Prediction of TBM penetration rate from brittleness indexes using multiple regression analysis

Modeling Earth Systems and Environment, Feb 2018

One of the most important aspects in the excavation of tunnels with a Tunnel Boring Machine (TBM) is the reliable prediction of its penetration rate. This affects the planning and other decision making on the organization of the construction site of the tunneling project, and, therefore, total costs. In this study, raw data obtained from the experimental works of different researchers were used to establish the new statistical models for prediction of rock TBM penetration rate from brittleness indexes, B1, B2, and B3. For this, correlation between the TBM penetration rate with brittleness indexes statistically was investigated using multiple regression analyses. In these analyses, the TBM penetration rate was considered to be the dependent variable, which is dependent on the independent variables of the brittleness indexes. The validity of the predictive models was validated by statistical tests. The results showed that statistical models are in good accuracy for prediction of TBM penetration rate, and thus making a rapid assessment of the TBM performance.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2Fs40808-018-0432-2.pdf

Prediction of TBM penetration rate from brittleness indexes using multiple regression analysis

Modeling Earth Systems and Environment Prediction of TBM penetration rate from brittleness indexes using multiple regression analysis A. Jamshidi 0 0 Department of Geology, Faculty of Basic Sciences, Lorestan University , Khorramabad , Islamic Republic of Iran One of the most important aspects in the excavation of tunnels with a Tunnel Boring Machine (TBM) is the reliable prediction of its penetration rate. This affects the planning and other decision making on the organization of the construction site of the tunneling project, and, therefore, total costs. In this study, raw data obtained from the experimental works of different researchers were used to establish the new statistical models for prediction of rock TBM penetration rate from brittleness indexes, B1, B2, and B3. For this, correlation between the TBM penetration rate with brittleness indexes statistically was investigated using multiple regression analyses. In these analyses, the TBM penetration rate was considered to be the dependent variable, which is dependent on the independent variables of the brittleness indexes. The validity of the predictive models was validated by statistical tests. The results showed that statistical models are in good accuracy for prediction of TBM penetration rate, and thus making a rapid assessment of the TBM performance. TBM; Penetration rate; Brittleness indexes; Statistical models Introduction Tunnel Boring Machine (TBM) performance can be measured in terms of the penetration rate. Three main parameters, machine design related parameters, geological conditions and geotechnical properties of rocks along the tunnel alignment affect the TBM penetration rate (Yagiz and Karahan 2015) . Although the parameters of drilling machine equipment can be controlled, change to the geological conditions and geotechnical properties of rocks cannot be. Penetration rate (PR) which is also referred to as Rate of penetration (ROP), and often expressed in m/h and refers to the linear footage of excavation per unit time, when machine engages the ground and is in production (Rostami 2016) . Having some prior knowledge of the TBM penetration rate in rock excavation projects is very helpful to plan construction time and to control cost. Penetration rate prediction is considered as a complex and difficult work because of the interaction between rock mass and TBM, but a meaningful task because it is significant for time planning, cost control and choosing the excavation method (Yagiz 2002). The development of various predictive models of the TBM penetration rate has been main objective and is still under progress for many years (Graham 1976; Hughes 1986; Rostami and Ozdemir 1993; Kahraman et al. 2003; Gong and Zhao 2009; Yagiz and Karahan 2011, 2015; Farrokh et al. 2012; Coffi Adoko et al. 2017) . Existing prediction approaches include theoretical and empirical models (Barton 2000; Sapigni et al. 2002) , simple and multiple regression analyses (Delisio and Zhao 2014; Farrokh et al. 2012; Khademi Hamidi et al. 2010) , artificial intelligence techniques such as artificial neural networks (Benardos and Kaliampakos 2004; Salimi et al. 2016; Shao et al. 2013) , fuzzy inference systems (Acaroglu et  al. 2008; Alvarez Grima et al. 2000; Yazdani-Chamzini et al. 2013) , support vector regression analysis (Mahdevari et al. 2014) , particle swarm optimization (Yagiz and Karahan 2011) and other advanced optimization algorithms (Yagiz and Karahan 2015) . In general, these