Geotechnical and Geological Engineering (2006) 24: 1243–1258 DOI 10.1007/s10706-005-1404-7


Springer 2006

Analysis of sinkhole occurrences over abandoned mines using fuzzy reasoning: a case study DEBASIS DEB1 and SUNG O. CHOI2,w 1

Mining Engineering Department, IIT, Kharagpur, India Korea Institute of Geoscience & Mineral Resources (KIGAM), Daejeon, Korea

2

(Received 22 April 2005; accepted 25 July 2005) Abstract. In Korea most of the old mine workings were worked with room and pillar method or sublevel caving method and today they possess great possibility of surface subsidence especially for shallow depth mines. In most of the cases, mine roadways, rooms and pillars are irregular in shape and information about the local geology is uncertain. For these reasons, it is difficult to standardize the estimating method of subsidence especially sinkhole type over abandoned mine area. This paper describes the application procedure for the fuzzy reasoning techniques to analyze the possibility of sinkhole occurrences over abandoned mines. This technique is implemented in software which can simplify the analysis procedure and present the possibility of sinkhole subsidence without having precise information about local geological/mining conditions. This technique has been applied to forecast sinkhole possibilities at Bonghwa site where a massive sinkhole has already been occurred. Key words. fuzzy reasoning technique, fuzzy rules, sinkhole subsidence.

1. Introduction A number of abandoned mines exist in many countries including Korea and some of which possess potential for surface subsidence. In the UK, more than 70,000 old mine workings are reported and some of them may be three centuries old (Whittaker et al., 1989). In the USA, 354 subsidence incidents were reported over Pittsburgh Coal bed, most of which in the form of sinkholes (Gray et al., 1977). In 1985, Marino et al. reported that both trough and sinkhole type subsidence occurred in Illinois over shallow depth room and pillar mines (Whittaker et al., 1989). After extensive study of surface subsidence in the USA, Gray et al. (1977) commented that the most prevalent subsidence features over abandoned mine land are sinkholes, with depth of sinkhole more than 3 ft, and trough or sags less than 3 ft. After studying subsidence incidents in Germany, the sudden cave-ins and irregular depressions in the form of sinkholes over near-surface abandoned mines have been reported to possess a serious risk on the populated area nearby (Kratzsch, 1985). In Korea, 1,244 mines including 338 coal mines and 906 non-coal mines ceased operations since the early 1990s, and 9 coal mines and 723 non-coal mines are w

Corresponding author: E-mail: [email protected]

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D. DEB AND S.O. CHOI

currently being worked. Surface subsidence created due to the existence of abandoned mines can damage public property and natural forest, commonly known as geohazards in Korea. The sinkhole occurrence in the Boopyung graveyard was one of the examples of subsidence in Korea. It happened due to roof fall and pillar failure in near-surface openings which were developed during metal mining operations, and was restored by the sand slurry pumping into the openings (KIGAM report, 1993). Choi et al. (2004) suggested that several mining/geological parameters should be emphasized for evaluating the surface subsidence in abandoned mine area, and these parameters should be dealt with adding an extra weight in order to increase a reality in numerical analysis. All of the above mentioned literatures suggest that sinkhole development is a process of collapsed junction having weak/fractured roof and then progression of collapse chimney up to the surface at shallow depth of cover. In general, sinkhole is in the form of conical depression/cavity suddenly appears on the surface. The major factors which contribute to sinkhole formation are width of mine opening/gallery (W), height of opening (M), depth of cover (H), rock type and thickness of roof, water condition, pillar strength, time elapsed after mining operation was ceased, inclination of the seam and others. Whittaker et al. (1989) reported that width of gallery, depth of cover and roof conditions are the primary factors for the determination of sinkhole occurrences and higher chances are associated with lower H, higher W and weak roof conditions. Peng (1992) had also commented on the similar factors which contributed in sinkhole development in the Pittsburgh Coal bed. However, most of the reported sinkhole occurrences are not statistically related to these factors. The major difficulty lies in the crisp representation of W, H, roof conditions, water and time factors numerically and then trying to correlate with sinkhole dimension such as depth and diameter. For example, an abandoned mine roof can be better represented as ‘‘weak roof’’ or ‘‘strong roof’’ rather than quantifying with single numerical value. Thus representation of these parameters using linguistic terminology provides more realistic approach to apprehend the complex nature of roof geology. In a mine environment, a linguistic definition of roof classification or any parametric evaluation is more appropriate and representative rather than providing a numerical value such as W is 3 m or H is 6 m and so on. Fuzzy set theory is being used in every engineering and science disciplines where data cannot be represented using crisp set. It is said that one way of simplifying a complex system is to allow some degree of uncertainty in its description (Klir et al., 1988). Jiang et al. (1996) has effectively applied fuzzy set theories for the classification of longwall roof using field measured data. Applications of fuzzy sets and fuzzy logics are well established in mineral processing and other geo-mining fields such as mine subsidence analysis (Liao, 1993) and estimating roof fall rating (Deb, 2003). Recently, Mamdani’s fuzzy influence technique was applied to Geological Strength Index (GSI) for the assessment of slope stability (Sonmez et al., 2004). This paper outlines the analysis of vagueness in data using Mamdani’s fuzzy reasoning techniques and establishes relations between inputs and output based on fuzzy rules

