3.2 Tunnel methods and support

Rock Mechanics in Civil and Environmental Engineering – Zhao, Labiouse, Dudt & Mathier (eds) © 2010 Taylor & Francis Group, London, ISBN 978-0-415-58654-2

Performance prediction of hard rock TBM using rock mass classification K. Shahriar Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran

J. Sargheini & M. Hedayatzadeh Mining Engineering Group, Islamic Azad University, Tehran South Branch, Tehran, Iran

J. Khademi Hamidi Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran

ABSTRACT: The influence of rock mass properties on TBM performance was studied and a new empirical equation for predicting TBM performance in Alborz Service Tunnel developed by using multiple linear regression analysis in this study. Fabric indices of four rock mass classification systems along with uniaxial compressive strength of rock material normalized by cutter load and the angle between tunnel axis and joints were included in the model. Comparison of measured ROPs with those predicted by the multi-linear regression model showed good agreement with correlation coefficient of 0.89.

1

INTRODUCTION

Since the first hard rock TBM was successfully used in1950s, the performance analysis of machine and the development of accurate prediction models have been the ultimate goals of many researchers. Even though intact rock parameters, mainly uniaxial compressive and tensile strength, and/or predictive indices such as fracture toughness, Schmidt hammer, Shore hardness, Punch penetration and DRI tests have been widely used as input parameters for predicting TBM performance (Graham 1976, Farmer & Glossop 1980, Blinheim 1979, Bamfrod 1984, Dollinger et al. 1998), a variety of theoretical models (Roxborough & Phillips 1975, Ozdemir et al. 1978, Snowdon et al. 1982, Sanio 1985, Rostami & Ozdemir 1993) and empirical models (Bruland 1998, Nelson et al. 1999, Gong & Zhao 2008, Yagiz 2008, Hassanpour et al. 2009) has been also used for performance prediction. Besides, many researchers have made attempts to correlate TBM performance to rock mass classifications due to their simplicity and easy measurement (Cassinelli et al. 1982, Innaurato et al. 1991, Palmström 1995, Barton 2000, Sapigni et al. 2002, Ribacchi & Lembo-Fazio 2005, Bieniawski et al. 2006, Khademi Hamidi et al. 2010). In this study, a new empirical model of TBM performance is developed based on fabric index of four common rock mass classifications.

Figure 1. Alborz service tunnel between two maine tunnels.

the capital city of Tehran to the Caspian Sea in the North. The service tunnel with diameter of 5.20 m was excavated by an open gripper TBM in advance of two main tunnel tubes to be excavated subsequently. The purpose of the service tunnel is site investigation, drainage of the rock mass, providing access for main tunnel excavations and for service, ventilation and drainage during operation of the complete tunnel system (Fig. 1). Site investigation for the service tunnel included a geological surface mapping, a geophysical investigation along the alignment from the surface and some index laboratory tests on rock samples. No boreholes have been drilled. Eight engineering geological units recognized in the tunnel route including: Argillite 34%, Sandston 24%, Limestone 11%, Andesite 10%, Green tuff 9%, Crushed zone 5%, Gypsum 5% and Schist 2%.

PROJECT DISCRIPTION AND GEOLOGY

3 TBM PERFORMANCE PREDICTION MODEL BASED ON ROCK MASS FABRIC INDEX

Alborz service tunnel is the longest tunnel (6.4 km) along Tehran-Shomal Freeway, situated in the high elevation portions ofAlborz Mountain Range, connecting

Estimation of TBM Rate of Penetration (ROP) must include the affective parameters including: rock material and rock mass parameters, machine characteristics