models are established on the basis of experience gained and the data compiled from the past tunneling projects in order to derive the complex and non- linear relationship between the TBM penetration rate and the influencing rock mass parameters. Table 1 is a summary of advantages and disadvantages of these modelling concepts. Advantages Disadvantages The penetration rate may depend on various rock properties including strength, brittleness, distance between plane of weakness, orientation of discontinuities and also TBM specifications such as torque, thrust, RPM and disc diameter etc. So, the problem is highly complicated to be solved with simple regression approach (Yagiz and Karahan 2015) . On the basis of the geological conditions and geotechnical properties of rocks, there are two groups of statistical models for prediction of penetration rate. The first group of models is based on prediction of TBM performance by using a single intact rock parameter. For many researchers, uniaxial compressive and tensile strengths (UCS and BTS) are the most widely used properties for rock drillability (Graham 1976; Farmer and Glossop 1980; Hughes 1986; Karpuz et al. 1990; Akcin et al. 1994; Bilgin et al. 1996; Huang and Wang 1997; Kahraman 1999; Kahraman et al. 2003; Akun and Karpuz 2005; Tanaino 2005). Moreover, many different rock parameters, such as point load index, P-wave velocity, porosity, quartz content, Schmidt hammer number, Shore hardness, cone indenter number, drilling rate index (DRI), coefficient of rock strength (CRS), Cerchar abrasion index (CAI), rock brittleness, texture coefficient (TC), impact strength index (ISI), specific energy (SE), etc. can be used for prediction of TBM performance (McFeat-Smith and Fowel 1977; How arth 1987; Kovscek et al. 1988 ; Nilsen and Ozdemir 1993; Akcin et al. 1994; Kahraman 1999; Barton 2000; Kahraman et al. 2003). However, another group of predictive models attempt to correlate TBM performance to rock mass classifications. Among the most commonly used classification systems, Rock Mass Rating (RMR) and Rock Mass Quality Index (Q) have been used more frequently in TBM performance prediction. These models have been developed based on the historical field data of TBM performance in various ground conditions (Alber 1996; Bruland 1998; Barton 1999; Sapigni et al. 2002; Yagiz 2008; Gong and Zhao 2009; Khademi Hamidi et al. 2010; Benato and Oreste 2015; Yagiz and Karahan 2015; Salimi et al. 2016) . Although in most of the previous studies, different statistical models have been derived for prediction of TBM penetration rate for several decades, the models that are based on the rock brittleness have been limited. Altindag (2000, 2002) found significant correlations between his proposed new brittleness concept (B3) and the penetration rate of percussive drills. Kahraman (2002) statistically studied the relationships between TBM penetration rate and three different brittleness indexes using the raw data obtained from the experimental works of different researchers. It concluded that penetration rate does not exhibit a correlation with the brittleness of B1 and B2, but it is strongly correlated with the brittleness of B3. Influence of rock brittleness on TBM penetration rate in Singapore granite were investigated by Gong and Zhao (2007) . These researchers found that TBM penetration rate increases with increasing rock brittleness. Altindag (2010) assessed the relationships between penetration rate with rock brittleness indexes B1, B2 and B3. Results showed that the lower correlation coefficients were found between brittleness B1 and penetration rate, than brittleness B2 and B3. In this study, by analyzing the raw data sets obtained from the experimental works, multiple regression models are proposed for prediction of TBM penetration rate from brittleness indexes, B1, B2 and B3. Brittleness Brittleness is considered as one of the most important properties of rocks, which affect the TBM penetration rate of rocks. Nevertheless, there is no agreement between different authors whether as to definition, or as to measure brittleness. Different researchers mean, express and use it differently (Coates 1966; Hetenyi 1966; Ramsey 1967; Obert and Duvall 1967; Reichmuth 1967; Hucka and Das 1974; McFeat-Smith 1977; Singh 1986; Goktan 1991, 1992; Inyang and Pitt 1990; Inyang 1991; George 1995; Altindag 1997, 2000, 2002; Copur 1999; Kahraman 2002). Brittleness, in the Glossary of Geology and Related Sciences, is defined as a property of materials that rupture or fracture with little or no plastic flow (AGI 1960) . Morley (1944) and Hetenyi (1966) define brittleness as the lack of ductility. Ramsey (1967) defined brittleness as follows: ‘‘When the internal cohesion of rocks is broken, the rocks are said to be brittle’’. Obert and Duvall (1967) defined brittleness as follows: ‘‘materials