Identification and Evaluation of Active Fault in the

Reservior Head of Three Gorges Project based on

Grey Statistical Model

LID Zuqiang Changjiang Institute of Survey Planning Design and

Research Changjiang Water Resources Commission

Wuhan, China, 430010

LIDYong Hubei Institute of Water Resource and Water Power Survey

Planning and Design, Wuhan, China, 430070

Abstract-It often plays an important role in the earthquake

prediction to monitor and identify fault rupture. Based on five

years' live fault rupture observational data of the three gorges

project's reservior head area, this paper applies grey statistical

model to analyze eight live fault ruptures and identify seven live

fault ruptures according to O.lmm displacement criterion per

year which is regarded as index for grey type. Because the

proposed method takes dislocating rate's discrete effect into

account, the identification and evaluation results from a

numerical example confirmed that this method is closer to reality

compared with traditional average method.

Keywords-live fault rupture, recogniton, evaluation, grey

statistics, three gorges project

I. INTRODUCTION

Because the capacity of the three gorges project reservoir is huge, the stability of bank and head of reservoir will directly influence the dam safety. Therefore, monitoring and researching about the bank and head of reservoir, which may exist geological defects and induce geological disasters such as major earthquakes, is an important problem.

It has been probed that there are numerous geological fault zones, many potential natural earthquakes and geological disaster zone in the certain radiation geographical area of the three gorges dam site. Long-term monitoring practice proves that some fractures are more active. Although the intensity of fractures is not big, their activity is much more frequent. In view of the above, relevant departments began to layout high­precision safety monitoring facilities in the three gorges project area and its surrounding areas from 1978. Meanwhile, several main fractures and geological unit boundary (Xiangxi river valley) are stationed to have cross-fault short leveling regularly and short baseline monitoring. Its purpose is to collect crustal activity data, analyze its activities rules and feedback or predict

978-1-61284-491-6111/$26.00 ©2011 IEEE 503

ZHANGJun College of Land Management

Huazhong Agricultural University Wuhan, China, 430070

LID Yanjie Changjing Institute of Survey Planning Design and

Research Changjiang Water Resources Commission

Wuhan, China, 430010

on abnormal conditions in this area. After observation of some years, the quantification and amplitude of most measuring lines of fault rupture have already been mastered.

Before and after strong earthquakes, fault inside epicenter's certain scope may appear different level of activity change. For example, the movement rate and stress modes of fault may appear changes different from normal state. Therefore, monitoring of the fault rupture is one of the important means to observe earthquake precursor phenomena, How to analyze and classify the activity of active fault becomes a problem worthy to discuss. This paper puts forward grey statistical model to identify and classify live fault rupture.

II. MONITORING CONDITION OF FAULT RUPTURE IN THE RESERVOIR HEAD AREA

The head's crustal deformation monitoring of Three Gorges Reservoir involves the observation of the rupture of backbone fracture mainly (relative vertical displacement and relative horizontal displacement). In addition to laying the gap measuring line outside two geological unit's edge position, others are laid crossing fault (see table 1). Observation methods using conventional first-class precision leveling measurement and precision baseline measure techniques, as in [1]. There were three kinds of observation period which are ten-day measurement; months test measurement and season measurement before May 1998. Observation period has been changed to observe in May and November per year since May 1998. In Zigui, the period of ZhouPing's indoor precision leveling measurement and precision baseline measurement was daily observation before June 1998. After July 1998, the period of observation is once per week. The observation error of many years' statistics can meet the specification requirements.