ANALYSIS OF SINKHOLE OCCURRENCES OVER ABANDONED MINES

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designed based on reported data. A software has been developed to implement fuzzy reasoning techniques especially applicable for the assessment of sinkhole possibility. In September 2004, a massive sinkhole was formed over an abandoned metal mine in Bonghwa area over Kumho mine creating a hole of size 44
22
50 m3. From site inspection, it was envisaged that several neighboring area are also susceptible for sinkhole occurrences. Fuzzy reasoning technique is applied to estimate the possibility of sinkhole occurrences over that area and a geohazard map is developed showing the contours of sinkhole possibilities.

2. Parameters Effecting Sinkhole Formation Four parameters, W, H/M, pillar strength factor (P/M) and roof Index (R) are found to be directly related to occurrences of sinkhole (Whittaker et al., 1989; Peng, 1992). Each of these parameters are classified into five linguistic hedge groups of ‘‘Low’’, ‘‘Medium’’, ‘‘High’’ , ‘‘Very Low’’ and ‘‘Very High’’ based on their respective values or range of values. The possibility of sinkhole formation (S) is also grouped with five linguistic hedges as mentioned above. For each parameter, fuzzy membership grades are assigned for each group within that parameter. The output, S can be obtained using linguistic terminology or can be reduced to a representative numerical value. Apart from these factors, presence of water can also significantly affect the sinkhole formation process. Time elapsed after the mining operation was ceased also plays an important role in sinkhole process. However, later two factors are not included in the present study.

3. Fuzzy Memberships 3.1. DEFINITION OF FUZZY SET Consider a set X which has N number of variables or parameters as follows: X ¼ fX1 ; X2 ; . . . ; XN g

ð1Þ

The fuzzy set A is defined by assigning to each individual variable a value between 0 and 1, called membership grades, 0 being absolute uncertainty and 1 being complete certainty. In mathematical term, the fuzzy set A will be A ¼ flA ðX1 Þ; lA ðX2 Þ; . . . ; lA g

ð2Þ

where lA(X1) is the membership grade of the variable and defined as lA ðXi Þ ! ½0; 1 i ¼ 1; 2; . . . ; N

ð3Þ

In this study, fuzzy membership grades are computed using BELL shaped curve. For each variable and for every linguistic hedge, membership grade is obtained using the following relationship: lA1 ½xðiÞ ¼

1 1 þ ðfxðiÞ  cl g=al Þ2bl

;

for i ¼ 0 to nDiv

ð4Þ

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D. DEB AND S.O. CHOI

where al, bl and cl are the BELL curve parameters for lth linguistic hedge of that variable. nDiv refers to number of points. The membership grades for Very Low and Very High are estimated as lVeryLow ðXÞ ¼ lLow ðXÞ2