2

397

and operational parameters as well as in-situ boundary conditions. However, developing a predictive model which can take into account all these parameters all together has been always a hard nut to crack. This is why over three decades after its conception, no single universal model has been proposed for TBM performance prediction. Over the years, many rock mass classification systems have been introduced in mining and civil engineering. These models are often used in many empirical design practices in rock engineering contrasting with their original intent and applications. A good example is the use of available rock mass classification systems, which were primarily developed for design of ground support systems, in estimation of TBM performance in various tunneling projects. This is due to the simplicity and worldwide acceptance of the classification systems in general engineering practices, and in particular in underground mining and construction. The results of many investigations in this issue showed a weak correlation exists between TBM penetration rate and rock mass classifications. As was stated by Zhao 2007, this is because of this that the parameters in rock mass classifications were related to support design; they were not selected to describe rock mass boreability. In addition, these rock mass classifications are independent of TBM characteristics. This limitation may be overcome by tuning up the rock mass classifications through adjusting the predefined ratings assigned to the input parameters. 3.1

Table 1. F index of four rock mass classifications (Tzamos & Sofianos 2006). FQ = (RQD/Jn · Jr /Ja ) FRMR = R2 + R3 + R4 FGSI = GSI FRMi = JP

BS = (RQD/Jn ), JC = (Jr /Ja ) BS = (R2 + R3 ), JC = R4 BS = SR, JC = SCR BS = (Vb ), JC = (jC)

(2) (3) (4) (5)

Jn , Jr and Ja = input parameters of Q system; SR, SCR = structural rating and surface condition rating of GSI; Vb , jC = block volume and joint coefficient factor in RMi. Table 2.

Descriptive statistics of generated database.

Variables

N

Min.

Max.

Mean

Variance

FQ Ff (MPa/tonf) Falpha (degree) ROP (m/h)

34 34 34 34

0.08 1.98 8.00 2.85

23.90 5.80 83.0 5.30

8.26 4.49 39.41 3.93

28.79 0.982 381.93 0.535

The relation between FRMR and FGSI with FQ is as the followings:

In this study, fabric index of Q system was measured in the field and then transformed into fabric indices of other systems.

Rock mass fabric index (F index)

Tzamos & Sofianos (2006) correlate four rock mass classifications including RMR, Q, GSI and RMi by introducing rock mass fabric (denoted as F index). The common parameters of these systems, which concern and characterize solely the rock mass (excluding boundary conditions such as stress regime and water pressure), are those used for rating the rock structure and the joint surface conditions. Rock structure is quantified by the block size or the discontinuity spacing ratings (BS) and the joint surface conditions are quantified by the joint conditions ratings (JC). For instance, in the RMR system, the parameters concerning rock structure are the RQD and the spacing of discontinuities, denoted as parameters R2 and R3 . Their sum, R2 + R3 , defines the BS component. The JC component, which represents condition of discontinuities, is defined by the parameter denoted as R4 . The sum

defines the rock mass fabric index of the RMR system (FRMR ). The fabric indices of the other systems (FQ , FGSI and FRMi ) are given in Table 1. All the four indices were correlated through chart and equations developed by using a database gathered from several projects (Tzamos & Sofianos 2006).

3.2 Developed TBM performance prediction model Dataset for performance analysis consists of 34 records from 34 tunnel sections along the 6.4 km bored Alborz service tunnel containing input parameters of the fabric index of Q classification system, uniaxial compressive strength of rock material (UCS), the angle between tunnel axis and the joint sets (alpha), the TBM thrust and the measured TBM rate of penetration (ROP). In this study, the UCS normalized by cutter load (Ff ) is used in the model. Descriptive statistical distribution of variables in the database and input parameters for developed model is summarized in Table 2. Influence of each variable in obtained model has been investigated by performing multiple linear regression analysis. Figures 2–4 illustrate the correlations between the individual independent variables and the actual measured ROP. The Figures also, include the coefficients of correlation (R2 ) which is an indicator of correlation strength. In given condition, the Ff shows the highest R2 value, 0.74. The R2 value decreases in the order of the FQ (0.71) and Falpha (0.46). Accordingly, the uniaxial compressive strength of rock material normalized by cutter load and FQ are the most significant variables, the angle α shows the least correlations with ROP. As shown in the Figure 2, with increase in FQ , the ROP decreases. With increase of FQ the ratio RQD/Jn