III. GREY STATISTICAL MODEL[1 ] [2]

If monitor n(i = 1,2,. .. , n) faults, which monitoring d" dl2 dIm station has m(j = 1,2,. .. , m) unit time observation of fault d21 d22 d2m rupture rate effect, sample matrix of fault rupture amount rate D= Cdi) = (1) effect quantity can be gotten as follows:

dn , dn2 dnm TABLE I. PROJECT DlSTRJBUTlON LIST OF MONITORJNG FAULT CONDITIONS IN THE RESERVIOR HEAD AREA

Project First observation Measuring line location Cross-fault name

Measuring line

date leneth(km)

Zhouping indoor baseline in January 1978. Zhouping in Zigui Xiannvshan fracture (north section) 0.024 Zigui Zigui county Zhouping indoor

January 1978. Zhouping in Zigui Xiannvshan fracture (north section) 0.024 water level Zhouping West-east leveling in January 1978. Zhouping in Zigui Xiannvshan fracture (north section) 0.18 Zigui

Zhouping South-north leveling in January 1978. Zhouping in Zigui Xiannvshan fracture (north section) 0.43 Zigui Huangkou leveling in Zigui January 1992. Zhouping in Zigui Xiannvshan fracture (north section) 0.14

Qinglinkou leveling in January 1980 Hejiaping in Changyang Xiannvshan fracture (middle section) 0.86 Changyang Gaowanxi leveling in Zigui January 1989 Zhouping in Zigui Jiuwanxi fracture 0.34

Gaoqiao leveling in Xingshan May 1998 West-north Ikm Gaoqiao in Xingshan Gaoqiao fracture 0.39

ShuiTianba leveling in Zigui August 1998 7th Group of Shangba village of Shuitianba western fracture 0.35 Shuitianba in Zigui

Daxiakou leveling in Xingshan November 1980 Daxiakou in Xingshan Daxiakou geological unit 1.74 boundary(Xiangxi Valley)

Dashuitian leveling in Zigui August 1998 Dashuitian village of ShuiTianba in

Shuitianba eastern fracture 0.63 Zigui

where dI J,d2 J,.· ·,dn J represent for the j times

observation of n monitoring stations in the spatial displacement

samples, dij(i = 1,2,.· ·,n ;j = 1,2,.· ·,m) represents for

the sample values j statistical unit to i displacement statistic. Now active fault can be classified into four grey types, which are activity violent (AA), activity (class A), micro activities (grade B) and not activities (grade C).

If there are sCk = 1,2,.· ·,s) grey types, transforming j sample values into each projectj's grey type evaluations, called grey statistical evaluation for j project through the transformation.

If K grey type's whiting values function of j sample

is if Cd) E [0,1] , the standard whiting values function form is

as follows: (see Fig. 1)

fk ,

o d5cl). d5(2).

Figure I. standard whiting values function form

504

. . EquatIOn (2) IS mathematICs model of standard whltmg

values function as follows:

if Cd) = ifcdJCl),dJC2),dJC3),dJC4)) (2)

WheredJ(l),dJC2),dJ(3),dJC4) is the turning point

of if Cd) . From Fig.l, we can know that the expression of

standard whiting values function as follows:

f/Cd) = dJ(2)-dJ(l)

,

1, dJ(4)-d

dJ(4)-dJC3) ,

d \l [dJ (l),dJ C 4)]

dE[dJ(l),dJC2)]

d E[dJ(2),dJC3)]

d E[dJ(3),dJC4)]

(3)

Letting K grey type's whiting values function's critical

value A� as (4) of j sample, general standard whiting values

function degenerates into three basic types in practical.

(4)

A. Upper limited measurement of whiting values function: Supposing active fault rate more than some numerical value,

we regard the fault as activity violent (AA). Then grey type's

whiting values function if (d) does not have the third or the

fourth turning point. Its form can be shown in Fig.2.

Figure 2. upper limited measurement of white weight function form

Upper limit measurement of whiting values function can be written as (5):

0, d < dy (1)

if (d) = d -dY(l)

dE [dy (1), dy (2)] (5) dy (2) -dy (1)

,

1, d? dY(2)

Then critical value A� of upper limited measurement of K grey type whiting values function of) sample is as (6):

A� = dY(2) (6)

B. Moderate limited measurement of whiting values function: Supposing active fault rate fluctuates at some numerical

value, we regard the faults as activities (A grade). Then the third and fourth turning point overlap, its form is shown in Fig. 3.

