A methodology for evaluation and classification of rock mass quality on tunnel engineering

Tunnelling and Underground Space Technology 22 (2007) 377 387 Tunnelling and Underground Space Technology incorporating Trenchless Technology Research www.elsevier.com/locate/tust A methodology for evaluation and classification of rock mass quality on tunnel engineering Chao-Shi Chen, Ya-Ching Liu * Department of Resources Engineering, National Cheng Kung University, Tainan, Taiwan Received 4 May 2006; received in revised form 18 October 2006; accepted 18 October 2006 Available online 30 November 2006 Abstract In this paper a new methodology for evaluation and classification of rock mass quality that can be applied to rock tunneling is presented. An evaluation model based on combing the analytic hierarchy process (AHP) and the fuzzy Delphi method (FDM) for assessing the rock mass rating is the main procedure. This research treats rock mass classification as a group decision problem, and applies the fuzzy logic theory as the criterion to calculate the weighting of factors. The main advantage of this procedure is that it can effectively change the weighting of each rating parameter with the variation of geological conditions. The proposed method was evaluated and applied to the actual cases that are the two tunnels along the Second Northern Highway around Taipei area in Taiwan, namely Mu- Zha and Hsin-Tien tunnels. It was found that the determined results were in a good agreement with the original data assessed by the RMR. Results of the analyses show that it can be provided a more quantitative measure of rock mass and hence minimize judgmental bias. The proposed method should be more feasible for future tunnel construction and for suggestions of tunnel support design in the geological area of Taiwan. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Rock mass classification; Fuzzy Delphi method; Analytic hierarchy process method 1. Introduction Due to the high percentage of mountainous area in Taiwan, up to 75%, tunneling projects have been very frequently included in the construction of many roads and railways. The mechanism of tunnel engineering is quite complicated. Applying mechanical analytical method in design of tunnel supports is, to a certain degree, also difficult. To this day, empirical design methods are still commonly used in the engineering practices. In the 1970s, several rock mass classification systems were proposed for tunneling and underground excavation, which belonged to the empirical design methods with rudiment of the expert system. In the last decades, the rock mass classification concept has been applied * Corresponding author. E-mail addresses: chencs@mail.ncku.edu.tw (C.-S. Chen), n4891106@ mail.ncku.edu.tw (Y.-C. Liu). extensively on engineering design and construction such as tunnels, slopes and, foundations for a long time. The main objective of rock mass classification is used to provide quantitative data and guidelines for engineering purpose that can improve originally abstract descriptions of geological formation. Until now for rock engineering, the most commonly used rock mass classification systems are RSR (Wickham et al., 1972), RMR (Bieniawski, 1973, 1975, 1979, 1989), and Q-system (Barton et al., 1974). However, these traditional classification systems, which ignored the regional and local geological features and rock properties, were constructed with the fixed weight for each rating factor. They often result a certain degree of rating deviation in the same case by different investigators. In addition, the main island of Taiwan is relatively young in geological era and situates at plate borders, thus rock property, rock strength, overburden, excavation span and groundwater are greatly different from those in the area where the well-known rock mass 0886-7798/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2006.10.003

378 C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 classifications originated. Therefore, it is necessary to establish a new rock mass classification system for engineering practices in Taiwan. The main objective of this paper is to present a systemic procedure combined the analytic hierarchy process (Saaty, 1980) and the fuzzy Delphi method (Kaufmann and Gupta, 1988) for assessing the rock mass rating. The proposed method is based on the concept of the hierarchy structure for rock mass quality evaluation which can display the relationship of each criterion (or parameter) and define easily the feasible model for different project, purpose and geology. This research treats the rock classification as a group decision problem because that is analogous to multi-feature pattern recognition problem involving the past history accumulated and the professional opinions of engineer. How can we lower down uncertainties in expert opinion and the decision process? The fuzzy logic theory on the criterion of weighting calculations is applied. The fuzzy Delphi method not only saves the survey time and cost but also denotes the group opinions clearly. The main advantage of this procedure is that it can also effectively change the weighting of each rating parameter with the variation of geological conditions based on two rounds of investigations and comprehensive discussions by a group of experts. In this paper, the proposed method can be successfully applied to determine the ratings of rock mass for the cases of tunneling. 135 cross-sections of two tunnels in the Second Northern Highway were selected to assess the rating of rock mass. It was found that the results determined by the proposed method were in a good agreement with the original data assessed by the RMR. Table 1 Fundamental scale of the AHP (Saaty, 1980) Intensity of Definition importance Explanation 1 Equal importance Two activities contribute equally to the objective 2 Weak 3 Moderate importance Experience and judgment slightly favor one activity over another 4 Moderate plus 5 Strong importance Experience and judgment strongly favor one activity over another 6 Strong plus 7 Very strong or demonstrated importance An activity is favored very strongly over another; its dominance demonstrated in practice 8 Very, very strong 9 Extreme importance The evidence favoring one activity over another is of the highest possible order of affirmation Reciprocals of above Rationals If activity i has one of the above nonzero numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i Ratios arising from the scale A reasonable assumption If consistency were to be forced by obtaining n numerical values to span the matrix State Problems Decision of Assessment Factors and Hierarchy for RMR Pairwise Comparison Calculation of Priority Vector and Maximum Eigenvalue Consistence Check Weights of Factors Fig. 1. A flow chart of the proposed method.

