guÍa

Rock Mass Quality Classification Based on RMR and Fuzzy Comprehensive Evaluation

1Chao PENG, *2Qifeng GUO, 3Fenhua REN, 4Shengjun MIAO, 5Dong JI

1~5 School of Civil and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China

1, First Author [email protected] *2,Corresponding Author [email protected]

[email protected] [email protected]

[email protected]

Abstract This paper, which bases on Fuzzy Mathematics Theory, viewed the classification of rock masses as

a multi-attribute decision. Combined with the Analytic Hierarchy Process theory, the model of fuzzy comprehensive evaluation is established to classify the deep rock quality. This method makes up the disadvantages of uncertainty and subjectivity of traditional method of RMR to enable the evaluation of deep rock mass more reliable under complicated geologic environments. At last, the method has been used in the rock mass classification of Sanshandao Gold Mine. Compared with the conventional methods, the result of this method is closer to the fact, which indicates that fuzzy comprehensive evaluation method is reasonable and feasible.

Keywords: Deep Rock Mass Quality, RMR Method, Fuzzy Comprehensive Evaluation, AHP

1. Introduction

In an actual production process, whether a safe and efficient production can carry out is directly related to the rock mass quality. A comprehensive evaluation of the rock mass quality is a simple and quick way to value the rock mass quality. And it is also an essential part of the design and construction of underground works. The ultimate purpose of the comprehensive evaluation of the rock mass quality is to determine the stability of the rock mass, and to provide a quantitative data for engineering design. Therefore, the rock quality evaluation is always an important topic in the field of rock engineering research.

There are various methods to evaluate rock mass. These methods developed from a simple judgment by a single factor to a multi-factor comprehensive classification. Currently, the rock mass evaluation methods in China include RMR, Q-System and the national standards of engineering classification of rock standard [1]. But, these traditional methods have their own defects [2]. Taking RMR classification system for example, this method is unreasonable because it uses a fixed scoring and evaluating factors to make a simple evaluation. Such as, only a tiny difference in the classification boundary indicators will divide the rocks into two different types. So, only taking the uncertainty, complexity and ambiguity factors of the rock mass quality into account, the rock mass quality evaluation can be accurate and reliable. This article evaluates the quality of the rock mass by fuzzy mathematics and analytic hierarchy process, and gets a result which is more consistent with the actual geological conditions. 2. The principle of fuzzy comprehensive evaluation

Fuzzy Comprehensive Evaluation Method [3] is a multifactorial decision in the fuzzy environment to make a comprehensive evaluation of things affected by multiple factors in a fuzzy environment. To make a fuzzy comprehensive evaluation, firstly, we must define two sets.

1 2 3, , , mU = u u u u . U is a collection of m comprehensive evaluation factors, which calls

factor set.

Rock Mass Quality Classification Based on RMR and Fuzzy Comprehensive Evaluation Chao PENG, Qifeng GUO, Fenhua REN, Shengjun MIAO, Dong JI

Journal of Convergence Information Technology(JCIT) Volume8, Number10, May 2013 doi:10.4156/jcit.vol8.issue10.13

101

1 2 3= , , , nV v v v v . V is a collection of n decisions reviews, which calls evaluation set.

The role and weights of various factors in the decision-making are different; therefore the judgment is different too. So, we define a fuzzy set A called the importance of U of the weight set.

1 2 3= , , mA a a a a

Where ai represents the ith factor weight, and ai satisfies the normalization condition:

1

= 1m

ii

a ( i=1,2,3…m ) (1)

If we make a fuzzy evaluation for every iu , then we can get an evaluation set of single factor as

follows, which is a fuzzy subset of the decision of evaluation set V. 1 2 3, , ,ij i i i inr r r r r .

Therefore, these evaluations of influencing factors of which the number is m constitute the total

single factor evaluation matrix R, = ij m nR r

which indicates the fuzzy relationship between the

factors set U and the evaluation set V, where ijr represents the membership degree of ith factors to the

decisions review jv .