Moderate limit measurement of whiting values function can be written as (7):

fk j

1

o dY(2). Figure 3. moderate limited measurement of white weight function form

505

f/(d) =

0, d-dJ(1)

dJ(2)-dJ(1) , dJ(4)-d

dJ(4)-dJ(2) ,

d � [dJ (1), dJ (4)]

dE [dJ (1),dJ (2)] (7)

Then critical value A� of upper limited measurement of K grey type whiting values function of) sample is as follows (8):

A� = dY(2) (8)

C. Lower limited measurement of whiting values function: Supposing active fault rate is smaller than a certain value

(or less than 2 times, says fault error), we regard that fault as not activities (grade C). Then grey type's whiting values

function if (d) does not have the first or second turning

point, its form is shown in FigA.

Whiting values function with lower limit measure as (9):

0, d �[O,dJ(4)] f/Cd) = 1, d E[O,dJ(3)] (9)

dJ(4)-d d E[dJ(3),dYC4)) dJ(4)-dJC3) ,

Then critical value A� of ) sample, K grey type's lower

limited measurement whiting values function is as (10):

A� = dy(3) (10)

,�(3) ,�(4) d

Figure 4. low limited measurement of white weight function form

TABLE II. RIPPING SPEED OBSERVATION DATA PER YEAR

Number Fault name 1997-1998 1998-1999 1999-2000 2000-2001 Average

(mm)

1 Zhouping east-west line in Zigui 0.38 2 Zhouping south-north line in Zigui 0.50 3 Huangkou in Zigui 0.52 4 Qinglinkou in Changyang 0.22 5 Gaowanxi in Zigui 0.47 6 Gaoqiao in Xingshan 0.78 7 ShuiTianba in Zigui 0.39 8 Daxiakou in Xingshan 0.52

There are two kinds of A� , objective critical value and

relative critical value. Objective critical value is generally determined according to experience or the advice of experts, while the relative critical value may be based on sample matrix to determine.

Setting the unit global sum r/ for K grey whiting values of J

) sample's column ( dlj' d2j,. .. , dnj ) as (11):

n 17; = L�k(dij) ( 1 1 )

i�1 Summing up 17 k again, we get the unit grey global sum

J

17 j of) sample's column as (12):

s s n 17j = L17; = LL�k(dij) ( 12)

k�1 hI i�1 We get the grey evaluation value ak (j project to k grey

J type) as (13):

n k L�k(dij)

(J"k = 1J..L =

---,i",,�I!....-__ _ J 17)

Considering that there are

s(k = 1 2 .. · s) " ,

(13)

kinds of grey types, we get grey evaluation sequence a j of)

project as (14):

2 ai' . .. , as] J

( 14)

If

( 15)

Then we conclude that ) project belongs to k' grey type noting} E k*.

IV. THE RECOGNITION OF ACTIVE FAULT RUPTURE

506

(mm) (mm) (mm) (mm)

0.15 0.12 0.15 0.20 0.08 0.40 0.41 0.35 0.03 0.08 0.07 0.18 0.21 0.03 0.19 0.16 0.13 0.16 0.23 0.25 0.51 0.85 0.19 0.58 0.81 0.54 0.53 0.57 0.03 0.28 0.23 0.26

ThIS paper uses 8 faults' nppmg speed observation data from 1997 to 2001 (see table 2), according to the grey statistics method for analysis, and recognize active fault rupture situation.

A. Determine the grey type and whiting values function According to"Hydropower Project Regional Structure

Stability Reconnaissance Technical Regulation" (DLlT, 5335-2006) as in [4], direct discrimination mark of active fault is the displacement greater than 0.1 mm/a. So fault is divided into active fault and not active (stable) fault. Threshold for greater than 0.1 mm is active fault and no greater than 0.1 mm is not active fault. Grey type whiting function is that active fault grey type (greater than 0.1 mm) is applied to whiting values function

expression with upper limit measurement f) as (16).

fl(d.) = ---2.... = 10dij' {d .