C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 379 Fig. 2. The hierarchy of the rock mass quality evaluation on tunneling project. Dear Sirs: The academic questionnaire is to investigate for evaluation and classification of rock mass quality. It is sincerely invited that you spend a few minutes to complete the questionnaire and return to us at your earliest convenience. No personal or corporate information will be made public. Please be assured that your answers will be kept in strict confidence and take the time to fill out this questionnaire as accurately as possible. Your help is crucial to this research. We deeply appreciate your cooperation. Thank you Yours faithfully Questionnaire design For example: Based on the hierarchy for rock mass evaluation, please fill your opinion inside the below table to judge the degree of importance by Saaty s scale. If the expert think Rock material essentiality is weak important than Groundwater, he/she may write down 3 in the corresponding blank. The rest may be deduced by analogy. Please start writing down the scale of contribution at the following matrix based on your expertise. Reading order: from left to right Table 1 Pairwise comparison of the 1 st layer Rock material essentiality Rock material essentiality Groundwater Features of discontinuities 1 3 5 Groundwater 1/3 1 1/2 Features of discontinuities 1/5 2 1 Fig. 3. An example of the questionnaire for rock mass evaluation.

380 C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 Results show that it can be used to determine the rock mass ratings of tunneling as a simple design assessment method for tunnel supports system and suite for tunnel engineering in Taiwan. 2. Methodology Although currently used rock mass rating systems as RMR and NGI-Q system still can be applied for the consolidated rock before Miocene. But, some of the factors weighting should be reviewed and adjusted to fit with Taiwan s special geological background. For that soft rock younger than Miocene and other composite strata, appropriate rock mass classification for tunnel should be established in the near future. The objective of this study is to introduce a different viewpoint to establish the rock mass quality evaluation model. This research treats the rock classification as a group decision problem. In developing the analytical framework, two issues are addressed. We expressed briefly as follows: many decisions involve criteria and goals, many of which are conflicting with some quantitative and some qualitative. We called this type of decision-making as multiple criteria decision-making (MCDM). One of the methods employed to support MCDM is the AHP. It is a powerful approach to adjust the factors weighting to fit with Taiwan s special geological background. In addition to MCDM, another key point is that groups must make decisions. It is known that group decision-making is a very important and powerful tool to accelerate the consensus of various opinions from experts, which are experienced in practices. In this section, the FDM was taken to synthesize their responses for the questionnaires. The FDM is a methodology in which subjective data of experts are transformed into quasi-objective data using the statistical analysis and fuzzy operations. The main advantages of FDM are that it can reduce the numbers of surveys to save time and cost and it also includes the individual attributes of all experts. From the above-mentioned point, the same way can be applied on the problem of rock mass quality evaluation. The newly developed systemic procedure presented in this paper is based on combining the AHP and the FDM in tunnel engineering. Fig. 1 illustrates the flow chart of this paper. 3. Structure the hierarchy from the top (the objectives from a decision-maker s viewpoint) through the intermediate levels (criteria on which subsequent levels depend) to the lowest level, which usually contains the list of alternatives. 4. Design the format of questionnaire items as to process according to the hierarchy in step 2. And then to collect input by a pairwise comparison of decision elements. 5. On the basis of the data obtained from the respondents through the questionnaires, construct a set of pair-wise comparison matrices (size n n) for each of the lower levels with one matrix for each element in the level immediately above by using the relative scale 2.1. Rock mass quality evaluation analysis In this paper the major steps for evaluating rock mass quality rating proposed in an orderly manner are shown in the following: 1. Define the problem (group decision making) and determine its goal (rock mass rating). 2. Selection and determination of evaluating rock mass parameters for different types of engineering projects (such as tunnels or slopes). Fig. 4. The location of two case tunnels along the Second Northern Highway.