ð5Þ

lVeryHigh ðXÞ ¼ lHigh ðXÞ2

3.2. FUZZY MEMBERSHIP GRADES OF W Gallery width (W) or extension of unsupported roof span is an important parameter for development of collapsed chimney or sinkhole. In general, wider gallery will be more favorable for sinkhole development since higher tensile stress develops in the middle of the span. Theoretically, limiting tensile stress of roof strata is directly proportional to the square of the unsupported roof span or gallery width and diameter of the sinkhole is directly related to opening span. Many abandoned mines are left with irregular shaped pillars and thus dimension of opening is not uniform everywhere. Apart from that, type of junctions, 3- or 4-way also influences the effective width of opening. In this study, average gallery width is considered to develop the fuzzy membership grade. Recorded data of sinkholes from USA, UK and other countries show that possibility of sinkholes is great if gallery width exceeds about 7–8 m. The occurrences of sinkhole diminish if the gallery width is below 4 m. Based on these data, fuzzy membership grade of gallery width is developed as shown in Figure 1. It is noted that a ‘‘Low W’’ is defined with a membership grade of 1.0 at W=3.0 m or less and then it gradually decline to 0. On the other hand, a ‘‘High W’’ means a membership grade of 0 for W=5 m or below and gradually increases to 1.0 at W=9.5 m or above. A ‘‘Medium W’’ signifies membership grade of 1.0 at W=6.5 m and then it reduces once W exceeds or recedes from 6.5 m. The constants of BELL shaped curves for different linguistic hedges for this variable and others are given in Table 1.

Memebership Grade

1.000 0.800 0.600 0.400 0.200 0.000 3.000

4.000

5.000

6.000

7.000

8.000

9.000

Gallery width, W (m)

Low

Medium

Figure 1. Membership grade of gallery width, W.

High

Very Low

Very High

10.000

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ANALYSIS OF SINKHOLE OCCURRENCES OVER ABANDONED MINES Table 1. Parameters of BELL curve for different variables

W a

H/M b

c

a

P/M b

c

a

R b

c

a

S b

c

a

b

c

Low 1.5 2.0 3.0 3.5 2.0 1.0 1.5 2.0 1.0 2.0 2.0 0.0 25.0 2.0 0.0 Medium 1.5 3.0 6.5 2.0 2.0 8.0 1.0 2.0 4.5 1.0 2.0 3.5 15.0 2.0 50.00 High 2.5 3.0 10.0 4.5 3.0 15.0 2.0 3.0 8.0 2.0 2.0 7.0 35.0 3.0 100.0

3.3. FUZZY MEMBERSHIP GRADES OF H/M Overburden depth is one of the major factors which ultimately determine sinkhole appearance on the surface. Peng (1992) reported that ratio of cover depth (H) to opening height (M) below 4–5 are favorable for sinkhole formation with a maximum value of 11. One study in the UK referred that maximum height of collapse can be 10 times of mining height with an average value of 3–5 m (Whittaker et al., 1989). Based on these and other studies, 15 values of H/M ranging from 1 to 15 are considered for the definition of fuzzy membership grades of three linguistics hedges as mentioned above. Figure 2 shows the membership grades of these hedges based on different values of H/M. In this case, a ‘‘Low H/M’’ is defined with the membership grade of 1.0 when the H/M value is 1 or less and this grade decreases to 0 at the H/M value 10 or above. On the other hand, a ‘‘High H/M’’ means a membership grade of 1.0 at H/M value of 14 or above and 0 at H/M value of 5 or less. 3.4. FUZZY MEMBERSHIP GRADES OF P/M

Memebership Grade

The ratio of pillar width (P) to mining height (M) is a factor signifying pillar strength. In general, higher ratio implies more load bearing capacity of the pillar and may be deterrent for sinkhole development. Note that insitu strength of pillar rock is not considered in the present study due to difficulty of data acquisition. Mine maps

1.000 0.800 0.600 0.400 0.200 0.000 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

H/M

Low

Medium

High

Very Low

Figure 2. Membership grade of depth to mining height ratio, H/M.

