Predicting penetration rate of hard rock tunnel boring machine using fuzzy logic

Bull Eng Geol Environ (204) 73:23 35 DOI 0.007/s0064-03-0497-0 ORIGINAL PAPER Predicting penetration rate of hard rock tunnel boring machine using fuzzy logic Ebrahim Ghasemi Saffet Yagiz Mohammad Ataei Received: 4 June 202 / Accepted: 4 July 203 / Published online: 24 November 203 Ó Springer-Verlag Berlin Heidelberg 203 Abstract Predicting the penetration rate of a tunnel boring machine (TBM) plays an important role in the economic and time planning of tunneling projects. In the past years, various empirical methods have been developed for the prediction of TBM penetration rates using traditional statistical analysis techniques. Soft computing techniques are now being used as an alternative statistical tool. In this study, a fuzzy logic model was developed to predict the penetration rate based on collected data from one hard rock TBM tunnel (the Queens Water Tunnel # 3, Stage 2) in New York City, USA. The model predicts the penetration rate of the TBM using rock properties such as uniaxial compressive strength, rock brittleness, distance between planes of weakness and the orientation of discontinuities in the rock mass. The results indicated that the fuzzy model can be used as a reliable predictor of TBM penetration rate for the studied tunneling project. The determination coefficient (R 2 ), the variance account for and the root mean square error indices of the proposed fuzzy model are 0.8930, 89.06 and 0.3, respectively. Keywords Tunnel boring machine (TBM) Rate of penetration (ROP) Rock properties Fuzzy logic E. Ghasemi (&) M. Ataei Department of Mining, Petroleum and Geophysics Engineering, Shahrood University of Technology, Daneshgah Blvd., P.O. Box 3699956, Shahrood, Iran e-mail: ebrahim62.gh@gmail.com; e.ghasemi@shahroodut.ac.ir S. Yagiz Department of Geological Engineering, Pamukkale University, 20020 Denizli, Turkey Introduction Tunnel boring machines (TBMs) have found widespread application in tunnel construction and are used for excavating tunnels in nearly all types of rock masses and geological conditions. The successful application of TBM technology is directly related to an accurate estimation of performance, which is critical for project schedule and cost. Error in performance estimation can result in project delays and cost over runs as seen in many case histories. The TBM performance prediction requires estimating the rate of penetration (ROP), machine advance rate (AR) and machine utilization (Sapigni et al. 2002). During rock excavation processes, many parameters including machine parameters, geological conditions and site-specific conditions affect the machine performance level. The complex relationship between these parameters makes predicting the performance of the machine very difficult. Since the first TBM machine was built, the performance prediction of the machines have been the ultimate goals of many studies and numerous predictive models have been developed. These performance prediction models can be generally classified as theoretical, semi-theoretical and empirical models (Zhao and Hassanpour 20). The theoretical and semi-theoretical models are based on the analysis of the forces or the specific energy required to excavate a unit volume of rock, which are related to the intact rock and rock mass properties such as rock material compressive, tensile and shear strength, rock quality designation (RQD) or joint spacing and so on. Examples of theoretical and semi-theoretical models can be found in Roxborough and Phillips (975), Fowel and McFeat-Smith (976), Ozdemir (977), Farmer and Glossop (980), Sanio (985), Sato et al. (99) and Rostami (997). The empirical performance prediction models are mainly based

24 E. Ghasemi et al. on the past experiences and the statistical interpretations of the previously recorded field data in various ground conditions. Empirical approaches are the most widely used in the tunneling industry. One outstanding example of an empirical model is the Norwegian hard rock prognosis system developed by Blindheim (979) and later updated by Bamford (984), Lislerud (988) and Bruland (999). Tarkoy (973), Cassinelli et al. (982), Innaurato et al. (99), Barton (999), Nelson et al. (985, 999), Alber (996, 2000), Grima et al. (2000), Yagiz (2002, 2008), Sapigni et al. (2002), Ribacchi and Lembo-Fazio (2005), Benardos and Kaliampakos (2004), Ramezanzadeh (2005), Bieniawski et al. (2006), Zhao et al. (2007), Yagiz et al. (2009), Gong and Zhao (2009), Gholamnejad and Tayarani (200), Hassanpour et al. (2009, 200, 20), Khademi Hamidi et al. (200a) and Farrokh et al. (202) introduced other types of empirical models. Intact and mass rock properties, rock mass classifications, machine and operational parameters were used for developing these empirical models. The main output in most performance prediction models is ROP. ROP is defined as the distance excavated divided by the operating time during a continuous excavation phase (Sapigni et al. 2002). In tunneling projects, a reliable estimation of ROP is needed for time planning and cost