As a result, we can get the fuzzy comprehensive evaluation model trimers (U, V, R), and do a fuzzy transformation to make comprehensive evaluation as follows:

1 2 3, , , nB A R b b b b (2)

where 1

m

i i ijib a r

. B is a fuzzy submatrix of the evaluation set V, and then we can classify it

according to the principle of maximum degree of membership after we get it. 3. Determine the weights of evaluation indexes by AHP

There are several methods determining the evaluation factors weight, and the majority of them are based on expert evaluation method or statistics. Such as expert scoring method, gray relational analysis and analytic hierarchy process. Analytic hierarchy process [4] is a system analysis method proposed by Professor T.L.Saaty in the United States in the 1970s, which is an effective way to determine the factor weights. The basic idea is as follows: The complex issues can be divided into simple factors, and make a pairwise comparisons can be made with these factors; Then we can get a target weight representing the relative importance of various factors in the evaluation system, which enable to translate the complex issues into a weighted single objective problem. AHP is a method with strong logic, practicality and systematicness, which can weight coefficients of the evaluation factors accurately.

This article selected analytic hierarchy process to evaluate factors weight: Firstly, determine the evaluation indexes; secondly, make pairwise comparisons according to people’s understandings of the relative importance between each indexes, and use the scaling method of 1 to 9 and its reciprocal (see Table 1) to construct of the judgment matrix T [6].

11 12 1

21 22 2

1 2

m

m

m m mm

u u u

u u uT

u u u

Calculate λmax which is the largest eigenvalue of judgment matrix T and its corresponding feature vectors, and then normalized these feature vectors. The weight set A of evaluation factors can be

obtained as follows: 1 2 3= , , mA a a a a


102

Table 1. Classification and measurement of importance Scale Description

1 ui and uj are equally important 3 ui is slightly more important than uj 5 ui is more important than uj 7 ui is much more important than uj 9 ui is extremely more important than uj

2，4，6，8 represents the intermediate values of the adjacent scale 1~3，3~5，5~7，7~9 Reciprocal uj=1/ui

Finally, we need to do a consistency test for weight set A to make sure that the non-uniformity is

acceptable. We can calculate according to Formula 3 and Formula 4 as follows [7].

max

1

nCI

n

(3)

CICR

RI (4)

where CI is consistency index; n is matrix order; CR is random consistency ratio; RI is average randomness indicators.

If CR <0.1, it means that consistency test is satisfied and the weighting coefficient was assigned reasonable. Otherwise, we need to adjust the value of the matrix element, and re-assigned the value of the weight coefficient. 4. Project examples

Sanshandao Gold Mine is one of the main mines of Shandong Gold Group, and it is also the sole undersea gold mine in our country at present. The depth of exploitation has reached -600m level and tunnel developing has reached to -690m. With the increasing depth of mining, the production conditions are deteriorating. Therefore, we need to evaluate the quality of the rock mass to guide the mine production and ensure its safety. 4.1. Determine of the Factor set U and the Evaluation set V

The issue of classification of rock mass is a multi-attribute decision-making problem. RMR evaluation system includes six evaluations: compressive strength of rock (Rc); rock quality designation (RQD); joint spacing (d); jointed condition (f); groundwater state (A) and amendment impact on the project by Jointed direction (k). Combined with the research subject of this paper, under a deep complex geological environment, in-situ stress also has an important impact on the rock quality. So we add another factor to the rock quality evaluation—the in-situ stress (s). The deep rock mass quality evaluation system is shown in Figure 1.

So, factors set is

1 2 3 4 5 6 7, , , , , , , , , , , ,cU u u u u u u u R RQD d f A k s (5)


103

Figure 1. Deep rock mass quality evaluation system

This article intends to use the five-category classification method. That is to say the rock mass is divided into five classes: class (very good), (good), (general), (poor) and (very poor).Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ

So, evaluation set is 1 2 3 4 5= , , , ,V v v v v v Ⅴ, Ⅳ, Ⅲ, Ⅱ, Ⅰ (6)

Standards for classification of underground rock quality are displayed in Table 2.