such as cast iron and many rocks usually terminate by fracture at or only slightly beyond the yield stress’’. Hucka and Das (1974) stated that with higher brittleness the following facts can be observed: • Low values of elongation • Fracture failure • Formation of fines • Higher ratio of compressive to tensile strength • Higher resilience • Higher angle of internal friction • Formation of cracks in indentation George (1995) defined that rock brittleness is the ability of a rock material to deform continuously and perpetually without apparent permanent deformations along with the application of stress surpassing the necessary stresses for microcracking of the material. Direct standard testing method for determination of rock brittleness have not available yet. Therefore, rock brittleness is indirectly obtained as a function of rock strength. Uniaxial compressive and Brazilian tensile strengths are simply defined and easily obtained; they are often used in determining the brittleness (Altindag 2002; Kahraman 2002) . In this study, three most common approaches are used for measuring brittleness value. B1 = c∕ t B2 = ( c × t)∕2, MPa2 (3) B3 = √B2, MPa where, B1, B2 and B3 are brittleness indexes, σc is the uniaxial compressive strength (MPa) and σt is the Brazilian tensile strength (MPa). Brittleness indexes, B1, B2 and B3 are widely used in the literature such as Beron et al., (1983 ), Chiu and Johnston (1983) , Kim and Lade (1984) , Vardoulakis (1984) , Koulikov (1987) , Inyang and Pitt (1990) , Goktan (1991) , Inyang (1991), Kahraman (2002), and Atici and Ersoy (2009). Materials and methods Three separate data sets were compiled from the review of experimental works of different researchers. (Selim and Bruce 1970; Bilgin et al. 1993; Kahraman 1999) . Uniaxial compressive strength, Brazilian tensile strength and penetration rate data obtained from the different researchers, and calculated brittleness indexes values (B1, B2, and B3) by the author were listed in Tables 2, 3 and 4. The relationships between the TBM penetration rate values and brittleness indexes were investigated by simple and multiple regression models and most suitable regression model for estimating the penetration rate from the brittleness indexes were proposed. The methodology of the research is given in Fig. 1. The distribution of the three different rock classes for all studied rocks is given in Fig. 2. The rock classes that was included in this study are 22 sedimentary, 5 igneous and 1 metamorphic. Studied rocks are classified according to their UCS values as suggested in ISRM (2007) (Fig. 3). This Figure shows that rocks were classified as having a weak strength (5–25 MPa), low strength (25–50 MPa), medium strength (50–100 MPa), high strength (100–250 MPa) and very high strength (> 250 MPa). According to the classification of rocks based on the brit tleness of B1 by Aftes (2003) (Table 5), most of the rocks are classified as rocks with middle brittle (B1: 10–15), and the other rocks fall into the classes with low brittle (B1 < 10) and brittle (B1: 15–25). Results and discussion (1) (2) Traditionally, statistical methods such as simple and multiple regression techniques are used to found prediction models. In addition to these conventional methods, new techniques have garnered considerable attention. These techniques are based on genetic algorithm, support vector regression, and GA, hybrid ANN and imperialist competitive algorithm, and hybrid ANN and particle swarm optimization technique Three separate data sets were compiled from the review of experimental works of different researchers Uniaxial compressive strength (UCS) was compiled from data sets Brazilian tensile strength (BTS) was compiled from data sets TBM penetration rate (PR) was compiled from data sets Brittleness indexes (B1, B2, B3) calculation B1 B2 B3 Relationship between TBM penetration rate values and brittleness indexes (B1, B2, B3) by simple regression model Relationship between TBM penetration rate values and brittleness indexes (B1, B2, B3) by multiple regression model Results and discussion (Barzegar et al. 2016; Barzegar and Moghaddam 2016; Heddam 2016a, b; Keshavarzi et al. 2016) . Simple regression is the simplest form of regression analysis involving one independent variable and one dependent variable. In this regression, the dependent variable is approximated by an independent variable. Multiple regression analysis is an approach for modeling the relationship between a dependent variable and two or more independent variables. This technique is more amenable to ceteris paribus analysis because it allows researchers to explicitly control many other factors (independent variables) that simultaneously affect the dependent variable. In this study, simple and In this section, simple regression analysis is carried out to find relationships between TBM