398

Uniaxial compressive strength of intact rock (UCS) has a crucial influence on penetration rate in such a way that penetration rate will decrease with increased UCS. The effect of TBM thrust on ROP has been also studied by many researchers. In this study, UCS is normalized by cutter load and used in the model. The normalized UCS is expected to show more logical result due to elimination of the effect of machine thrust in the model. As illustrated in Figure 3, with increase in (UCS/F) the penetration rate will decrease. The α angle, representing orientation of discontinuities and the axis of the tunnel, have been measured in the field by measuring strike and dip of the joints mapped at the face. The α in degrees, can be calculated using the following equation (suggested by Bruland (1998)): Figure 2. Relation between measured ROP and FQ .

where, αf and αs are dip and strike of encountered planes of discontinuities in rock mass, and αt is the direction of the tunnel axis in degrees. The relationship between ROP and the α angle illustrated in Figure 4, is almost consistent with that of the results of field and numerical studies by Bruland (1998), Yagiz (2008) and Gong et al. (2005). In order to develop a linear equation, all the parameters for setting up the model including dependent and independent variables should have a rather normal distribution. It is necessary to check for any type of multicollinearity in the regression model. Multicollinearity occurs in regression models when two or more independent variables are highly correlated. The variance inflation factor (VIF) analysis performed on independent variables shows that there is no intercorrelation between independent parameters. Hence, the three independent variables of FQ , Ff , and Fα with good correlation coefficient with ROP are used in the predictive model. In this section three multi-linear regression models by using the software packages for standard statistical analysis (SPSS) are proposed. Correlation coefficient of three proposed models are (0.67), (0.87) and (0.895) for model 1 to 3, respectively. All these models have a significance less than 0.05 which is an indicator of model validation in viewpoint of statistics. Hence, the third model because of its highest correlation coefficient is selected as the main model. The new multiple linear regression model was empirically obtained is as follows:

Figure 3. Relation between measured ROP and Ff .

Figure 4. Relation between measured ROP and Fα .

increases. This means that the number of joint set is decreased, which led to more difficult boring process and decrease in penetration rate. Similarly, the increase of FQ will cause the increase of ratio (Jr/Ja) which led to more stiff joint condition and less boreability.

where, FQ = (RQD/Jn *Jr /Ja ) is fabric index of Q classification system, Ff = (UCS/load per cutter) and Fα = logα. A comparison between the measured and estimated ROP of the model is illustrated in Figure 5. As seen in the figure, the predicted data are in good agreement with the measured ones in database with a good correlation coefficient of 89%. Through equations 6 and 7 and related charts proposed by Tzamos and Sofianos 2006, the fabric indices

399

Figure 5. Comparison between measured and predicted ROP.

of four rock mass classifications can be interchanged. Hence, a general model may be derived from proposed model in which the four fabric indices are used. 4

CONCLUSIONS

By using a multiple regression analysis on field data collected from 6.4 km of TBM driven Alborz service tunnel, a predictive model for rate of penetration was proposed by use of fabric index of rock mass. The analysis of relationship between TBM ROP and the three independent variables of FQ , normalized UCS by cutter load and the angle joints with tunnel axis (alpha) showed that these parameters had meaningful correlations with the ROP. A multi-variable linear regression showed a correlation between the measured ROP and three input parameters with correlation coefficient of 0.89. The statistical significance and validity of the obtained models showed that the obtained relationship is reliable for the given database of TBM field performance. Additional studies are underway to combine the obtained results with additional data from other tunnelling operations to extend the model to other machine and ground types. REFERENCES Bamford, W.F. 1984. Rock test indices are being successfully correlated with tunnel boring machine performance. Proc. 5th Australian Tunneling Conference, Vol. 2, 9–22. Barton, N. 2000. TBM tunnelling in jointed and faulted rock. Rotterdam: Balkema, Brookfield, p. 173. Bieniawski, Z.T., Tamames, B.C., Fernandez, J.M.G., Hernandez, M.A. 2006. Rock Mass Excavability (RME) Indicator: new way to selecting the optimum tunnel construction method, ITA-AITES World Tunnel Congress & 32nd ITA General Assembly, Seoul. Blindheim, O.T. 1979. Boreability predictions for tunneling. PhD Thesis, The Norwegian Institute of Technology, p. 406. Bruland, A. 1998. Hard rock tunnel boring. PhD Thesis, Norwegian University of Science and Technology, Trondheim.