J lJ 0.1 1,

dij E [0,0.1) ( 16) dij � 0.1

No active fault grey type ( no greater than O.lmm ) is applied to whiting values function with lower limited

measurement ff as (17):

1, dij E [0,0.1] d

2 _ ---2.... = 2 -10d .. 0.1 lJ'

0,

dij E (0.1,0.2) ( 17)

dij � 0.2

B. Calculate the whiting values of unit global sum 17 k J

17 17; = L�k(dij)

i�1 According to the last formula, we calculate the

j(j = 1, 2, 3, 4)

( 18)

statistical sample belonging to k(k = 1, 2) grey type and their

unit global sum 17k of whiting values (see table 3). J

C. Calculate) sample column's unit grey global sum 17 j 2 2 8

171 = L17; = LL.0k(dij) =4.00+1.80= 5.80;

k�l k�l i�l

Number

1

2

3

4

5

6

7

8

TABLE III. UNIT GLOBAL SUM OF WHITING VALUES SCHEDULE

Unit global sum 1 2 3 4 5 6 7 8

r/ 4.00 3.80 2.80 3.30 4.00 4.00 4.00 3.30 }

172 1.80 1.00 3.00 1.10 1.10 0.10 0.00 1.00

}

TABLE IV. THE GREY EV ALUA TION VALUE a k ( J PROJECT TO K GREY TYPE) SCHEDULE J

Grey evaluation value 1 2 3 4 5 6 7 8

al J 0.69 0.79 0.48 0.75 0.78 0.98 1.00 0.77

a2 J 0.31 0.21 0.52 0.25 0.22 0.Q2 0.00 0.23

TABLE V. THE RECOGNITON RESULTS OF ACTIVE FAULTS SCHEDULE

Fault name Recognition result of grey statistics Recognition result of conventional average

method method

east-west line of Zhouping in Zigui Active fault Active fault south-north line of Zhouping in Active fault Active fault Zigui

Huangkou in Zigui No active fault Active fault

Qinglinkou in Changyang Active fault Active fault

Gaowanxi in Zigui Active fault Active fault

Gaoqiao in Xingshan Active fault Active fault

ShuiTianba in Zigui Active fault Active fault

Daxiakou in Xingshan Active fault Active fault . .

172 = 4.80; 173 = 5.80; 174 = 4.40; 175 = 5.10;

176 = 4.10; 177 = 4.00; 178 = 4.30

By SImIlarly analyzmg, we get the recogmtIon results of active faults (see table 5).

Using the conventional methods, namely taking all faults monitoring stations' average dislocation rate to analysis and make judgment, we get the average results in table 5. As we can know from table 5, compared to the recognition results By using conventional methods , the recognition results by using grey statistical methods of active fault has discrepancy on Zigui county drought mouth . As we can know from table 2, dislocation rate of Huangkou in Zigui is greater than 0.1 mm from 1997 to 1998; dislocation rate is less than 0.1 mm in the later four years. Namely the fault is no active fault. That dislocation rate is greater than 0.1 mm from 1997 to 1998 is probably caused by measurement error or other disturbance factors. As the grey statistical evaluation method has considered dislocation rate and other discrete factors, thus the results are closer to reality.

D. Calculate the grey evaluation value ak (j project to k J

grey type) 8

17� "Lf/(dij) Uk

= i�l (19) } 2 8 17j "L"Lf/(dij)

k�l i�l According to (19), we calculate the grey evaluation value

ak (j project to k grey type, see table 4). J

E. Determine j project's grey evaluation sequence a., and J

then judge the grey type

And

al = [alk ] = [all an = [0.69 0.31]

k* =1,(j=I)E(k* =1): Zhouping in Zigui county east-west line fault belongs to active fault.

507

V. ACTIVE FAULT GRADES EVALUATION

Only by recognizing there's fault dislocation or not cannot meets the needs of project. In most cases, it needs to evaluate grades according to the fault dislocation. According to the speed of fault dislocation, active fault of Three Gorges Reservoir area can be divided into the following three grades as in [1]:

Grade A: dislocation speed per year >0.6 mm;

Grade B: dislocation speed per year lays between 0.1 mm andO.6 mm;

Grade C: dislocation speed per year not more than 0.1 mm.