Very High

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D. DEB AND S.O. CHOI

shows that irregular pillars may exists in the abandoned mines width ranging from 2 to 20 m. Thus a ‘‘High P/M’’ ratio is assigned a membership grade of 1.0 at P/M of 7.5 and above as shown in Figure 3. A ‘‘Low P/M’’ ratio means a membership grade of 1.0 for P/M less than 1 and this value diminishes to 0 at P/M of 5 or more. 3.5. FUZZY MEMBERSHIP GRADES OF R Geological conditions of rock strata can be approximated using Geological Strength Index (GSI) or Rock Mass Rating (RMR) or Q value or shear strength. However, it requires underground exposure of roof strata or drill cores of the same. In many cases, underground exposure is not possible due to safety conditions of abandoned mine workings. Hence, drill cores or the observation of surface cracks and depression may lead to some understanding of the overburden characteristics. In this study, a parameter, Roof Index (R) is defined to quantify roof conditions based on GSI and thickness of the rock strata as given below:
X N N X R¼ ðricm
ti Þ ti ð6Þ i¼1

i¼1

where the rock mass strength of ith roof strata ¼ rici ðsÞa , s ¼ exp½ðGSI  100Þ =9; a ¼ ð1=2Þ þ ð1=6Þ½ðexpðGSI=15Þ  expð20=3Þ; rici is the uniaxial compressive strength of ith intact rock, GSI is the Geological strength index, ti is the thickness of ith roof strata, and N is the number of rock strata above the worked seam. The parameter, R is a rough measure of competency of the roof. Higher rock mass strength signifies competent rock mass and causes higher value of R. Practically the value of R can be lower than 0.1 and as high as 10. Calculations based on known rock types such as limestone, sandstone and shale having GSI ranging from 20 to 80, it is found that value of R ranges from 0 to 7 (0 not inclusive). In this study, the membership grade of ‘‘Low R’’ is 1.0 when the value of R is 0.5 or less and it gradually decreases to 0 when the R value is 5 or over (Figure 4). On the contrary, a ricm is

Memebership Grade

1.000 0.800 0.600 0.400 0.200 0.000 1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

P/M Low

Medium

High

Very Low

Figure 3. Membership grade of pillar width to height ratio, P/M.

Very High

7.5

8

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ANALYSIS OF SINKHOLE OCCURRENCES OVER ABANDONED MINES

‘‘High R’’ is defined with the membership grade of 1.0 when the value of R is 6.5 or above and 0 when the same is 1.5 or less. 3.6. FUZZY MEMBERSHIP GRADES OF S

Memebership Grade

Possibility of sinkhole (S) is defined as an index between 0 and 100, 0 being no possibility and 100 meaning absolute chance of sinkhole occurrences. A possibility index of more than 70 is considered to be in the higher side. One the contrary, a S value less than 20 signifies lower possibility of sinkhole occurrences. Figure 5 describes five linguistic hedges ‘‘Very Low’’, ‘‘Low’’, ‘‘Medium’’, ‘‘High’’ and ‘‘Very High’’ possibility of sinkhole occurrences. The ‘‘Low S’’ is defined with membership grade of 1.0 when the value of S is 8 or less and that of 0.0 when the S value is 60 and more. On the other hand, ‘‘High S’’ means a membership grade of 1.0 when the S value is 90 or over and that of 0.0 when the S value is 25 or less. The membership grade of ‘‘Medium S’’ is defined as 1.0 for a value of 50 and this grade declines both sides and becomes 0 at S value of 10 and 90.

1.000 0.800 0.600 0.400 0.200 0.000 0

2

1

3

4

6

5

7

Roof Index (R) Low

Medium

High

Very Low

Very High

Memebership Grade

Figure 4. Membership grade of Roof Index, R.

1.00 0.80 0.60 0.40 0.20 0.00 0

10

20

30

40

50

60

70

80

90

Possibility of Sinkhole Low

Medium

High

Figure 5. Membership grade of sinkhole possibility, S.

Very Low

Very High

100

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D. DEB AND S.O. CHOI

3.7. FUZZY REASONING FOR THE ASSESSMENT OF SINKHOLE OCCURRENCES A general fuzzy rule for the assessment of sinkhole can be expressed as If W is A and H=M is B and P=M is C and R is D Then S is E where A, B, C and D represent fuzzy set of W, H/M, P/M and R, respectively and E signifies the fuzzy set of S. One such rule can be written with linguistic hedges as If W is High and H=M is Low and P=M is High and R is Low Then S is High In order to analyze a rule mathematically, a fuzzy relational matrix is derived using Mamdani’s method as follows: F ¼ A and B and C and D ! E ¼ ðA
B
CÞ
E Z ¼ lA ðpÞ ^ lB ðqÞ ^ lC ðrÞ ^ lD ðsÞ ^ lE ðwÞ P
Q
R
S
W