Cassinelli, F., Cina, S., Innaurato, N., Mancini, R., Sampaolo, A. 1982. Power consumption and metal wear in tunnel-boring machines: analysis of tunnel-boring operation in hard rock. Tunnelling ’82, Inst. Min. Metall., 73–81. Dollinger, G.L., Handewith, J.H., Breeds, C.D. 1998. Use of punch tests for estimating TBM performance. Tunnell. Undergr. Space Technol. 13(4), 403–408. Farmer, I.W., Glossop, N.H. 1980. Mechanics of disc cutter penetration. Tunnels Tunnel. Int., 12(6), 22–25. Gong, Q.M. & Zhao, J. 2009. Development of a rock mass characteristics model for TBM penetration rate prediction. Int. J. Rock Mech. Min. Sci. 46(1), 8–18. Gong, Q.M., Zhao, J., Jiao, Y.Y. 2005. Numerical modeling of the effects of joint orientation on rock fragmentation by TBM cutters. Tunnell. Undergr. Space Technol. 20, 183–91. Graham, P.C. 1976. Rock exploration for machine manufacturers. In: Bieniawski, Z.T., (Ed.), Exploration for rock engineering. Johannesburg, Balkema, 173–80. Hassanpour, J., Rostami, J., Khamehchiyan, M., Bruland, A., Tavakoli, H.R. 2009. TBM performance analysis in pyroclastic rocks: A case history of Karaj water conveyance tunnel. Rock Mech Rock Eng, doi: 10.1007/s00603-0090060-2. Innaurato, N., Mancini, R., Rondena, E., Zaninetti, A. 1991. Forecasting and effective TBM performances in a rapid excavation of a tunnel in Italy. Proc. 7th Int. Congress ISRM, Aachen, 1009–14. Ozdemir, L., Miller, R., Wang, F.D. 1978. Mechanical Tunnel Boring Prediction and Machine Design. Final Project Report to NSF APR73-07776-A03, Colorado School of Mines. Palmström, A. 1995. RMi-a rock mass characterization system for rock engineering purposes. PhD Thesis, University of Oslo, p. 400. Ribacchi, R. & Lembo-Fazio,A. 2005. Influence of rock mass parameters on the performance of a TBM in a gneissic formation (Varzo Tunnel). Rock Mech Rock Eng 38, 105–27. Rostami, J. & Ozdemir, L. 1993. A new model for performance prediction of hard rock TBM. Proc. Rapid Excavation and Tunnelling Conference, 793–809. Roxborough, F.F. & Phillips, H.R. 1975. Rock excavation by disc cutter. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 12, 361–66. Sanio, H.P. 1985. Prediction of the performance of disc cutters in anisotropic rock. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 22, 153–61. Sapigni, M., Berti, M., Behtaz, E., Busillo, A., Cardone, G. 2002. TBM performance estimation using rock mass classification. Int. J. Rock Mech. Min. Sci. 39, 771–88. Snowdon, R.A., Ryley, M.D., Temporal, J. 1982. A study of disc cutting in selected British rocks. Int. J. Rock Mech. Min. Sci. 19, 107–21. Tzamos, S. & Sofianos, A.I. 2006. A correlation of four rock mass classification systems through their fabric indices. Int. J. Rock Mech. Min. Sci., 477–95. Yagiz, S. 2008. Utilizing rock mass properties for predicting TBM performance in hard rock condition. Tunnell. Undergr. Space Technol. 23(3), 326–39. Zhao, J. 2007. Tunnelling in rocks- present technology and future challenges. Keynote lectures. ITA-AITES World Tunnel Congress & 33rd ITA General Assembly, Prague, 22–32. Khademi Hamidi, J., Shahriar, K., Rezai, B., Rostami, J. 2010. Performance prediction of hard rock TBM using Rock Mass Rating (RMR) system. Tunnell. Undergr. Space Technol. doi:10.1016/j.tust.2010.01.008.