penetration rate and brittleness indexes of studied rocks. For this purpose, data given in Tables 1, 2 and 3 were analyzed using the least square regression method. The author this work attempted to develop the best correlation, linear (y = ax + b), power (y = axb), exponential (y = aex) or logarithmic (y = a + ln x), between penetration rate with brittleness indexes B1, B2 and B3 to attain the most reliable empirical model. The model of the best fit line, the 95% confidence limits and the determination coefficients (R2) were determined for each correlation. The results of simple regression analysis and the determination coefficients are summarized in Table 6 and graphically illustrated in Figs. 4, 5 and 6. It can be seen from this Table that low correlations were found between penetration rate with brittleness indexes for all data sets in this study (R2 ranging from 0.40 to 0.78). However, there are better correlations between penetration rate with B2 (R2 = 0.78) and B1 (R2 = 0.71) in data sets of Selim and Bruce (1970) and Bilgin et al., (1993), respectively. According to the statistical models derived from this study (Table 5), penetration rate decreases with increasing brittleness indexes B1, B2 and B3 for all data sets, except regression model between penetration rate and brittleness index B1 in Kahraman (1999) research. The derived statistical models in this study were com pared with those available in the literature. The results of this study are in accordance with the findings of Kahraman (2002) and Altindag (2010) . Kahraman (2002) obtained an exponential relationship with high correlation coefficient UCS25–50 MPa Low Strength UCS 5–25 MPa UCS 100–250 MPa UCS > 250 MPa Very weak Weak Medium High Very high between the penetration rate of rotary drills and the brittleness of B1. Altindag (2010) investigated the relationships between penetration rate with rock brittleness indexes B1, B2 and B3. Results of this researcher showed that penetration rate decreases with increasing brittleness indexes. However, there is a significant difference between the results of this study, Kahraman (2002) and Altindag (2010) with Gong and Zhao (2007) results. Gong and Zhao (2007) evaluated the effect of rock brittleness on TBM penetration rate in Singapore granite. Their results show that penetration rate increases with increasing brittleness index B1. Model based on multiple regression analysis Multiple regression analysis was performed to determine the relationships between penetration rate and brittleness indexes. In these analyses, the dependent variable is the penetration rate and the independent variables are brittleness indexes B1, B2 and B3. In this study, the general model for prediction of penetration rate is as follows: Equation code no. Regression model S1 S2 S3 S4 S5 S6 S7 S8 S9 Selim and Bruce (1970) Bilgin et al., (1993) Kahraman (1999) y = 115.63e-0.061x R² = 0.3965 y = -0.5727x + 230.42 R² = 0.6319 y = -9.975x + 257.18 R² = 0.5867 10 20 30 40 50 70 80 90 100 60 B3 (MPa) Fig. 4 Relationship between TBM penetration rate with a B1, b B2, c B3 (from Table 2) PR = 0 + 1B1 + 2B2 + 3B3 where PR is the predicted value of the TBM penetration rate, B1, B2 and B3 are the brittleness indexes, α0 is a constant, and α1, α2 and α3 are the regression coefficients of B1, B2 and B3, respectively. The data given in Tables 2, 3 and 4 were analyzed using SPSS®.v.21 statistical software. The results of these analyses are summarized in Table 6. Determination coefficient, standard error of estimate, F statistics test and the plots of actual values vs. predicted values were used for the evaluation of the produced models from the multiple regression analyses. The degree of fit to a curve can be measured by the value of the determination coefficient (R2), which measures the proportion of variation in the dependent variable, and the standard error of estimate (SEE), which is an important (4) 0 2 4 6 8 14 16 18 20 10 12 B3 (MPa) Fig. 5 Relationship between TBM penetration rate with a B1, b B2, c B3 (from Table 3) measure for indicating how close the actual data points fall to the predicted values on the regression curve. The R2 and SEE values for multiple regression models are given in Table 6. The R2 values of models M1, M2 and M3 given in Table 7 is higher than 0.81 that are at acceptable level. This shows that the proposed models fit the data well and are capable for prediction of penetration rate. The SEE value for models M1, M2 and M3 is 7.96, 34.99 and 3.47, respectively. These measures show that the models given in Table 7 can be accepted as a reliable predictor for the penetration rate. The variance analysis technique is used for testing significance of regression in multiple regressions. For this purpose, the F statistics test was performed for testing the global usefulness of the models. This test is widely