

A.The defin

evelopment of middle and small fault struc

and the method of quantization

(1)The thickness of coal m

of thickness of shanxi formation and taiyuan formation

(2)Abn

sures(Mxhdyc): The difference between borehole thickness of coal measures and average thickness of coal measures in DongPang mine field

Mxhdyc˙Mxhdˉ

? , Mxhd_pjz is average thickness al measures in DongPang mine field

(3)coal seam thickness(Mchd): thick

able coal seam

(4)Abnormality

(Mchdyc): the difference between borehole or unit thickness of coal seamand average thickness of coal seam in DongPang mine field

Mchdyc˙Mchdˉ

ion?, Mchd_pjz is average thickness al seam in DongPang mine field

(5)Bedrock thickness of coal

d):Total thickness of strata above main mineable coal seam, namely not including thickness of overlying strata series of main mineable coal seam of loose overburden layer

2010 International Conference on Computing, Control and Industrial Engineering

(6)Thickness of loose layer of coal overlying strata (Ssc): The total of thickness of tertiary and quaternary

(7)Elevation of coal floor(Dbbg): Altitude of main mineable coal floor, namely structure fluctuation status of main mineable coal seam present

(8)Abnormality of elevation of coal floor(Dgbf): change range of elevation of main mineable coal floor present

Based on trend analysis of elevation of coal floor, trend value d is obtained ; subtract the trend value d from measured value z, the residual value is r. Let the average value of all the positive residual values (namely r>0) dd as the standard of measuring the elevating of measured coal floor of one borehole abnormal or not, namely abnormal limit. If the residual

value of one borehole r>0, is denoted by R +. If R +-dd>0,then that the elevation of coal seam floor is abnormal; if R +-dd<0,then that the elevation of coal seam floor is within the abnormal limit , namely normal. Conversely, the residual value of one borehole r<0, is denoted R -. If R --dd>0,then that the elevation of coal seam floor is within the abnormal limit; if R --dd <0,then that the elevation of coal seam floor is abnormal. For one unit, if abnormality of elevation of coal floor of the unit is calculated, abnormality values of the unit’s searching field need to be weighted and averaged.

(9)The maximal apparent dip of coal seam (Mcqj): In the element, the maximal apparent dip of coal seam is defined as the maximal value of apparent dip of coal seam(￠)of all borehole sites .The apparent dip of coal seam of borehole sites is defined as the difference (h) between the elevations of borehole coal floor and that of central coal floor (obtained from weighted average of the elevations of all borehole coal floor in the element) and the arc tangent function of the quotient of level distance (d)from the borehole to the midpoint of the unit, namely:

￠=arctan (h/d) ?

(10)The basement elevation of coal measures (Mxjd)?The altitude of bottom surface of benxi formation or (when benxi formation is absent) taiyuan formation

(11)The difference between the elevation of main mineable coal floor and the basement elevation of coal measures.

Mc_jy ˙Dbbg-Mc_jy ?

(12)Integrated hardness of overburden strata of coal seam(Psyd)?hardness of the upper overburden strata series of main mineable coal seam, namely anti destructive capability

In the research of the geotechnical engineering and mining subsidence, the common classification method of rock is Protodyakonov taxonomy which was put forward by M.M. Protodyakonov at 1926.The determination method of classification index is as follow:

q = Rpress/1000 ?

In the equation ?: q-Protodyakonov coefficient, also called rock rigidity coefficient; Rpress-uniaxial compressive strength of rock(N/cm 2

).

Fig.1.Calculation

method of Tbyy and Bbyy Based on rock hardness coefficient, the overburden synthesis Protodyakonov rigidity is defined as follow:

|

|

n

i

n

i i m

q m Q 1

1

/

?

In the equation ?: Q ˉthe overburden synthesis Protodyakonov rigidity; m i ˉstratified thickness of normal of overburden strata unit: m; q i ˉstratified evaluation coefficient of lithology of overburden strata i, also called rock rigidity coefficient; n- the stratified number of overburden strata

(13)Influence coefficient of hard rock within 30m above coal seam roof(Tbyy): anti destructive capability of coal seam roof

| n

i i i L h Tbyy 1

)]1/([ ?