TABLE VI. GREY EV ALUA TION VALUE OF ITEM J TO GREY TYPE K

Evaluate Result of Grey Statistics 1 2 3 4 5 6 7 8 crl

J 0.25 0.40 0.22 0.27 0.34 0.73 0.65 0.37

cr2 J 0.40 0.43 0.20 0.46 0.44 0.25 0.35 0.43

cr3 J 0.34 0.17 0.58 0.27 0.22 0.02 0.00 0.21

TABLE VII. ACTIVE FAULT GRADES EVALUATION RESULT

Number Fault name Evaluate Result of Grey Traditional Average Value Recognize

Statistics Result

1 Zhouping east-west line in Zigui

2 Zhouping south-north line in

Zigui 3 Huangkou in Zigui

4 Qinglinkou in Changyang

5 Gaowanxi in Zigui

6 Gaoqiao in Xingshan

7 Shuitianba in Zigui

8 Daxiakou in Xingshan

Active fault IS dIvIded mto there grey types: grade A, grade B and grade C. When threshold is larger than 0.6 mm, it belongs to grade A. When the threshold is about 0.35 mm, it is

Grade B. When the threshold is not more than 0.1 mm, it is Grade C. As a result, grey type whitening functions are as below. Active fault grey type of grade A (>0.6 mm) is

maximum measuring whitening function I) : { d

II (d .. ) = --.!L. , dij E [0,0.6) J I} 0.6

1, di) � 0.6

Active fault grey type of Grade B (about 0.35 mm) is

moderate measuring whitening function If : d ..

_I} ,dij E [0,0.35] 0.35

d .. If (di)) = 2 - _I} ,dij E (0.35,0.6)

0.35 O,di) � 0.6

Active fault grey type of Grade C (not more than 0.1 mm)

is maximum measuring whitening function If :

By this method, we can calculate grey evaluation value cr: in table 6 and active fault grades evaluation result in table 7.

B

B

C

B

B

A

A

B

508

B

B

B

B

B

B

B

B

Takmg average value of each fault momtormg point's dislocation speed to do the analysis and judgment, the result is as in table 7. Compared with the evaluation result by grey statistical method, there's some difference in fault recognition of Huangkou fault in Zigui, Gaoqiao fault in Xingshan and Shuitianba fault in Zigui. As to Huangkou fault in Zigui recognition difference, it has been explained in table 2. In Xingshan and Gaoqiao, there are 4 faults which rate of the speed are larger than Grade A's threshold of 0.6 mm. There is 1 fault in Shuitianba larger than Grade A's threshold of 0.6 mm, and there are 2 faults close to 0.6 mm. As a result, the difference of grade evaluation is the discrete result when grey statistical method takes dislocation speed rate into concern.

VI. CONCLUTION

According to the fault dislocation rate, this paper provided an advanced active fault rupture identification and classification method based on grey statistical model. Through the analysis of observation results of eight faults' dislocation rate in Three Gorges Project's reservoir head from 1997 to 2001 using grey statistical model, it is concluded that the fault rupture of Huangkou is not obvious, the rest of fault rupture are obvious. Gaoqiao and Shuitianba faults activity level are higher than other faults. Compared with the conventional average method, the result of grey statistical method has discrepancy in individual faults. The main reason is that the grey statistical model has taken the fault dislocating rate sequence's discrete effect into account. The result of active fault recognition and grading evaluation is closer to reality. The method broadens the application scope of gray theory.

REFERENCES

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[2] DENG Julong.The basic grey theory. Wuhan: Huazhong Science and Technology University Press.2002.2.

[3] LIU Sifeng, DANG Yaoguo, FANG Zhigeng. The theory of Grey Systen and its Application (5th Edtion). Beijing: Science Press, 2010.5

[4] Hydropower project regional structure stability reconnaissance technical regulation DLiT 5335-2006.

[5] LIN bin, XIA Xinli, CUI Long et al. Discussion on Activity of Fault F2 Kizil Reservoir in Xinjiang. Journal of Engineering Geology, Wuhan, Vol 17(6):780-787,2009

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