where symbol  signifies a ‘‘min operator’’. The variable p contains in P as p 2 P and a representative value of W as defined in Figure 1. Similarly other variables are defined. In this case F is a matrix of five-dimensional space. Now for a premise (fact) having If W is A0 and H=M is B0 and P=M is C0 and R is D0 The membership grade of S can be obtained as lE0 ðwÞ ¼ f_p ½lA0 ðpÞ ^ lA ðpÞg ^ f_q ½lB0 ðqÞ ^ lB ðqÞg |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} x1

x2

^ f_r ½lC0 ðrÞ ^ lC ðrÞg ^ f_S ½lD0 ðsÞ ^ lD ðsÞg ^lE ðwÞ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} x3

ð7Þ

x4

¼ ðx1 ^ x2 ^ x3 ^ x4 Þ ^ lE ðwÞ Here symbol _ denotes the ‘‘max operator’’ and x1 refers the maxima or degree of compatibility between the membership functions of A¢\A and so on. The above procedure can also be executed by replacing min operator with product operator. For a given premise or fact, the above procedure is applied considering each fuzzy rule and ½lE0 ðwÞi ði ¼ 1; . . . ; m; m being the number of fuzzy rules) are obtained. Then the maxima of all these fuzzy membership grades are computed as: lE0 ðwÞ ¼ ½lE0 ðwÞ1 _ ½lE0 ðwÞ2 _    _ ½lE0 ðwÞm ¼

m [ ½lE0 ðwÞi

ð8Þ

i¼1

After the fuzzy set E¢ is estimated, defuzzyfication (a real value between 0 and 100) of this set can be obtained using a suitable a-cut (a is any value between 0 and 1) and applying weighted mean of membership grades. If wi represents the ith value of S and if lE0 ðwi Þ is greater than or equal to a, then defuzzified value of S is expressed as

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ANALYSIS OF SINKHOLE OCCURRENCES OVER ABANDONED MINES

P Sa ¼

i

ðwi
lE0 ðwi ÞÞ P lE0 ðwi Þ

ð9Þ

i

3.8. 3.8. FUZZY RULES Based on the recorded data from USA, UK, other European countries and Korean sites, 19 fuzzy rules are developed as shown in Table 2. In general, these rules state that for high W, low H/M and low R, possibility of sinkhole occurrences is high. Moreover, higher W and lower P/M may also yield higher possibility of sinkhole index. On the contrary, a low S is expected when lower W, higher H/M and higher R is obtained. Note that these rules are neither exhaustive nor complete for assessing the possibility of all sinkhole formation. However, in this study, these rules are used to assess the possibility sinkhole occurrences and are found to be effective.

4. Development of a Fuzzy Sinkhole Software and Application to Bonghwa Site 4.1. DEVELOPMENT OF FUZZY SINKHOLE PROGRAM Fuzzy sinkhole program has been developed using Visual Basic to estimate possibility of sinkhole occurrences over an abandoned or active mine working. Its a user Table 2. Fuzzy rules for determining possibility of sinkhole occurrences

No. IF W

AND H/M

AND P/M

AND R

THEN S

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

and and and and and and and and and and and and and and and and and and and

and and and and and and and and and and and and and and and and and and and

and and and and and and and and and and and and and and and and and and and

then then then then then then then then then then then then then then then then then then then

If If If If If If If If If If If If If If If If If If If

High Very High High Low Low Low Low Medium High Medium High Low Medium Medium High High High Very High Medium

Low Low Low High Very High High Low Low Low Medium Low Medium Low Medium High Medium Very High Very High Very High

High Low Medium High Medium Medium High Low High Medium Low High Medium High High Medium Low Low Low

Low Low Very Low High Very High High Low Low High Medium Medium Medium Medium High High Low Low High Medium

High Very High Very High Low Very Low Low Medium High Medium Low High Low Medium Low Low High Medium Medium Very Low