Table 2. Standards of rock quality evaluation Rock Quality Classification

Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ

compressive strength Rc/MPa

>200 100~200 50~100 25~50 <25

rock quality designation RQD/%

90~100 75~90 50~75 25~50 0~25

joint spacing d/m >2 0.6~2 0.2~0.6 0.06~0.2 <0.06

joint condition f very rough rough general smooth or

interlayer<5mm interlayer>5mm

groundwater state A dry wet damp dripping gushing

correction value k very

favorable favorable general infaust very infaust

correction value s >8 6~8 4~6 2~4 0~2

4.2. Select the membership function to determine fuzzy relationship matrix

The studies of fuzzy evaluation on rock stability, in fact, are reviews of the evaluation factors set mapping to a set of decision-making. The core of the method which uses fuzzy mathematics to evaluate the rock mass quality is to determine the function and membership. Fuzzy relation matrix

= ij m nR r

represents the membership of each evaluation factors to each decision reviews. Therefore,

membership can be regard as a function of the data and quality standards of the evaluation factors. The type of continuous membership function in rock engineering fuzzy evaluation includes normality, ridge, triangular fuzzy and trapezoidal functions [8].

During the rock mass evaluation process of continuous evaluation, if the value of the influencing factors drops in a certain interval, rock mass quality mostly belongs to the class which corresponds to the interval. But there is still a small part which belongs to other classes. Therefore, we choose the normality as our continuous membership function, and expression is


104

2

expi

x au x

c

(7)

where x is the characterization index value of the evaluation factors; a, c is a coefficient.

Normal distribution is generally believed that: if the study area is divided into n levels, in a given

fuzzy divided interval the midpoint (x = a) is the average of the interval, where 1u a . At the

endpoints of an interval, the membership degree to both intervals adjacent of the point is identical, which can be described by the following form

2

exp 0.5x a

c

(8)

where a1, a2 (a1>a2) indicating the level of physical quantities fuzzy interval boundary values

respectively. Thus from Formula (8) we can get

1 2 2a a a (9)

1 2 1 .66c a a (10)

In this paper, the study area is divided into 1~5 classes, which correspond to the classification of rock masses class ~ . For the first level, the division interval is x ≤ bⅤ Ⅰ 1, and the value of x is [0, b1];

For the last level, the division interval is x＞bn-1, and the midpoint is a= bn-1 + 0.5bn-1. Then, combining Formula (9) and (10) with Table 2, we can obtain the function coefficients of each evaluation factors (see Table 3)

Table 3. Function coefficients of each evaluation factors

Rock Quality Classification

Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ

a5 c5 a4 c4 a3 c3 a2 c2 a1 c1

Rc/MPa 300 120.48 150 60.24 75 30.12 37.5 15.06 12.5 15.06

RQD/% 95 6.02 82.5 9.04 62.5 15.06 37.5 15.06 12.5 15.06

d/m 3 1.2 1.3 0.84 0.4 0.24 0.13 0.08 0.03 0.04

s 12 4.82 7 1.20 5 1.20 3 1.20 1 1.20

A membership function of two-terminal can be written as:

4

2

44 5

4

2

55 5

5

5

0

1 exp

exp

1

x a

x aa x b

cu

x ab x a

c

x a

Ⅰ (11)

1

2

11 1

1

2

11 2

1

1

exp

1 exp

x a

x au a x b

c

x ab x a

c

Ⅴ (12)

When we build the membership function of the intermediate-level interval, we should take the two half adjacent intervals into consideration. Take the (n-1)th level interval[bn-2,bn-1] for example, we can construct the following functions


105

2

2

22 2

2

2

12 11

1

2

1

0

1 exp

exp

1 exp

0

n

nn n

n

nn nn

n

nn n

n

n

x a

x aa x b

c

x au b x b

c

x ab x a

c

x a

(13)

For discrete evaluation [11], the degree of membership is assessed by classification method, and it is divided into five grades as follows: very good (0.9), good (0.7), general (0.5), bad (0.3), very bad (0.1).