control. The literature contains a considerable number of empirical predictor models obtained from conventional statistical techniques. In recent years, some new soft computing techniques such as artificial neural networks, fuzzy inference systems, evolutionary computation, etc. and their hybrids have been successfully employed for developing predictive models. These techniques have attracted more attention in many research fields, because they can tolerate a wide range of uncertainty. Soft computing techniques are now being used as an alternative statistical tool. The fuzzy logic (FL) technique is a branch of soft computing and has been developed since the 960s. FL is considered to be the most intelligent tool for simulating complex problems. In recent years, an increase in the FL applications in the field of tunneling, mining, rock mechanic and engineering geology has been observed. For example, Sonmez et al. (2003) and Aydin (2004) used fuzzy approaches for rock mass classification. Deb (2003) and Ghasemi and Ataei (202) evaluated the performance of the roof in coal mines using fuzzy set theory. Karadogan et al. (2008) applied fuzzy set theory for the selection of underground mining method. Grima et al. (2000), Acaroglu et al. (2008), Khademi Hamidi et al. (200b) and Acaroglu (20) employed fuzzy set theory for the prediction of TBM performance and trench excavation machines. Dodagoudar and Venkatachalam (2000) employed fuzzy set theory for the assessment of rock slope stability. Tzamos and Sofianos (2006) applied the fuzzy logic concept to the prediction of support systems in tunnels. Fisne et al. (20), Monjezi et al. (200), Rezaei et al. (20) and Ghasemi et al. (202) developed fuzzy models for the analysis and prediction of the effects of blasting operations such as ground vibration, flyrock and backbreak. Li et al. (200) applied fuzzy models to the analysis of rock displacement and ground subsidence due to underground mining. Azimi et al. (200) applied fuzzy sets to predict the blastability of rock masses. Iphar and Goktan (2006) developed a fuzzy model to predict rock mass diggability for surface mine equipment selection. Ataei et al. (2009) used fuzzy logic for the determination of coal mine mechanization. Fuzzy set theory has been used for the prediction of rock properties such as uniaxial compressive strength, modulus of elasticity and brittleness by Grima and Babuska (999), Gokceoglu (2002), Kayabasi et al. (2003), Gokceoglu and Zorlu (2004), Sonmez et al. (2004) and Yagiz and Gokceoglu (200). In this study, an effort has been made to predict ROP with the help of a FL approach. In fact, the main aim of this study is to find the suitability of the application of FL to predicting TBM performance. Based on studies performed by Yagiz (2008), Gong and Zhao (2009) and Hassanpour et al. (20), the most important parameters affecting TBM penetration rates are rock properties including the compressive strength and tensile strength of the rock material, brittleness and the frequency of the rock joints. In this study, using Queens Water Tunnel database compiled by Yagiz (2008), a fuzzy model is presented for the prediction of TBM penetration rates. The database is composed of intact rock properties including uniaxial compressive strength (UCS), Brazilian tensile strength (BTS) and brittleness index (BI) and also rock mass properties including distance between planes of weakness (DPW) and the alpha angle (a) [the angle between plane of weakness and TBM-driven direction] together with actual measured TBM penetration rates in the tunnel site. This database was collected from about 7.5 km of tunnel excavated in various hard rocks. Background of fuzzy logic Most of the world s knowledge is uncertain and imprecise and thus the description of all actual systems inherently contains incomplete and imprecise information. In order to deal with such situations, a fuzzy approach based on FL seems to be the most appropriate. The details of FL can be found in numerous papers (Zadeh 965; Ross 995). The FL is a matter of the fuzzy set theory that is particularly used to deal with subjects having ambiguities and uncertainties. Fuzzy set theory was first formulized by Zadeh (965) as a mathematical way to represent linguistic vagueness. A fuzzy set is an extension of a crisp set but

Predicting penetration rate 25 does not have any sharp and precise boundaries, unlike a crisp set. A block diagram of a typical FL system is presented in Fig.. As outlined in Fig., a fuzzy rule-based system consists of four parts: fuzzifier, knowledge base, fuzzy inference system and defuzzifier. The fuzzifier converts crisp input to fuzzy values or linguistic information using membership functions. The main part of the fuzzy system is the knowledge base in which both rule base and database are jointly referred. The database defines the membership functions of the fuzzy sets used in the fuzzy rules whereas the rule base contains a number of fuzzy if then rules. The if then rules, also known as the fuzzy rules, provide a system for describing complex systems by relating input and output parameters