In the equation ?: n üthe layer number of hard rock within 30m above coal seam floor; i üthe layer numbers of hard rock; h i ü the layer thickness of hard rock ; Li üthe distance between bottom surface of hard rock and top surface of coal seam,which is showed in Fig.1.

(14)Influence coefficient of hard rock within 20m above coal seam floor (Bbyy): anti destructive capability of coal seam floor. The calculation method is similar to that of influence coefficient of hard rock, within 30m above coal seam roof, which is showed in Fig.1.

B.definition of divided data of development features of fault structure and its method of quantization

By comparison of the results of qualitative analysis on fault structure of mine and results of fractal

study, it is obtained that fault fractal dimension is a comprehensive embodiment of fault amount , scale ,combination form, horizontal extending length and inhomogeneity of distribution, and can be a quantitative index of complex degree of fault structure . By the research result of fractal dimension on fault fracture in DongPang mine field , it can be also proved that fault fractal dimension is a comprehensive index of fracture quantity, group number, and length of fracture trace, fracture cutting relation and inhomogeneity of fracture distribution, and evaluating complex degree of fault structure block section by fault network has the advantage that other indexes can not compare.

In order to study and compare the complex degrees of each unit fracture, fault fractal dimension of unit Ds is measured by grid-covered method. The calculation method is : let each side of the element into two, can be divided into 4 square lattices whose side length is 1/2 of side length of unit(denoted by R ),the number of lattices of faults entering N(R/2) is calculated out, then , each of square lattices with the side length , 1/2 of side length of unit are divided respectively into square lattices whose side length is 1/4 of side length of unit, and the number of lattices of faults entering N(R/4) is calculated out respectively,… analogy in turn, namely side length of square lattices is changed by the rate of 1/2, and the number of relevant lattices is calculated N(r) .If there is a self-similar structure in faults of research are, there is the following relation:

lnN(r)=A+Bln(r) ?

Based on least square method or one-dimensional linear regression analysis, can be obtained the slope of straight line and correlation coefficient of linear equation and standard deviation of it, absolute value of linear slope, namely fault fractal dimension of research area, namely : Ds = |B|

In order to compare, were calculated out the indexes of evaluation unit(Dcts), including its fault density(Dcmd), number of faults(Dcts), fault length(Dccd), fault throw(Dcdj), fault intensity(Dcqd ) etc. Among them, fault intensity is defined as:

| u n

i i i L h Dcqd 1

][ ?

In the equation ?, n üfault quantity of unit; i üfault number; hi üfault throw; Li ülength of evaluation unit.

III.

A NALYSIS ON THE MAIN AFFECTING FACTORS

OF MIDDLE AND SMALL SIZE FAULT STRUCTURE

Mining area one, two, three, six, seven and nine have been exploited in DongPang mine field at present. Moreover, part of middle and small faults are disclosed

in some roadways .The area is regarded as proved area which is divided into 73 grids with 4004h 400,20 evaluation index values of every unit are calculated ,can be obtained the original data of quantitative analysis. Due to the limited space, they are not been listed here. And then, based on the quantitative analysis methods of gradual regression analysis method, grey relational analysis method and corresponding analysis method etc, main controlling factors of affecting the development of middle and small faults in DongPang mine field are screened out to lay a foundation for development degree prediction of fault fracture in non-mining areas.

A.analysis method of gradual regression

According to the need of analysis method of gradual regression, the factors need to be predicted are for dependent variable, and that prediction factors for independent variable. A threshold is given(F*), then according to the threshold, independent variable is screened automatically by computers ,the main perdition factors are reserved, independent variable ,secondary or independent are rejected, finally a best regression equation is presented.