400

Rock Mechanics in Civil and Environmental Engineering – Zhao, Labiouse, Dudt & Mathier (eds) © 2010 Taylor & Francis Group, London, ISBN 978-0-415-58654-2

Performance prediction of hard rock TBM using rock mass classification K. Shahriar Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran

J. Sargheini & M. Hedayatzadeh Mining Engineering Group, Islamic Azad University, Tehran South Branch, Tehran, Iran

J. Khademi Hamidi Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran

ABSTRACT: The influence of rock mass properties on TBM performance was studied and a new empirical equation for predicting TBM performance in Alborz Service Tunnel developed by using multiple linear regression analysis in this study. Fabric indices of four rock mass classification systems along with uniaxial compressive strength of rock material normalized by cutter load and the angle between tunnel axis and joints were included in the model. Comparison of measured ROPs with those predicted by the multi-linear regression model showed good agreement with correlation coefficient of 0.89.

1

INTRODUCTION

Since the first hard rock TBM was successfully used in1950s, the performance analysis of machine and the development of accurate prediction models have been the ultimate goals of many researchers. Even though intact rock parameters, mainly uniaxial compressive and tensile strength, and/or predictive indices such as fracture toughness, Schmidt hammer, Shore hardness, Punch penetration and DRI tests have been widely used as input parameters for predicting TBM performance (Graham 1976, Farmer & Glossop 1980, Blinheim 1979, Bamfrod 1984, Dollinger et al. 1998), a variety of theoretical models (Roxborough & Phillips 1975, Ozdemir et al. 1978, Snowdon et al. 1982, Sanio 1985, Rostami & Ozdemir 1993) and empirical models (Bruland 1998, Nelson et al. 1999, Gong & Zhao 2008, Yagiz 2008, Hassanpour et al. 2009) has been also used for performance prediction. Besides, many researchers have made attempts to correlate TBM performance to rock mass classifications due to their simplicity and easy measurement (Cassinelli et al. 1982, Innaurato et al. 1991, Palmström 1995, Barton 2000, Sapigni et al. 2002, Ribacchi & Lembo-Fazio 2005, Bieniawski et al. 2006, Khademi Hamidi et al. 2010). In this study, a new empirical model of TBM performance is developed based on fabric index of four common rock mass classifications.

Figure 1. Alborz service tunnel between two maine tunnels.

the capital city of Tehran to the Caspian Sea in the North. The service tunnel with diameter of 5.20 m was excavated by an open gripper TBM in advance of two main tunnel tubes to be excavated subsequently. The purpose of the service tunnel is site investigation, drainage of the rock mass, providing access for main tunnel excavations and for service, ventilation and drainage during operation of the complete tunnel system (Fig. 1). Site investigation for the service tunnel included a geological surface mapping, a geophysical investigation along the alignment from the surface and some index laboratory tests on rock samples. No boreholes have been drilled. Eight engineering geological units recognized in the tunnel route including: Argillite 34%, Sandston 24%, Limestone 11%, Andesite 10%, Green tuff 9%, Crushed zone 5%, Gypsum 5% and Schist 2%.

PROJECT DISCRIPTION AND GEOLOGY

3 TBM PERFORMANCE PREDICTION MODEL BASED ON ROCK MASS FABRIC INDEX

Alborz service tunnel is the longest tunnel (6.4 km) along Tehran-Shomal Freeway, situated in the high elevation portions ofAlborz Mountain Range, connecting

Estimation of TBM Rate of Penetration (ROP) must include the affective parameters including: rock material and rock mass parameters, machine characteristics