used M1 M2 M3 y = 1.7854x + 0.8574 R² = 0.4747 8 10 12 14 16 18 20 B1 y = -3.626ln(x) + 38.976 R² = 0.4632 100 200 500 600 300 B2 (MPa2) 400 y = -7.251ln(x) + 38.976 R² = 0.4632 15 B3 (MPa) 5 10 20 25 Fig. 6 Relationship between TBM penetration rate with a B1, b B2, c B3 (from Table 4) in regression and analysis of variance. The computations for F statistics test are shown in Table 7. For all models, significance F–value within the 95% confidence interval is lower than 0.05. If the F–ratio is greater than the F-tabulated value obtained from the F distribution table, then it can be said that the regression is significant (Stoodley and Lewis 1980) . Since all the computed F–ratios of the models are greater than the F-tabulated value, it could be concluded that those are significant and so are appropriate for prediction of penetration rate. Although, the determination coefficients (R2) of the models are between 0.81 and 0.95 and this is good value, it is not identifies the valid models necessarily. Therefore, for validating the models M1, M2 and M3, the actual values were plotted against the predicted values. A summary of the results of the actual and predicted penetration rate values are given in Tables 8, 9 and 10 and graphically in Figs. 7, 8 and 9. The error in the predicted value is represented by the distance that each data point has from the 1:1 diagonal line. A point lying on the line indicates an exact prediction. The figures indicate that the data points fall close to the 1:1 slope line and are scattered uniformly around it, suggesting that models appropriate for prediction of TBM penetration rate using brittleness indexes. On the other hand, it is seen in Figs. 7, 8 and 9 that a significant concurrence is identified between actual and predicted penetration rate values, with a high determination coefficients (R2) between 0.81 and 0.93, indicating strong relationships. The results of multiple regression analysis (Table 7) were compared with simple regression analysis (Table 6) based on their determination coefficients. It is worth to noting that there is a significant difference between the determination coefficients these analyses. The determination coefficients derived using multiple regression models were generally higher than those obtained using simple regression models. For instance, in Selim and Bruce (1970) research, the determination coefficient value based on multiple regression models is 0.93 (Table 7, Eq. M1); whereas those obtained by simple regression models are 0.40 to 0.78 (Table 6, Eq. S1, S2 and S3). Therefore, models based on multiple regression Determination Standard error coefficient (R2) of estimate (SEE) analysis are more reliable than those obtained by simple regression analysis for prediction of penetration rate. 1:1 diagonal line R2 = 0.81 10 20 30 40 50 60 70 Actual TBM penetration rate (cm/min) 80 90 100 Fig. 7 The actual values of penetration rate from Selim and Bruce (1970) research and their predicted values from Eq.  (M1) developed in this study 30 60 90 120 150 180 210 Actual TBM penetration rate (cm/min) 240 270 In this study, simple and multiple regression analyses were performed for prediction of TBM penetration rate from brittleness indexes B1, B2 and B3. For this, the raw data sets obtained from the experimental works were used. Based on statistical analyses, simple and multiple regression models were developed and their significant was assessed by determination coefficient (R2), standard error of estimate (SEE), 1:1 diagonal line F statistics test and the plots of actual values vs. predicted values. Using data analysis higher determination coefficient val ues (R2) were obtained for the multiple regression models (ranging of 0.81–0.93) as compared with those that obtained for the simple regression models (ranging of 0.40–0.78). This shows that multiple regression models are the more appropriate and reliable than simple regression models for prediction of penetration rate using the brittleness indexes. The practical application of the proposed multiple regres sion models is that simple brittleness indexes B1, B2 and B3, which determined based on compressive and tensile strengths, can be used for prediction of penetration rate. Consequently, the multiple regression models developed in this study provides significant practical advantages for decision making on the organization of the construction site of the tunneling project, and, therefore, total costs. Open Access This article is distributed under the terms of the Crea tive Commons Attribution 4.0 International License (http://creativeco mmons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 1 3 Acaroglu O , Ozdemir L. Asbury B ( 2008 ) A fuzzy logic model to predict specific energy requirement for TBM performance prediction . Tunnell Undergr Space Technol 23 : 600 - 608 . https://doi. org/10.1016/j.tust. 2007 . 