C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 381 measurement which is the same as Saaty s scale (1980) shown in Table 1. The pair-wise comparisons are done in terms of which element dominates the other. 6. Use the eigenvalue method to estimate the consistence index. 7. Determine whether the input data satisfies a consistence check. If it does not, go back to step 1and redo the pairwise comparisons. In this step, the inconsistency of judgments through the matrix can be captured using the largest eigenvalue, k max. Given an n n square matrix, a number, (k max n), measures the deviation of the judgments from the consistent approximation. The closer k max is to n, the more consistent is the result. The deviation of consistency is represented by the consistency index (CI), which is defined as, CI ¼ðk max nþ=ðn 1Þ: ð1þ 8. Calculate the relative fuzzy weights of the decision elements using the following three steps based on the FDM and aggregate the relative fuzzy weights to obtain scores for the decision alternation. (1) Compute the triangular fuzzy numbers (TFNs) fa ij as defined in Eq. (2). In this work, TFNs that represent the pessimistic, moderate and optimistic estimate are used to represent the opinions of experts for each activity time. ~a ij ¼ða ij ; d ij ; c ij Þ; ð2þ a ij ¼ Minðb ijk Þ; k ¼ 1;...; n; ð3þ d ij ¼ Yn k¼1 b ijk! 1=n; k ¼ 1;...; n; ð4þ c ij ¼ Maxðb ijk Þ; k ¼ 1;...; n; ð5þ Table 2 General information of two tunnel sites Name Hsin-Tien tunnel Mu-Zha tunnel Tunnel features Lithology Thick sandstone Sandstone Average sandstone and shale Average sandstone Shale Tuff Site position along the highway 16 + 474k 17 + 423k 13 + 623k 11 + 128k Numbers of cross-section selected 50 85 Excavation method NATM NATM Drilling and blasting Road-header machine Usage Highway Highway NATM: the new Austrian tunneling method, so named by Rabcewicz (1964) and now generally known as NATM. Fig. 5. The standard cross-section of the two tunnels (three-lanes with sidewalk).

382 C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 Fig. 6. Geological profile map of the Mu-Zha tunnel. where aij 6 dij 6 cij, aij, dij, cij 2 [1/9, 1] [ [1, 9] and aij, dij, cij are obtained from Eqs. (3) (5). aij indicates the lower bound and cij indicates the upper bound. bijk indicates the relative intensity of importance of expert k between activities i and j. n is the number of experts in consisting of a group. (2) Following outlined above, we obtained a fuzzy posie tive reciprocal matrix A e ¼ ½~ A aij ; ~ aij ~ aji 1; 8i; j ¼ 1; 2;... ; n; or 2 ð1; 1; 1Þ ða12 ; d12 ; c12 Þ e ¼6 A 4 ð1=c12 ; 1=d12 ; 1=a12 Þ ð1; 1; 1Þ ða13 ; d13 ; c13 Þ 3 7 ða23 ; d23 ; c23 Þ 5 ð1=c13 ; 1=d13 ; 1=a13 Þ ð1=c23 ; 1=d23 ; 1=a23 Þ ð1; 1; 1Þ ð6þ (3) Calculate the relative fuzzy weights of the evaluation factors. e i ¼ ~aij ~ain 1=n ; Z 1 ei¼ Z ei Z ei Z en W ð7þ where, ae1 ae2 ffi ða1 a2 ; d1 d2 ; c1 c2 Þ: Fig. 7. The field condition for shaft excavation method of the Hsin-Tien tunnel. Fig. 8. The field condition for shaft excavation method of the Mu-Zha tunnel.