2

397

and operational parameters as well as in-situ boundary conditions. However, developing a predictive model which can take into account all these parameters all together has been always a hard nut to crack. This is why over three decades after its conception, no single universal model has been proposed for TBM performance prediction. Over the years, many rock mass classification systems have been introduced in mining and civil engineering. These models are often used in many empirical design practices in rock engineering contrasting with their original intent and applications. A good example is the use of available rock mass classification systems, which were primarily developed for design of ground support systems, in estimation of TBM performance in various tunneling projects. This is due to the simplicity and worldwide acceptance of the classification systems in general engineering practices, and in particular in underground mining and construction. The results of many investigations in this issue showed a weak correlation exists between TBM penetration rate and rock mass classifications. As was stated by Zhao 2007, this is because of this that the parameters in rock mass classifications were related to support design; they were not selected to describe rock mass boreability. In addition, these rock mass classifications are independent of TBM characteristics. This limitation may be overcome by tuning up the rock mass classifications through adjusting the predefined ratings assigned to the input parameters. 3.1

Table 1. F index of four rock mass classifications (Tzamos & Sofianos 2006). FQ = (RQD/Jn · Jr /Ja ) FRMR = R2 + R3 + R4 FGSI = GSI FRMi = JP

BS = (RQD/Jn ), JC = (Jr /Ja ) BS = (R2 + R3 ), JC = R4 BS = SR, JC = SCR BS = (Vb ), JC = (jC)

(2) (3) (4) (5)

Jn , Jr and Ja = input parameters of Q system; SR, SCR = structural rating and surface condition rating of GSI; Vb , jC = block volume and joint coefficient factor in RMi. Table 2.

Descriptive statistics of generated database.

Variables

N

Min.

Max.

Mean

Variance

FQ Ff (MPa/tonf) Falpha (degree) ROP (m/h)

34 34 34 34

0.08 1.98 8.00 2.85

23.90 5.80 83.0 5.30

8.26 4.49 39.41 3.93

28.79 0.982 381.93 0.535

The relation between FRMR and FGSI with FQ is as the followings:

In this study, fabric index of Q system was measured in the field and then transformed into fabric indices of other systems.

Rock mass fabric index (F index)

Tzamos & Sofianos (2006) correlate four rock mass classifications including RMR, Q, GSI and RMi by introducing rock mass fabric (denoted as F index). The common parameters of these systems, which concern and characterize solely the rock mass (excluding boundary conditions such as stress regime and water pressure), are those used for rating the rock structure and the joint surface conditions. Rock structure is quantified by the block size or the discontinuity spacing ratings (BS) and the joint surface conditions are quantified by the joint conditions ratings (JC). For instance, in the RMR system, the parameters concerning rock structure are the RQD and the spacing of discontinuities, denoted as parameters R2 and R3 . Their sum, R2 + R3 , defines the BS component. The JC component, which represents condition of discontinuities, is defined by the parameter denoted as R4 . The sum

defines the rock mass fabric index of the RMR system (FRMR ). The fabric indices of the other systems (FQ , FGSI and FRMi ) are given in Table 1. All the four indices were correlated through chart and equations developed by using a database gathered from several projects (Tzamos & Sofianos 2006).

3.2 Developed TBM performance prediction model Dataset for performance analysis consists of 34 records from 34 tunnel sections along the 6.4 km bored Alborz service tunnel containing input parameters of the fabric index of Q classification system, uniaxial compressive strength of rock material (UCS), the angle between tunnel axis and the joint sets (alpha), the TBM thrust and the measured TBM rate of penetration (ROP). In this study, the UCS normalized by cutter load (Ff ) is used in the model. Descriptive statistical distribution of variables in the database and input parameters for developed model is summarized in Table 2. Influence of each variable in obtained model has been investigated by performing multiple linear regression analysis. Figures 2–4 illustrate the correlations between the individual independent variables and the actual measured ROP. The Figures also, include the coefficients of correlation (R2 ) which is an indicator of correlation strength. In given condition, the Ff shows the highest R2 value, 0.74. The R2 value decreases in the order of the FQ (0.71) and Falpha (0.46). Accordingly, the uniaxial compressive strength of rock material normalized by cutter load and FQ are the most significant variables, the angle α shows the least correlations with ROP. As shown in the Figure 2, with increase in FQ , the ROP decreases. With increase of FQ the ratio RQD/Jn