Assessed value is given in according with the assignment criteria, and then we construct membership functions by trapezoidal membership functions as follows:

1 0.15

2.5 10 0.15 0.25

0 0.25x

x

u x x

x

Ⅴ (14)

0 0.75

10 7.5 0.75 0.85

1 0.85x

x

u x x

x

Ⅰ (15)

0 0.15

10 1.5 0.15 0.25

1 0.25 0.35

4.5 10 0.35 0.45

0 0.45

x

x

x x

u x

x x

x

Ⅳ (16)

0 0.55

10 5.5 0.55 0.65

1 0.65 0.75

8.5 10 0.75 0.85

0 0.85

x

x

x x

u x

x x

x

Ⅱ (17)

0 0.35

10 3.5 0.35 0.45

1 0.45 0.55

6.5 10 0.55 0.65

0 0.65

x

x

x x

u x

x x

x

Ⅲ (18)

Based on the engineering exploration and related experimental data, rock mass quality evaluation of Sanshandao Gold Mine are shown in Table 4

Table 4. Quality index value of deep rock mass

Values of the

indicators Rc/MPa RQD/% d/m f A k s

-510m level 106.46 87.4 0.297 general damp general 4.6

-555m level 72.30 89.5 0.416 general damp dripping general 3.0

-600m level 70.83 72..6 0.310 interlayer<5mm gushing infaust 2.9

Thus, membership matrix = ij m n

R r

can be determined as follows:


106

510

0 0.529 0.408 0 0

0.255 0.745 0 0 0

0 0 0.832 0.168 0

0 0 1 0 0

0 0 1 0 0

0 0 1 0 0

0 0 0.089 0.11 0

R

555

0 0 0.992 0.008 0

0.451 0.549 0 0 0

0 0.004 0.996 0 0

0 0 1 0 0

0 0 0.5 0.5 0

0 0 1 0 0

0 0 0 1 0

R

600

0 0 0.981 0.019 0

0 0 0.637 0.363 0

0 0 0.869 0.131 0

0 0 0 1 0

0 0 0 0 1

0 0 0 1 0

0 0 0 0.993 0.007

R

4.3. Determine the weight of evaluation index

Use 1~9 and its reciprocal scale method to determine the factors, the relative importance of the pairwise comparison matrix T is

1 1 2 2 3 3 3

1 1 2 2 2 3 3

1/ 2 1/ 2 1 1 2 2 1

1/ 2 1/ 2 1 1 2 2 2

1/ 3 1/ 2 1/ 2 1/ 2 1 1 1/ 2

1/ 3 1/ 3 1/ 2 1/ 2 1 1 1

1/ 3 1/ 3 1 1/ 2 2 1 1

T

After calculation, we can get: the largest eigenvalue of calculated matrix is λmax = 7.1225, consistency index CI = 0.021, and average randomness indicators RI = 1.320. So, consistency ratio CR = 0.015 <0.1, means that the results meet the conformance requirements. Normalized the corresponding eigenvector of λmax, we get A = [0.2275, 0.2069, 0.1276, 0.1411, 0.0850, 0.1262, 0.1257].

4.4. Comprehensive fuzzy evaluation

With weight vector A of the evaluation factors and membership degree matrix R of factors, we can do a fuzzy transformation, and make comprehensive evaluation using weighted average model.


107

11 1

1 2 3 1 2 3

1

( , , ) , , ,n

m n

m mn

r r

B AR a a a a b b b b

r r

Therefore, the -510m level comprehensive evaluation of the rock mass quality matrix is B-510 = [0.0528, 0.2888, 0.5625, 0.0353, 0]. And according to the principle of maximum degree of membership, the -510m level belongs to (general) rock mass. Ⅲ

Similarly, we can get results: -555m level B-555 = [0.0933, 0.1141, 0.6626, 0.1700, 0], Ⅲ class (general); -600m level B-600 = [0, 0, 0.4659, 0.4883, 0.0859], Ⅳ class (poor).

In order to verify the correctness of this method [14], we compare the results with traditional methods (see Table 5).

Table 5. The comparison results obtained from different methods

Classification methods BQ RMR Q-System Method in the paper

-510m level Ⅲ Ⅲ+ Ⅱ- Ⅲ

-555m level Ⅳ Ⅲ+ Ⅲ- Ⅲ

-600m level Ⅳ Ⅳ Ⅳ- Ⅳ

Those results which are in agreement with the results getting from traditional methods show

that this method is reliable and reasonable. 5. Conclusion

Based on the study of rock quality evaluation factors and combined with RMR method, analytic hierarchy process and fuzzy mathematical theory, this paper considers the vagueness of the evaluation, and overcome the deficiencies of the traditional methods. We conclude that, the fuzzy comprehensive evaluation method is more reasonable.