C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 383 Table 3a Partial results of the rock mass rating and classification on the Hsin-Tien tunnel Case Nos. 1 2 3 4 49 50 Site position 16.474k 16.421k 16.391k 16.350k 17.112k 17.064k Strength 2 2 2 2 2 2 RQD 4 4 4 4 8 8 Spacing 4 6 6 4 8 8 Condition 4 6 6 4 8 8 Groundwater 8 8 8 8 8 8 Orientation 12 10 10 10 10 10 Rating in this study 31 43 43 33 60 60 RMR 26 40 40 28 59 59 Classification in this study V V V V III III Classification Of RMR IV IV IV IV III III Table 3b Partial results of the rock mass rating and classification on the Mu-Zha tunnel Case Nos. 51 52 53 54 134 135 Site position 13.582k 13.573k 13.562k 13.529k 12.197k 12.195k Strength 2 2 2 2 2 2 RQD 4 6 4 4 6 6 Spacing 4 4 4 4 6 6 Condition 4 4 4 4 6 6 Groundwater 8 8 8 8 8 8 Orientation 5 5 10 10 10 10 Rating in this study 38 42 33 33 47 47 RMR 33 38 28 28 45 45 Classification in this study V V VI VI IV IV Classification Of RMR IV IV IV IV III III The symbol here denotes the multiplication of fuzzy numbers and the symbol, and here denotes the addition of fuzzy numbers. fw i is a row vector in consist of a fuzzy weight of the ith factor. ew i ¼ ðw 1 ; w 2 ; w 3 Þ, and W i is a fuzzy weight of the ith factor. W i ¼ ð Q 3 j¼1 w jþ 1=3. Table 4 The interval ratings to account for evaluating parameters in tunneling (Bieniawski, 1989) Total rating (goal) Main aspects (subject) Rock quality indexes (criteria) Range of values Score Rock essential Intact rock strength >250 100 250 50 100 25 50 5 25 1 5 <1 material Uniaxial compressive 10 8 6 4 2 1 0 strength (MPa) RQD% (rock quality 90 100 75 90 50 75 25 50 <25 None designation) 10 8 6 4 2 Groundwater Groundwater condition Completely dry Damp Wet Dripping Flowing None General condition 10 8 6 4 2 Feature of Spacing of >2 m 0.6 2 m 200 600 mm 60 200 mm <60 mm None discontinuities discontinuities 10 8 6 4 0 Conditions of A B C D E None discontinuities a 10 8 6 4 0 a Conditions of discontinuities Criteria A B C D E Conditions of discontinuities Very rough surfaces; Not continuous; No Separation; Unweathered wall rock Slightly rough surfaces; Separation < 1 mm; Slightly weathered walls Slightly rough surfaces; Separation < 1 mm; Highly weathered walls Slickenside surfaces; Continuous gouge < 5 mm thick or separation 1 5 mm Continuous soft gouge > 5 mm thick or separation > 5 mm

384 C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 Table 5 The descriptive statistics of rock mass ratings by RMR and the proposed method Valid N Mean Min Max Range Variance Standard deviation Standard error This study 135 44.9 8 71 63 148.51 12.187 1.049 RMR 135 42.1 6 69 63 165.23 12.854 1.106 on the findings of the field investigation, literature review and collected assistant data, five parameters were found relevant to rock mass quality. In the present study, there are three main aspects for rock mass quality evaluation on the tunnels, i.e., rock material essentiality (including intact rock strength and RQD), groundwater, and features of discontinuities (including spacing and condition). The proposed evaluating system for tunnels contains three layers of hierarchy as shown in Fig. 2. 2.2.2. Determining the weights of factors The total weights were determined by the proposed method and should be conformed to the consistence check as described in the previous section. We can see the example of the questionnaire shown such as Fig. 3. For the geomathematical analysis, matrix coding was done and rating values were designated for subcategories of each parameter to construct pull down menus. Through one round of investigation papers, replied by 13 experts and through a series of comprehensive discussions, the assessment factors and fuzzy weights can be decided as Fig. 2. Our original evaluating system contains three layers of hierarchy as shown in the following. The number listed in the brackets is the total weight of each element. Fig. 9. Distributions of the rock mass rating which are calculated by the RMR and the proposed method. 2.2. Rock mass quality evaluation on tunnel engineering 2.2.1. Decision of factors for rock mass quality evaluation Among all stages in Fig. 1, the stage for factors decision and hierarchy is technically the most important one. Based Table 6 Rock mass rating classified for the tunnels along the Second Northern Highway in Taiwan (modified) Class number Q-value RMR FDAHP (This paper proposed) I >40 >77 >76 II 40 10 77 65 76 66 III 10 4 65 56 66 57 IV 4 1 56 44 57 46 V 1 0.2 44 30 46 34 VI 0.2 0.01 30 2.6 34 9.2 F1 rock material essentiality (0.357) F 11 intact rock strength (0.528) F 12 RQD (0.472) F2 groundwater (0.162) F3 features of discontinuities (0.481) F 31 discontinuous spacing (0.417) F 32 discontinuous condition (0.583) Then, we can define that the rock mass total rating (TR) is equal to the summation of total weights of the three main aspects, TR ¼ðF 1 þ F 2 þ F 3Þ10; ð8þ F 1 ¼ 0:357 ð0:528 F 11 þ 0:472 F 12 Þ; ð9þ F 2 ¼ 0:162 F 21 ; ð10þ F 3 ¼ 0:481 ð0:417 F 31 þ 0:583 F 32 Þ; ð11þ where F1, F2, and F3 are the total rating with respect to the three main aspects. F 11 is the interval rating of intact rock strength, F 12 is interval rating of RQD, F 21 is the interval rating of ground water condition, F 31 is the interval rating of discontinuous spacing and F 32 is the interval rating of discontinuous condition (see Table 4). Finally, rock mass rating was calculated for each tunnel cross-section, higher values of the rating indicate higher