398

Uniaxial compressive strength of intact rock (UCS) has a crucial influence on penetration rate in such a way that penetration rate will decrease with increased UCS. The effect of TBM thrust on ROP has been also studied by many researchers. In this study, UCS is normalized by cutter load and used in the model. The normalized UCS is expected to show more logical result due to elimination of the effect of machine thrust in the model. As illustrated in Figure 3, with increase in (UCS/F) the penetration rate will decrease. The α angle, representing orientation of discontinuities and the axis of the tunnel, have been measured in the field by measuring strike and dip of the joints mapped at the face. The α in degrees, can be calculated using the following equation (suggested by Bruland (1998)): Figure 2. Relation between measured ROP and FQ .

where, αf and αs are dip and strike of encountered planes of discontinuities in rock mass, and αt is the direction of the tunnel axis in degrees. The relationship between ROP and the α angle illustrated in Figure 4, is almost consistent with that of the results of field and numerical studies by Bruland (1998), Yagiz (2008) and Gong et al. (2005). In order to develop a linear equation, all the parameters for setting up the model including dependent and independent variables should have a rather normal distribution. It is necessary to check for any type of multicollinearity in the regression model. Multicollinearity occurs in regression models when two or more independent variables are highly correlated. The variance inflation factor (VIF) analysis performed on independent variables shows that there is no intercorrelation between independent parameters. Hence, the three independent variables of FQ , Ff , and Fα with good correlation coefficient with ROP are used in the predictive model. In this section three multi-linear regression models by using the software packages for standard statistical analysis (SPSS) are proposed. Correlation coefficient of three proposed models are (0.67), (0.87) and (0.895) for model 1 to 3, respectively. All these models have a significance less than 0.05 which is an indicator of model validation in viewpoint of statistics. Hence, the third model because of its highest correlation coefficient is selected as the main model. The new multiple linear regression model was empirically obtained is as follows:

Figure 3. Relation between measured ROP and Ff .

Figure 4. Relation between measured ROP and Fα .

increases. This means that the number of joint set is decreased, which led to more difficult boring process and decrease in penetration rate. Similarly, the increase of FQ will cause the increase of ratio (Jr/Ja) which led to more stiff joint condition and less boreability.

where, FQ = (RQD/Jn *Jr /Ja ) is fabric index of Q classification system, Ff = (UCS/load per cutter) and Fα = logα. A comparison between the measured and estimated ROP of the model is illustrated in Figure 5. As seen in the figure, the predicted data are in good agreement with the measured ones in database with a good correlation coefficient of 89%. Through equations 6 and 7 and related charts proposed by Tzamos and Sofianos 2006, the fabric indices

399

Figure 5. Comparison between measured and predicted ROP.

of four rock mass classifications can be interchanged. Hence, a general model may be derived from proposed model in which the four fabric indices are used. 4

CONCLUSIONS

By using a multiple regression analysis on field data collected from 6.4 km of TBM driven Alborz service tunnel, a predictive model for rate of penetration was proposed by use of fabric index of rock mass. The analysis of relationship between TBM ROP and the three independent variables of FQ , normalized UCS by cutter load and the angle joints with tunnel axis (alpha) showed that these parameters had meaningful correlations with the ROP. A multi-variable linear regression showed a correlation between the measured ROP and three input parameters with correlation coefficient of 0.89. The statistical significance and validity of the obtained models showed that the obtained relationship is reliable for the given database of TBM field performance. Additional studies are underway to combine the obtained results with additional data from other tunnelling operations to extend the model to other machine and ground types. REFERENCES Bamford, W.F. 1984. Rock test indices are being successfully correlated with tunnel boring machine performance. Proc. 5th Australian Tunneling Conference, Vol. 2, 9–22. Barton, N. 2000. TBM tunnelling in jointed and faulted rock. Rotterdam: Balkema, Brookfield, p. 173. Bieniawski, Z.T., Tamames, B.C., Fernandez, J.M.G., Hernandez, M.A. 2006. Rock Mass Excavability (RME) Indicator: new way to selecting the optimum tunnel construction method, ITA-AITES World Tunnel Congress & 32nd ITA General Assembly, Seoul. Blindheim, O.T. 1979. Boreability predictions for tunneling. PhD Thesis, The Norwegian Institute of Technology, p. 406. Bruland, A. 1998. Hard rock tunnel boring. PhD Thesis, Norwegian University of Science and Technology, Trondheim.