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D. DEB AND S.O. CHOI

friendly, menu driven and easy to use program. All input and output variables are assigned with fuzzy input of linguistic hedges. The parameters of BELL curve are inserted for each linguistic hedge and every variable. The program automatically calculates the membership grades using Equation (10) and then equation 4 once the range of variables and number of division (nDiv) within this range are specified. xðiÞ ¼ R1 þ

i
ðR2  R1 Þ nDiv

for i ¼ 0 to nDiv

ð10Þ

where R1 and R2 are the range of the variable. Fuzzy rules are constructed by choosing options from combo-box of each variable as shown in Figure 6. Once all the input data is entered, possibility of sinkhole occurrences of a premise (fact) can be obtained and plotted for output. The defuzzified value of sinkhole possibility, a value between 0 and 100 is computed and given as output for a particular value of a-cut as shown in Figure 7. 4.2. BONGHWA SINKHOLE SITE, KOREA In September 2004, a massive sinkhole appeared on the surface in Bonghwa site located in Kyungbuk Province in Korea. On the surface, the sinkhole is elliptical in shape having a size of collapsed depth over 50 m. The trees and top soil were carried away into the mine voids as shown in Figure 8. This incident has marked the biggest sinkhole subsidence event in Korea. A multi-level zinc and lead mine, locally called as Kumho mine, was in operation since 1971 and ceased in June 2001. This mine had produced 137,000 tons of lead and 250,000 tons of zinc during entire life of the mine. The minimum and the maximum depth of cover of the mine were 50 and 561 m respectively. It is found that over 10,000 m of roadways were developed in the mine and the method of ore extraction was sub-level caving.

Figure 6. A property page for entering fuzzy rule in Fuzzy Sinkhole program.

ANALYSIS OF SINKHOLE OCCURRENCES OVER ABANDONED MINES

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Figure 7. A property page showing defuzzified value of a premise or fact.

Figure 8. Sinkhole occurred in Bonghwa (The hole size is 44 m
22 m and the depth is about 50 m).

4.3. GEOLOGY OF THE BONGHWA SITE The Bonghwa site is located in south-western part of Sungun-ri. The Kumho mine is located in Jangoon limestone formation of Jangoon Mountain. It is overlaid conformably by the Tooumri-formation, unconformably by the Yulri-formation and intruded by the Choonyang granite in the western side of the Kumho mine as shown in Figure 9 (Geological Survey of Korea, 1963). The Tooumri formation is represented by schist and phyllite and Yulri formation contains mica schist, phyllite and metamorphosed sandstone. Surface elevation of the sinkhole is 640 ML and the ore body was excavated up to 580 ML. As shown in Figure 8, rock mass surrounding the sinkhole consists of weathered and jointed limestone and has a vivid fault zone. The mine roof was composed of jointed limestone and it was weathered probably

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D. DEB AND S.O. CHOI

Figure 9. Geological map of Bonghwa site.

having Very Low roof index (R). From the preliminary study of the site, it is envisaged that the sinkhole may occur due to the combined origins of weak rock masses and natural limestone cavities (Choi, 2004). 4.4. APPLICATION OF FUZZY SINKHOLE PROGRAM IN BONGHWA SITE The mine is wide spread in this area and at different locations, the depth of cover is within 50 m having large excavation underneath. Due to this reasons, it was necessary to investigate if there are any other possible locations for sinkhole occurrences in that area. The authors applied the fuzzy sinkhole program to assess the possibility of sinkhole occurrences in other locations in the neighboring area. For this purpose, another nine locations are selected considering the extent of underground workings, depth of cover and local geological conditions as in Figure 10. This figure also shows the topographical map on this area, with the layout of underground mine working zone. The point LB01 in Figure 10 denotes sinkhole occurrence location and LB10 is assumed as a reference location where there is no possibility of sinkhole occurrences since no underground excavation was conducted underneath that location. The fuzzy input data for rest eight locations (LB02-09) were shown in Table 3. Using Fuzzy sinkhole program, membership grades and defuzzified value of sinkhole possibility for each locations are estimated. Figure 11 plots the membership grades of possibility of sinkhole of LB02 and LB03 locations. With a-cut of 0.6, it is found that the defuzzified values of sinkhole possibility are 87.63 and 6.33, respectively.

ANALYSIS OF SINKHOLE OCCURRENCES OVER ABANDONED MINES

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Figure 10. Topographical map and the section view of Kumho mine on the sinkhole occurrence area in Bonghwa, Korea.