C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 385 degrees of rock mass quality and could be classified to less support need. 3. Case study 3.1. Site description In this paper, two tunnel sites, namely Hsin-Tien and Mu-Zha tunnels along the Northern Second Highway around Taipei area in Taiwan were selected to make a rock mass quality evaluation by the proposed model. The location of two tunnels along the highway is shown in Fig. 4. This area mainly consists of sedimentary rocks of sandstone, shale, close-banded alternate layers of sandstone shale. The deepest overburden is only around 170 m that belongs to the shallow rock formation and strongly weathered. The uniaxial compressive strength distributes from 100 to 500 kg/cm 2. Geological information and tunnel features are summarized in Table 2. The standard main cross-section of the two tunnels is presented in Fig. 5. The geological profile map of Mu- Zha tunnel is shown as Fig. 6. The field condition for Table 7 Supporting system guideline for the tunnels in this paper Class number I II III Excavated procedure Cycle length <4.0 m <3.0 m <2.5 m Rock bolts 29U prestressed grout rock bolts 29U prestressed grout rock bolts L = 4.0 m @ 2.0 m 29U prestressed grout rock bolts L = 4.0 m @ 2.0 m L = 4.0 m locally 19-two segments Longitudinal @2.0 m 17-two segments L = 6.0 m 10-two segments Longitudinal @2.0 m Shotcrete 5 cm cover T: 10cm T: 15cm B: 5cm B: 15cm Wire mesh T: 1 5 mm U (100 100) T, B: 1 5 mm U (100 100) Light steel sets T: if required to install 100 100 H-shape steel Class number IV V VI Excavated procedure Cycle length 1.5 m 2.0 m 1.0 m 1.5 m 0.8 m 1.2 m Rock bolts 29U prestressed grout rock bolts L = 6.0 m @ 1.8 m 29U prestressed grout rock bolts L = 6.0 m @ 1.8 m 29U prestressed grout rock bolts L = 6.0 m @ 1.5 m 29-two segments Longitudinal @2.0 m 17-two segments L = 9.0 m 12-two segments Longitudinal @1.0 m 21-two segments L = 9.0 m 16-two segments Longitudinal @0.8 m Shotcrete T: 15cm T: 20cm T: 25cm B: 15cm B: 20cm B: 20cm I: 20cm Wire mesh T, B: l 5 mmu (100 100) T, B: 2 5 mmu (100 100) T, B: 2 5 mmu (100 100) I: l 5 mm (100 100) Light steel sets T:100 100 H-shape steel @ 1.5 m 2.0 m T: 125 1 25 H-shape steel @ 1.0 m 1.5 m T: 150 150 H-shape steel @ 0.8 m 1.2 m Cutting face support T: locally shotcrete T: fully 5 cm shotcrete or fully 10 cm wire net added B: if required to install Locally 5 cm shotcrete Invert Decided to set after measurement Yes Yes Pipe support Local Local Local 11/4 00 2 00 U pipe 11/4 00 2 00 U pipe 11/4 00 2 00 U pipe L = 3.0 m L = 3.0 m L = 2.0 m Deadline for support setting Immediately after arch excavation bench before second round Immediately after excavation close invert during 20 days Immediately after excavation close invert during 20 days Note: (1) T: crown, B: bench, I: invert. (2) The invert of Class V to added shotcrete (thickness 20 cm) depends on rock material and measurement results.