Cassinelli, F., Cina, S., Innaurato, N., Mancini, R., Sampaolo, A. 1982. Power consumption and metal wear in tunnel-boring machines: analysis of tunnel-boring operation in hard rock. Tunnelling ’82, Inst. Min. Metall., 73–81. Dollinger, G.L., Handewith, J.H., Breeds, C.D. 1998. Use of punch tests for estimating TBM performance. Tunnell. Undergr. Space Technol. 13(4), 403–408. Farmer, I.W., Glossop, N.H. 1980. Mechanics of disc cutter penetration. Tunnels Tunnel. Int., 12(6), 22–25. Gong, Q.M. & Zhao, J. 2009. Development of a rock mass characteristics model for TBM penetration rate prediction. Int. J. Rock Mech. Min. Sci. 46(1), 8–18. Gong, Q.M., Zhao, J., Jiao, Y.Y. 2005. Numerical modeling of the effects of joint orientation on rock fragmentation by TBM cutters. Tunnell. Undergr. Space Technol. 20, 183–91. Graham, P.C. 1976. Rock exploration for machine manufacturers. In: Bieniawski, Z.T., (Ed.), Exploration for rock engineering. Johannesburg, Balkema, 173–80. Hassanpour, J., Rostami, J., Khamehchiyan, M., Bruland, A., Tavakoli, H.R. 2009. TBM performance analysis in pyroclastic rocks: A case history of Karaj water conveyance tunnel. Rock Mech Rock Eng, doi: 10.1007/s00603-0090060-2. Innaurato, N., Mancini, R., Rondena, E., Zaninetti, A. 1991. Forecasting and effective TBM performances in a rapid excavation of a tunnel in Italy. Proc. 7th Int. Congress ISRM, Aachen, 1009–14. Ozdemir, L., Miller, R., Wang, F.D. 1978. Mechanical Tunnel Boring Prediction and Machine Design. Final Project Report to NSF APR73-07776-A03, Colorado School of Mines. Palmström, A. 1995. RMi-a rock mass characterization system for rock engineering purposes. PhD Thesis, University of Oslo, p. 400. Ribacchi, R. & Lembo-Fazio,A. 2005. Influence of rock mass parameters on the performance of a TBM in a gneissic formation (Varzo Tunnel). Rock Mech Rock Eng 38, 105–27. Rostami, J. & Ozdemir, L. 1993. A new model for performance prediction of hard rock TBM. Proc. Rapid Excavation and Tunnelling Conference, 793–809. Roxborough, F.F. & Phillips, H.R. 1975. Rock excavation by disc cutter. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 12, 361–66. Sanio, H.P. 1985. Prediction of the performance of disc cutters in anisotropic rock. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 22, 153–61. Sapigni, M., Berti, M., Behtaz, E., Busillo, A., Cardone, G. 2002. TBM performance estimation using rock mass classification. Int. J. Rock Mech. Min. Sci. 39, 771–88. Snowdon, R.A., Ryley, M.D., Temporal, J. 1982. A study of disc cutting in selected British rocks. Int. J. Rock Mech. Min. Sci. 19, 107–21. Tzamos, S. & Sofianos, A.I. 2006. A correlation of four rock mass classification systems through their fabric indices. Int. J. Rock Mech. Min. Sci., 477–95. Yagiz, S. 2008. Utilizing rock mass properties for predicting TBM performance in hard rock condition. Tunnell. Undergr. Space Technol. 23(3), 326–39. Zhao, J. 2007. Tunnelling in rocks- present technology and future challenges. Keynote lectures. ITA-AITES World Tunnel Congress & 33rd ITA General Assembly, Prague, 22–32. Khademi Hamidi, J., Shahriar, K., Rezai, B., Rostami, J. 2010. Performance prediction of hard rock TBM using Rock Mass Rating (RMR) system. Tunnell. Undergr. Space Technol. doi:10.1016/j.tust.2010.01.008.

400