Comprehensive evaluation of the rock mass model is established to evaluable the level of the deep rock mass, and to get rock mass evaluation matrix B. The conclusion is that the -510m, -555m, -600m rock mass belong to Class Ⅱ, class Ⅲ and class IV respectively, which are in accordance with the actual situation of the mine and superior to the results getting from traditional method. The results show that with the depth increasing, the rock mass quality is deteriorating. Especially, the -600m level rock mass belongs to the poor stability of rock mass, which requires to do some special supportive reinforcement and real-time monitoring of confining pressure in the mining process. 6. Acknowledgment

This work is supported by “national natural science foundation of China (No.51034001 and No. 11002021)”. 7. References [1] CAI Mei-feng, Rock Mechanics and Engineering, Science Press, China, 2000. [2] KANG Zhi-qiang, FENG Xia-ting, ZHOU Hui. “Application of extenics theory to evaluation of

underground cavern rock quality based on stratification analysis method”. Chinese Journal of Rock Mechanics and Engineering, vol. 25, no.2, pp. 3687-3693, 2006.

[3] LI An-gui, ZHANG Zhi-hong, Fuzzy Mathematics and Applications, University of Science & Technology Beijing Press, China, 1993.

[4] ZHAO Huan-chen, Analytic Hierarchy Process, Science Press, China, 1986. [5] ZhANG Chao-yi, MIAO Jian-song, WU Mu-qing. “Fairness resources scheduling based on AHP

in OFDMA relay system”. Journal of Convergence Information Technology, vol. 6, no.9, pp 380-388, 2011.


108

[6] WANG Xin-min, ZHAO Bin, ZHANG Qin-li. “Mining method choice based on AHP and fuzzy mathematics”. Journal of central south university (Science and technology), vol.39, no.5, pp.875-880, 2008.

[7] ZHANG Ji-jun. “Fuzzy Analytical Hierarchy Process”. Fuzzy systems and mathematics, vol 14, no.2, pp.80-88, 2000.

[8] SU Yong-hua. “Constructing method of fuzzy membership function of geotechnical parameters and its application”, Journal of Chinese Journal of Geotechnical Engineering, vol. 29, no.12, pp.1773~1779, 2007.

[9] LIU Hui, CHEN Yi-Zeng, "The Study on Logistics Management Patterns based on Fuzzy Comprehensive Evaluation Method", IJACT: International Journal of Advancements in Computing Technology, Vol. 4, No. 21, pp. 262 ~ 270, 2012

[10] TIAN Jian-wei, QI Wen-hui, LIU Xiao-xiao, LIU Jin, "Quality Model of Enterprise Information Portal Based on Fuzzy Comprehensive Evaluation", IJACT: International Journal of Advancements in Computing Technology, Vol. 4, No. 23, pp. 161 ~ 168, 2012.

[11] LIU Duan-ling, TAN Guo-huan, LI Qi-guang, XU Yue, WANG Yuan-han. “The stability of rock slope and fuzzy comprehensive evaluation method”. Chinese Journal of Rock Mechanics and Engineering, vol. 18, no.2, pp .170-175, 1999.

[12] LI Qiu-ying, Qi Hai-feng, WANG Bao-sen. “Study of the supply chain operational risk based on fuzzy comprehensive evaluation”. Journal of Convergence Information Technology, vol. 6, no.10, pp 71-80, 2011.

[13] YANG Ze-ping, LI Hai-bing, ZENG Xia-sheng. “Use of analytic hierarchy process method for classification of engineering rock mass”. Journal of engineering geology, vol.14, no.6, pp.830-834, 2006.

[14] WU Ai-qing, LIU Fu-zheng. “Advancement and application of the standard of engineering classification of rock masses”, Journal of Chinese Journal of Geotechnical Engineering, vol. 31, no.8, pp.1513~1523, 2012.


109

guÍa

Documents