386 C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 percentage (%) Class number Fig. 10. The distribution of rock mass class for the Mu-Zha tunnel. percentage (%) Class number Fig. 11. The distribution of rock mass class for the Hsin-Tien I IV tunnel. shaft excavation method of these two tunnels is separately in Figs. 7 and 8. 3.2. Results and discussion Based on the above discussion, we can compute the rock mass ratings combining case records and algorithm introduced in this paper. RMR and our approach data including ratings for each parameter were carefully selected from the site investigation reports for two different tunnel projects conducted in Taiwan. Information was recorded regarding the rating parameters for each tunnel site, from which ratings numbers were assigned and total ratings calculated. For the rock mass quality evaluation of two tunnel sites, parts of the results comparison carried from RMR and our approach are shown in Tables 3a and 3b and the interval ratings to account for evaluating parameters in this study are shown in Table 4. Because of the limitation of publication space, the entire comparison results cannot be shown in the paper. So that parts of these values are not integrals. The descriptive statistics result is presented in Table 5. Distributions of the rock mass rating which are calculated by RMR and this study from two sites are shown partly in Fig. 9. These results indicate that there is a small amount of distinction between them. The tunnels in this study were excavated by NATM (Rabcewicz, 1964). Support design for the drill and blast section is through use of empirical calculation. The rock mass is divided into six types referred to Table 6, following the geotechnical parameters taken into consideration by RMR and Q-System and this study proposed. Consequently, six types of corresponding tunnel supports are selected, as shown in Table 7 (Ministry of Transportation and Communications Taiwan Area National Expressway Engineering Bureau, 1999). The rock mass class distributions of Hsin-Tien and Mu-Zha tunnels were presented in Figs. 10 and 11. These indicate that the Mu-Zha tunnel gives a strongly peaked distribution with the values clustered tightly at a peak of 42.1% class IV and a small standard deviation. The classes range across four class including class III, IV, V and VI of the six possible classes. In contrast, the Hsin-Tien tunnel shows a greater variation, with a higher average distribution between class III, IV, V and VI. In this case, the classes vary across five of the six

C.-S. Chen, Y.-C. Liu / Tunnelling and Underground Space Technology 22 (2007) 377 387 387 categories. The geological condition is generally weak. Preliminary we performed evaluations of rock mass rating for tunnel sites by our approach and obtain agreed approximately with those expected. 4. Conclusions From the procedure described above, we conclude that the proposed method can be successfully applied to determine the ratings of rock mass quality for the cases of tunnel engineering. It was found that the determined results were in good agreement with the original data assessed by the RMR. Results of the analyses show that it can be provided a more quantitative measure of rock mass and hence minimize judgmental bias. The rock mass quality evaluation model in this paper can be applied to adjust the best feasible factors weighting for the field condition and project purpose. The proposed method should be more feasible for future tunnel construction and suggestions of tunnel support design in Taiwan. Acknowledgement This study is supported by a grant from Taiwan National Science Council through contract number NSC93-2211-E-006-002. References Barton, N., Lien, R., Lunde, J., 1974. Engineering classification of rock masses for the design of tunnel support. Rock Mechanics 6 (4), 189 236. Bieniawski, Z.T., 1973. Engineering classification of jointed rock masses. Transactions of South African Institution of Civil Engineers 15 (12), 335 344. Bieniawski, Z.T., 1975. Case studies: Prediction of rock mass behavior by the geomechanics classification. In: Proceedings of 2nd Australia New Zealand Conference Geomechanics, Brisbane. pp. 36 41. Bieniawski, Z.T., 1979. The geomechanics classification. In: Rock Engineering Application. In: Proceedings Fourth Congress of the International Society For Rock Mechanics, vol. 2. pp. 41 48. Bieniawski, Z.T., 1989. Engineering Rock Mass Classifications. Wiley, New York, pp. 251. Kaufmann, A., Gupta, M.M., 1988. Fuzzy Mathematical Models in Engineering and Management Science. North-Holland, Amsterdam. Ministry of Transportation and Communications Taiwan Area National Expressway Engineering Bureau, 1999 Introduction of the tunnel engineering along the Second Northern Highway, Taiwan (in Chinese). Rabcewicz, L.V., 1964. The New Austrian Tunneling Method, Water Power, vol.16, No. 11 12, vol.17, No. 1, London. Saaty, T.L., 1980. The Analytic Hierarchy Process. McGraw-Hill International Book Company, New York. Wickham, G.E., Tiedemann, H.R., Skinner, E.H., 1972. Support Determination Based On Geologic Predictions. In: Proceedings of Conference Rapid Excavation and Tunneling. pp. 43 64.