Here fault fractal dimension is regarded as dependent variable, other 19 indexes are regarded as independent variable which have analyzed by gradual regression.

According to the need of calculation program, dependent variable must be at the last column, so the movement of fault fractal dimension Dcfw(X14) is changed into (X20)

(X14)--fault throw Dcdj (X15) —cap thickness of bedrock

(X16)—coal seam-base thickness Mc_jy (X17)—hard rock effect of roof Tbyy; (X18)—hard rock effect of floor (X19)—thickness of unconsolidated layers ?When F*=0.1, regression equation is: Y=0.2368411+0.00099X(2)-0.052X(9)+0.002X(11)+0.047X(12)+0.0088X(13)-0.005X( 14)+0.014X(17)-0.03X(18)-0.00059X( 19)

Multiple correlation coefficient = .818163172251713

Standard deviation = 3.00181281861453E-02 F checkup value =14.17305

When multiple correlation coefficient is 81.8%, shows that in the equation, the relation of independent variable combination and the relation of dependent variable are close. Significance test is done, F0.05(20,60)=1.75;F0.01(20,60)=2.20;r0.05(80)=0.352;r0.01(80)=0.413 are obtained by lookup. This shows that whether F test or test of correlation coefficient, when confidence level is 0.01, regression equation is obvious, that is to say, the equation is credible.

By the analysis on the equation, the influencing factors of fault fractal dimension are: (X2)—abnormality of thickness of coal measures (X9)—comprehensive hardness of overlying strata (X11)—fault length

(X12)—fault number Dcts (X13)—fault density Dcqd (X14)üfault throw Dcdj;(X17)—hard rock effect of roof (X18)—hard rock effect of floor Bbyy(X19)—thickness of unconsolidated layers Ssc

When in the range of 0.2-3,class indexes of fault are always preserved in the regression equation; When F* is taken respectively as 2.5 and 3, only class indexes of fault are left(X11)-(X13).This showed that fault fractal dimension and class indexes of fault are in a close relation.

Besides class indexes of fault, the other independent variables which are chosen are all for medium indexes of structure, namely, comprehensive hardness of overlying strata , effect coefficient of hard rock of roof, effect coefficient of hard rock of floor, abnormality of thickness of coal measures and thickness of unconsolidated layers.

B. grey correlation analysis method

Correlation analysis of grey system is mainly used to analyze dynamic relationship between various factors of system and its features which changes with time, and then the main factors of system can be obtained. In the process of development of system, if the change situation of the two factors is basically consistent, namely, synchronous change degree is higher, and then it is considered that the relationship of the two factors is close or correlation degree is larger; or correlation degree of the two factors is smaller. So, correlation degree is quantitative description of correlation degree between various factors of system. Because fault fractal dimension is comprehensive embodiment of fault number, scale, combination form, level extension length and heterogeneous distribution, and can be a quantitative index ,therefore ,it is used as mother factor, and the other 19 factors likely related to fault fractal dimension are used as son factors.

Correlation degrees between fault fractal dimension (X14) and its influencing factors are obtained by computing as follows: G(14,1)=.875; G(14,2)=.305; G(14,3)=.873; G(14,4)=.555;

G(14,5)=.861; G(14,6)=.83; G(14,7)=.866;

G(14,8)=.865; G(14,9)=.872; G(14,10)=.925; G(14,11)=.918; G(14,12)=.925; G(14,13)=.864; G(14,14)=1.;

G(14,15)=.857;G(14,16)=.859;G(14,17)=.868;

(14,18)=.838; G(14,19)=.858; G(14,20)=.874?

The sorting of influencing factors of fault fractal dimension is as follows:

Fault density(X10), fault number(X12), fault length(X11), thickness of coal measures(X1), thickness of unconsolidated layers(X20), coal seam thickness(X3), comprehensive hardness of overlying strata(X9), coal seam-base thickness(X17), maximum apparent dip of coal seam(X7), basement elevation of coal measures(X8), fault density(X13), floor elevation of coal seam(X5), cap thickness of bedrock(X16), hard rock effect of floor(X19), fault throw(X15), hard rock effect of roof(X18), amplitude of floor elevation(X6), abnormality of coal seam thickness(X4) and

abnormality of coal measures(X2).