Similarly, defuzzified values of sinkhole possibility for other locations are computed and given in Table 3. Note that the assumed value of 100 on the LB01 means that the sinkhole has occurred as shown in Figure 6. The assumed value of 0 for the LB10 means that there is no possibility of sinkhole formation because of no mining activity underneath. 4.5. INTERPRETATION OF RESULTS From the above results, it is clear that locations LB02 and LB08 have higher possibility of sinkhole occurrences. The location LB02 lies near shaft-1 and depth of cover is also low. The mine voids underneath this location is also extensive.

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D. DEB AND S.O. CHOI

Table 3. Results of fuzzy sinkhole analysis on several points in the research area

ID no.

Input

LB01 LB02 LB03 LB04 LB05 LB06 LB07 LB08 LB09 LB10

Output

W

H/M

P/M

R

S

– Very High Medium Very High High Low Very High High Very Low –

– Low High Very High Very High Very High Very High Medium Medium –

– Low Low Very Low Low Medium Very Low Medium High –

– Low Medium High High Very High High Low Medium –

100* 87.63 6.33 50.00 50.00 9.17 50.00 87.17 9.17 0*

*Output values for LB01 and LB10 were assumed from the sinkhole occurrence and no mine activities, respectively.

Membership grade

1 0.8

α -cut = 0.6

0.6 0.4

LB 02

LB03

0.2 0 0

10

20

30

40

50

60

70

80

90

100

Possibility of Sinkhole Figure 11. Membership grades of sinkhole possibilities at locations LB02 and LB03.

Underneath the location LB08, multiple working levels exist having relatively shallower overburden consisting mainly weathered limestone. Figure 12 shows the contours of sinkhole possibilities on the study area in three-dimensional view. Based on this result, authors have recommended the Korea Forest Service, in-charge of all natural disaster occurring in national forests, Korea, for monitoring of ground movements of these two locations.

5. Conclusions As in many countries, Korea also has severe problems due to subsidence related damage on surface structures and natural forests. Most of the reported subsidence occurred over abandoned mine area. To prevent a disaster and to protect a personal property from a subsidence, a reasonable technique for estimating the subsidence

ANALYSIS OF SINKHOLE OCCURRENCES OVER ABANDONED MINES

Figure 12.

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Contours of possibility of sinkhole in Bonghwa site.

occurrence is needed to be developed. In this study, fuzzy reasoning techniques is applied to assess the possibility of sinkhole occurrences over abandoned mine area. This technique is especially useful where data are uncertain and statistical or analytical methods cannot be applied. Based on this study following conclusions can be drawn:

• For the assessment of sinkhole occurrences, W, H/M, P/M and R are sufficient input parameters. Although time and water factors can be added to enhance the analysis results. • Numerical representation of these parameters is almost impossible due to unavailability of relevant data, mine maps and detailed geological information. In addition, collection of such data is time consuming, expensive and at times unsafe. Thus application of any analytical or regression methods is almost impossible. On the other hand, fuzzy reasoning technique does not rely on the crisp form of data set rather uses linguistic terminology to process the output. At times, one may be only interested to know whether possibility of sinkhole occurrences at a particular location is ‘‘low’’, or ‘‘high’’ or ‘‘medium’’. Thus applying fuzzy sets of W, H/M, P/M and R to assess sinkhole possibility makes more practical sense. • The fuzzy sinkhole program is used to assess the possibility of sinkhole occurrences in Bonghwa site. It has proved to be a useful program for assessing the possibility of sinkhole occurrence. From this analysis, two other locations are found to be prone of sinkhole occurrences. The concerned governmental agency was notified for monitoring of ground movements on those locations. The authors will apply this technique to other regions in Korea with the added fuzzy rules, and make the geohazards map of sinkhole subsidence.

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• However, more fuzzy rules have to be incorporated to obtain more accurate results. It is also possible to have contradictory rules when large number of fuzzy rules is incorporated in the analysis. Fuzzy set theory can also analyze such rules in an effective manner although it is better not to have contradiction between the rules.

Acknowledgements This work is supported a grant research from the office of the Prime Minister of Korea (Basic Research Project).

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