11 .003 Aftes ( 2003 ) Guidelines for characterization of rock masses useful for the design and the construction of underground structures . Tunnels et ouvrages Souterrains 177 : 49 AGI ( 1960 ) Glossary of Geology and Related Sciences . American Geological Institute, Washington Akcin NA , Muftuoglu YV , Bas N ( 1994 ) Prediction of drilling performance for electro-hydraulic percussive drills . In: Pasamehmetoglu KD et  al (eds) Proceedings of the Third international symposium on mine planning and equipment selection . Balkema , Istanbul, pp 483 - 488 Akun ME , Karpuz C ( 2005 ) Drillability studies of surface-set diamond drilling in Zonguldak region sandstones from Turkey . Int J Rock Mech Min Sci 42 : 473 - 479 . https://doi.org/10.1016/j. ijrmms. 2004 . 11 .009 Alber M ( 1996 ) Prediction of penetration, utilization for hard rock TBMs . In: Proceedings of the International Conference of Eurock , Balkema, Rotterdam, pp 721 - 725 Altindag R ( 1997 ) The analysis of usability for the purposes of excavation mechanics of rock brittleness measurements (in Turkish) , Ph.D. thesis (Unpublished) , 1997 , Osmangazi University Altindag R ( 2000 ) An analysis of brittleness on percussive drilling . J Geosound 37 : 167 - 170 Altindag R ( 2002 ) The evaluation of rock brittleness concept on rotary blast hole drills . J S Afr Inst Min Metall 102 : 61 - 66 Altindag R ( 2010 ) Assessment of some brittleness indexes in rockdrilling efficiency . Rock Mech Rock Eng 43 : 361 - 370 . https:// doi.org/10.1007/s00603-009-0057-x Alvarez Grima M , Bruines PA , Verhoef PNW ( 2000 ) Modeling tunnel boring machine performance by neuro-fuzzy methods . Tunnell Undergr Space Technol 15 : 259 - 269 . https://doi. org/10.1016/S0886- 7798 ( 00 ) 00055 - 9 Atici U , Ersoy A ( 2009 ) Correlation of specific energy of cutting saws and drilling bits with rock brittleness and destruction energy . J Mater Process Technol 209 : 2602 - 2612 . https://doi. org/10.1016/j.jmatprotec. 2008 . 06 .004 Barton N ( 1999 ) TBM performance in rock using Q TBM . Tunnels Tunnell Int 31 : 41 - 48 Barton N ( 2000 ) TBM Tunnelling in Jointed and Faulted Rock . Balkema, Brookfield, Rotterdam Barzegar R , Moghaddam AA ( 2016 ) Combining the advantages of neural networks using the concept of committee machine in the groundwater salinity prediction . Model Earth Syst Environ 2 : 26 . https://doi.org/10.1007/s40808-015-0072-8 Barzegar R , Sattarpour M , Nikudel MR , Moghaddam AA ( 2016 ) Comparative evaluation of artificial intelligence models for prediction of uniaxial compressive strength of travertine rocks, case study: Azarshahr area , NW Iran. Model Earth Syst Environ 2 : 76 . https://doi.org/10.1007/s40808-016-0132-8 Benardos AG , Kaliampakos DC ( 2004 ) Modelling TBM performance with artificial neural networks . Tunnell Undergr Space Technol 19 : 597 - 605 . https://doi.org/10.1016/j.tust. 2004 . 02 .128 Benato A , Oreste P ( 2015 ) Prediction of penetration per revolution in TBM tunneling as a function of intact rock and rock mass characteristics . Int J Rock Mech Min Sci 74 : 119 - 127 . https:// doi.org/10.1016/j.ijrmms. 2014 . 12 .007 Beron AI , Vatolin ES , Koifman MI , Mohnachev MP , Chirkov SE ( 1983 ) Rock properties under diverse kinds and regimes of loading (in Russian) . Nedra , Moscow Bilgin N , Eskikaya S , Dincer T ( 1993 ) The performance analysis of large diameter blast hole rotary drills in Turkish Coal Enterprises . In: Almgren T , Kumar T , Vagenas T (eds) Proceedings the second International symposium on mine mechanics automation, Lulea , pp 129 - 135 Bilgin N , Yazıcı S , Eskikaya S ( 1996 ) A model to predict the performance of roadheaders and impact hammers in tunnel drivages . In: Barla M (ed), Prediction and performance in rock mechanics and Rock Engineering, Torino, vol 2 , pp 715 - 720 Bruland A ( 1998 ) Hard Rock Tunnel Boring . Ph.D. Thesis , Norwegian University of Science and Technology, Trondheim Chiu HK , Johnston IW ( 1983 ) The uniaxial properties of Melbourne mudstone . In: Proceedings the fifth Congress ISRM, Melbourne , pp 209 - 214 Coates DF ( 1966 ) Experimental criteria for classification of rock substances . Int J Rock Mech Min Sci 3 : 181 - 189 . https://doi. org/10.1016/ 0148 - 9062 ( 66 ) 90022 - 2 Coffi Adoko A , Gokceoglu C , Yagiz S ( 2017 ) Bayesian Prediction of TBM Penetration Rate in Rock Mass . Eng Geol 226 : 245 - 256 . https://doi.org/10.1016/j.enggeo. 2017 . 06 .014 Copur H ( 1999 ) Theoretical and experimental studies of rock cutting with Drag bits towards the development of a performance prediction model for roadheaders . Ph.D. thesis , Colorado School of Mines Delisio A , Zhao J ( 2014 ) A new model for TBM performance prediction in blocky rock conditions . Tunnell Undergr Space Technol 43 , 440 - 452 . https://doi.org/10.1016/j.tust. 2014 . 