Fig.2 Forecast sub-area chat of relative complexity degree of faults in DongPang coal field. I:boundary of coal field; II:bound of goaf; III: isoclines of

fault fractal dimension; IV:faults IV.P ARTITION ESTIMATE AND FORECAST OF RELATIVE COMPLEXITY DEGREE OF FAULT STRUCTURES DongPang mine field is divided into 331 units

according to a grid spacing of 350m h 350m, including

74 units in disclosed areas. All the fault fractal

dimension values in the mine field are predicted by the above network. According to relative complexity degree of fault structures, the division standards are the

following: grade I ---fault fractal dimension value ?

0.3; grade II ---0.3?fault fractal dimension value ?0.7; grade III --- fault fractal dimension value ?0.7.

The mine f ld is divided into 3 kinds of districts (Fig.2): relatively simple district of structure---transverse shading, filling with pale green; relatively complex district of structure---cross shading, filling with peachblow; and the middle structure between the two districts ---oblique shading, filling with pale red.

Based on Fig.2, comparative development units i ie n disc in Fi According to the whole prediction values of fau fract (1)Thickness c ts abnormality,

com is a close relation between fault fractal dime values of fault class are pred R EFERENCES

[1]Benoit B. Mandelb l geometry of nature f chaos, scale invariance and i,Sun Yan,ect. Significance of ctal dimension of fault jia ,ect.fractal e weierstrass mandelbrot fractal losed areas, a majority of them are part of relatively complex districts or middle structure districts; the units whose faults are thin relatively are part of relatively simple districts. The result of prediction is coincident with the actual situation : the monoclinic area in south is greater part of relatively simple districts of structure; almost all fault-folded area in north is relatively complex districts of structure.

However, the obvious contradiction can be found g. 2: in the east segment of middle fault zone, south of mining area 9, and mining area 6 and 8 is found many of faults, but the result of prediction is relatively simple districts of structure.

lt al dimension of unit ,the contour map was plotted (Fig. 3).It showed that fault fractal dimension of a part of units is less than 0, and just in the district (in Fig. 3,the district with the cross shading ,filling with

pink ),often there are more fault development .If the units with its fault fractal dimension ?0 are also fallen under relatively complex districts of structure, the contradiction above can be solved in some extent.

V.

C ONCLUSIONS

of oal measures, i prehensive hardness of overlying strata, hard rock effect of floor, hard rock effect of roof, thickness of unconsolidated layers ,thickness of coal seam , coal seam-base thickness ,are in the front rank of relational order and in the optimum regression equation respectively ; it shows that the relative complexity degree of fault structure is in association with coal measures and sedimentary characteristics of overlying strata, especially with hardness , there is more closer association.

(2)There nsion and class indexes of fault. This showed that fault length, fault density ,fault number and fault intensity comprehensively and can be indeed used as comprehensive index of fault number, fault scale, combination form,horizontal extending length and inhomogeneity of distribution.

(3)When evaluation index icted in undisclosed areas, only consider fault fractal dimension,fault length ,fault number ,fault density , fault intensity and other indexes are not necessary to be predicted one by one .And so fault fractal dimension is a reliable index of development degree of middle and -small faults in DongPang Mine Field.

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[3]Li Ben-liang,Zhang Xi-hu dimension value of fault systems in evaluating natural resources with tibet as an example[J]. Geological journal of china universities ,1999,5(1):17—21.

[4Lu xin-wei and ma dong-sheng. fra systems and antimony deposit distribution in central hunan[j]. Geological review, 1998, 44(5)? 542—546.

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Fig.3 Isoclines of forecasting the fault fractal dimension

I:boundary of coal field; II:bound of goaf; III: isoclines of fault fractal dimension; IV:faults