06 .004 Farmer IW , Glossop NH ( 1980 ) Mechanics of disc cutter penetration . Tunnels Tunnell Int 12 ( 6 ): 22 - 25 Farrokh E , Rostami J , Laughton C ( 2012 ) Study of various models for estimation of penetration rate of hard rock TBMs . Tunnell Undergr Space Technol 30 : 110 - 123 . https://doi.org/10.1016/j. tust. 2012 . 02 .012 George EA ( 1995 ) Brittle failure of rock material-test results and constitutive models. A.A . Balkema , Rotterdam, pp 123 - 128 Goktan RM ( 1991 ) Brittleness and micro-scale rock cutting efficiency . Min Sci Technol 13 : 237 - 241 . https://doi.org/10.1016/ 0167 - 9031 ( 91 ) 90339 -E Goktan RM ( 1992 ) Applicability of rock brittleness ratio in percussive drilling performance (in Turkish) . Anadolu University. J Eng Arch Fac 8 ( 1 ): 89 - 99 Gong QM , Zhao J ( 2007 ) Influence of rock brittleness on TBM penetration rate in Singapore granite . Tunnell Undergr Space Technol 22 : 317 - 324 . https://doi.org/10.1016/j.tust. 2006 . 07 .004 Gong QM , Zhao J ( 2009 ) Development of a rock mass characteristics model for TBM penetration rate prediction . Int J Rock Mech Min Sci 46 : 8 - 18 . https://doi.org/10.1016/j.ijrmms. 2008 . 03 .003 Graham PC ( 1976 ) Rock exploration for machine manufacturers . In: Bieniawski ZT (ed) Exploration for Rock Engineering . Balkema, Johannesburg, pp 173 - 180 Heddam S ( 2016a ) New modelling strategy based on radial basis function neural network (RBFNN) for predicting dissolved oxygen concentration using the components of the Gregorian calendar as inputs: case study of Clackamas River, Oregon , USA. Model Earth Syst Environ 2 : 167 . https://doi.org/10.1007/s40808-016-0232-5 Heddam S (2016b) Simultaneous modelling and forecasting of hourly dissolved oxygen concentration (DO) using radial basis function neural network (RBFNN) based approach: a case study from the Klamath River , Oregon, USA. Model Earth Syst Environ 2 : 135 . https://doi.org/10.1007/s40808-016-0197-4 Hetenyi M ( 1966 ) Handbook of experimental stress analysis . Wiley, NewYork Howarth DF ( 1987 ) The effect of pre-existing microcavities on mechanical rock performance in sedimentary and crystalline rocks . Int J Rock Mech Min Sci Geomech Abstr 24 : 223 - 233 . https ://doi.org/10.1016/ 0148 - 9062 ( 87 ) 90177 -X Huang SL , Wang ZW ( 1997 ) The mechanics of diamond core drilling of rocks . Int J Rock Mech Min Sci Geomech Abstr 34 : 134 . e1 - 134 . e14 . https://doi.org/10.1016/S1365- 1609 ( 97 ) 00233 - 5 Hucka V , Das B ( 1974 ) Brittleness determination of rocks by different methods . Int J Rock Mech Min Sci Geomech Abstr 11 : 389 - 392 . https://doi.org/10.1016/ 0148 - 9062 ( 74 ) 91109 - 7 Hughes HM ( 1986 ) The relative cuttability of coal-measures stone . Min Sci Technol 3 ( 2 ): 95 - 109 . https://doi.org/10.1016/S0167 - 9031 ( 86 ) 90250 - 1 Inyang HI ( 1991 ) Development of a preliminary rock mass classification scheme for near surface excavation . Int J Surf Min Reclam 5 : 65 - 74 Inyang HI , Pitt JM ( 1990 ) Standardisation of a percussive drill for measurement of the compressive strength of rocks, Rock Mech . In: Hustrulid, Johnson (eds) Contributions and Challenges, pp 489 - 496 ISRM ( 2007 ) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974 - 2006 . In: Ulusay R , Hudson JA (eds), Suggested Methods Prepared by the Commission on Testing Methods, International Society for Rock Mechanics . ISRM Turkish National Group, Ankara, Turkey Kahraman S ( 1999 ) Rotary and percussive drilling prediction using regression analysis . Int J Rock Mech Min Sci 36 : 981 - 989 . https ://doi.org/10.1016/S0148- 9062 ( 99 ) 00050 - 9 Kahraman S ( 2002 ) Correlation of TBM and drilling machine performances with rock brittleness . Eng Geol 65 ( 4 ): 269 - 283 . https ://doi.org/10.1016/S0013- 7952 ( 01 ) 00137 - 5 Kahraman S , Bilgin N , Feridunoglu C ( 2003 ) Dominant rock properties affecting the penetration rate of percussive drills . Int J Rock Mech Min Sci 40 : 711 - 723 . https://doi.org/10.1016/S1365 - 1609 ( 03 ) 00063 - 7 Karpuz C , Pasamehmetoglu AG , Dincer T , Muftuoglu Y ( 1990 ) Drillability studies on the rotary blasthole drilling of lignite overburden series . Int J Surf Min Reclam 4 : 89 - 93 Keshavarzi A , Bagherzadeh A , Ewis Omran ES ( 2016 ) Modeling of soil exchangeable sodium percentage using easily obtained indices and artificial intelligence-based models . Model Earth Syst Environ 2 : 130 . https://doi.org/10.1007/s40808-016-0185-8 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 25 : 333 - 345 . https://doi.org/10.1016/j.tust. 2010 . 01 .008 Kim MK , Lade PV ( 1984 ) Modelling rock strength in three dimensions . Int J Rock Mech Min Sci Geomech Abstr 21 : 21 - 33 . https ://doi.org/10.1016/ 0148 - 9062 ( 84 ) 90006 - 8 Koulikov VV ( 1987 ) Modelling of jointed rock mass. Problems of rock mechanics (in Russian) . Nauka , Moscow, pp 59 - 65 Kovscek PD , Taylor CD , Thimons ED ( 1988 ) Evaluation of waterjet-assisted drilling with handheld drills, U.S. Dept. of the interior , USBM RI-9174 , p 15 Mahdevari S , Shahriar K , Yagiz S , Akbarpour Shirazi M ( 2014 ) A support vector regression model for predicting tunnel boring machine penetration rates . Int J Rock Mech Min Sci 72 : 214 - 229 . https://doi.org/10.1016/j.ijrmms. 2014 . 09 .012 McFeat-Smith I ( 1977 ) Rock property testing for the assessment of tunneling machine performance . Tunnels Tunnell Int 9 : 29 - 31 McFeat-Smith I , Fowel RJ ( 1977 ) Correlation of rock properties and the cutting performance of tunnelling machines . In: Proceedings of a Conference on rock engineering . The University of Newcastle upon Tyne, pp 581 - 602 Morley A ( 1944 ) Strength of material . Longman, Green Nilsen B , Ozdemir L ( 1993 ) Hard rock tunnel boring prediction and field performance . In: Bowerman LD et al (eds) Proceedings of the Rapid Excavation and Tunnelling Conferences , Boston, MA, USA, pp 793 - 809 Obert L , Duvall WI ( 1967 ) Rock mechanics and the design of structures in rock . Wiley, NewYork, p 278 Ramsey JG ( 1967 ) Folding and fracturing of rocks . McGraw-Hill , London Reichmuth RD ( 1967 ) Point load testing of brittle materials to determine tensile strength and relative brittleness . In: Proceedings the ninth U.S. Symposium on Rock Mechanics (USRMS) , Golden, Colorado, pp 134 - 159 Rostami J , Ozdemir L ( 1993 ) A new model for performance prediction of hard rock TBM . In: Proceedings of Rapid Excavation and Tunneling Conference , Boston, pp 793 - 809 Rostami J ( 2016 ) Performance prediction of hard rock Tunnel Boring Machines (TBMs) in difficult ground . Tunnell Undergr Space Technol 57 : 173 - 182 . https://doi.org/10.1016/j.tust. 2016 . 01 .009 Salimi A , Rostami J , Moormann C , Delisio A ( 2016 ) Application of non-linear regression analysis and artificial intelligence algorithms for performance prediction of hard rock TBMs . Tunnell Undergr Space Technol 58 : 236 - 246 . https://doi.org/10.1016/j. tust. 2016 . 05 .009 Sapigni M , Berti M , Bethaz E , Busillo A , Cardone G ( 2002 ) TBM performance estimation using rock mass classifications . Int J Rock Mech Min Sci 39 : 771 - 788 . https://doi.org/10.1016/S1365 - 1609 ( 02 ) 00069 - 2 Selim AA , Bruce WE ( 1970 ) Prediction of penetration rate for percussive drilling , US Bureau of Mines RI 7396 Shao C , Li X , Su H ( 2013 ) Performance Prediction of Hard Rock TBM Based on Extreme Learning Machine . In: Lee J , Lee MC , Liu H , Ryu JH (eds) Intelligent Robotics and Applications: 6th International Conference, ICIRA 2013, Busan, South Korea, September 25-28 , 2013 , Proceedings, Part II. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 409 - 416 Singh PS ( 1986 ) Brittleness and the mechanical winning of coal . Min Sci Technol 3 : 173 - 180 . https://doi.org/10.1016/S0167 - 9031 ( 86 ) 90305 - 1 Stoodley KDC , Lewis T ( 1980 ) Stainton CLS . Applied statistical techniques . Ellis Horwood , England, pp 35 - 73 Tanaino AS ( 2005 ) Rock classification by drillability Part I: analysis of the available classifications . J Min Sci 41 ( 6 ): 541 - 549 . https:// doi.org/10.1007/s10913-006-0017-8 Vardoulakis I ( 1984 ) Rock bursting as a surface instability phenomenon . Int J Rock Mech Min Sci Geomech Abstr 21 : 137 - 144 . https:// doi.org/10.1016/ 0148 - 9062 ( 84 ) 91531 - 6 Yagiz S ( 2002 ) Development of Rock Fracture and Brittleness Indices to Quantify the Effects of Rock Mass Features and Toughness in the CSM Model Basic Penetration for Hard Rock Tunneling Machines ( Ph.D. Thesis) . Department of Mining and Earth Systems Engineering , Colorado School of Mines, Golden, Colorado, USA Yagiz S ( 2008 ) Utilizing rock mass properties for predicting TBM performance in hard rock condition . Tunnell Undergr Space Technol 23 : 326 - 339 . https://doi.org/10.1016/j.tust. 2007 . 04 .011 Yagiz S , Karahan H ( 2011 ) Prediction of hard rock TBM penetration rate using particle swarm optimization . Int J Rock Mech Min Sci 48 : 427 - 433 . https://doi.org/10.1016/j.ijrmms. 2011 . 02 .013 Yagiz S , Karahan H ( 2015 ) Application of various optimization techniques and comparison of their performances for predicting TBM penetration rate in rock mass . Int J Rock Mech Min Sci 80 : 308 - 315 . https://doi.org/10.1016/j.ijrmms. 2015 . 09 .019 Yazdani-Chamzini A , Razani M , Yakhchali SH , Zavadskas EK , Turskis Z ( 2013 ) Developing a fuzzy model based on subtractive clustering for road header performance prediction . Automatin Constr 35 : 111 - 120 . https://doi.org/10.1016/j.autcon. 2013 . 04 .001


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs40808-018-0432-2.pdf

A. Jamshidi. Prediction of TBM penetration rate from brittleness indexes using multiple regression analysis, Modeling Earth Systems and Environment, 2018, 383-394, DOI: 10.1007/s40808-018-0432-2