using linguistic variables. The fuzzy inference system (FIS), also known as the decision making unit, performs the inference operations on the rules. There are several FISs that have been employed in various applications and the most commonly used include: the Mamdani fuzzy model, the Takagi Sugeno Kang (TSK) fuzzy model, the Tsukamoto fuzzy model and the Singleton fuzzy model. The differences between these FISs lie in the consequences of their rules, and thus aggregation and defuzzification procedures differ accordingly. The defuzzifer converts fuzzy outcome to a crisp one. There are a number of defuzzifer methods in the literature such as centroid of area (COA) or center of gravity, mean of maximum (MOM), smallest of maximum (SOM), largest of maximum (LOM) and bisector of area (BOA). performance Robbins TBM (235 282) that was equipped with both 48.2 cm (9 in.) disc cutters and a rated load capacity of 30 tons (70,000 lb) per cutter was used to excavate this tunnel (Fig. 3). The basic specifications of this TBM are summarized in Table. The tunnel is one of the most complex engineering projects in the world due to the type of geological conditions encountered. The construction area along the tunnel is obstructed by geological conditions, including unexpected lithology and rock fabric orientation, a zone of crosscutting dikes and brittle faults. The geological complexity in the studied area includes variable highgrade granitic gneiss, amphibolite, orthogneiss, gneiss/ Site description and database The purpose of this study is to construct an FL model for predicting ROP. To do this, the database compiled by Yagiz (2008) from one hard rock TBM tunnel (the Queens Water Tunnel # 3, Stage 2) was used. The Queens Water Tunnel # 3, stage 2 was constructed between 997 and 2000 in order to improve the fresh water distribution throughout New York City, USA. The tunnel being about 7.5 km long and 7 m in diameter was excavated beneath Brooklyn and Queens at an average depth of 200 m below sea level in West-central Queens County (Fig. 2). A high Fig. 2 The location map of Queens Water Tunnel # 3, stage 2 (Yagiz et al. 2009) Fig. The structure of a typical fuzzy logic system Fig. 3 The front cutterhead and thrust assembly of the Queens TBM (Merguerian and Ozdemir 2003)

26 E. Ghasemi et al. Table Main specifications of Queens TBM (Yagiz 2008) Parameter Value Machine diameter 7.06 m Diameter range 6.5 8.5 m Cutters Series 9, 48.2 cm Number of disk cutters 50 Recommended individual cutter load 35 short tons (nominal) Max. operating cutterhead thrust,750 tons (nominal) Cutterhead power 4,220 hp Cutterhead speed 8.3 rpm Cutterhead torque,335 short tons (nominal) Thrust cylinder stroke.83 m Conveyor capacity (approx.) 8.4 m 3 /min TBM weight (approx.) 640 tons schist complex and rhyodacite dikes. Rock types excavated along the tunnel alignment are categorized by percentage in Fig. 4. The Queens Water Tunnel was studied in both field and laboratory in order to establish the database used for the development of ROP predictive models. The first part of the database was established by performing intact rock tests including uniaxial compressive strength (UCS), Brazilian tensile strength (BTS) and rock brittleness (BI) in accordance with the ASTM standard at the Earth Mechanics Institute of Colorado School of Mines in the USA. The second part was established in the field. In this section, the alpha angle was computed and the distance between planes of weakness (DPW) and the ROP in stroke base was measured. The ranges of input parameters in the database, including 5 cases, and their basic descriptive statistics are given in Table 2. Yagiz (2008) and Yagiz et al. (2009) performed a series of simple and multiple regression analyses on this database and found that each rock engineering property has a significant effect on the ROP in certain percentages but herein the BTS was excluded due to its insignificant effect on the rate of penetration. Thus, in the following, a fuzzy model is developed for predicting ROP using the UCS, BI, DPW and Alpha angle parameters. It should be noted that in this study, the database was divided into two groups randomly: one group for training and developing the fuzzy model including 80 % of the datasets (i.e., 2 datasets) and the other group including the rest of the datasets (i.e., 30 datasets) for testing the model performance. Fuzzy model to predict TBM penetration rate FL has been successfully applied to many real-world problems especially in modeling complex and imprecise Fig. 4 Distribution of rock types along the tunnel based on the field study (Yagiz and Karahan 20) Table 2 Basic descriptive statistics for the original database (Yagiz et al. 2009) Parameter (unit) Min. Avg. Max. SD Var. UCS (MPa) 8.3 50. 99.7 22.2 492.4 BTS (MPa) 6.7 9.5.4 0.9 0.8 BI (kn/mm) 25.0 34.6 58.0 8.5 7.6 DPW (m) 0.05.02 2.00 0.64 0.42 Alpha ( ) 2.0 44.7 89.0 23.3 54.9 Measured ROP (m/h).27 2.04 3.07 0.36 0.3 Total number of data points is 5 systems in the science and engineering fields during the past two decades. ROP is one of these complex problems. In this section, a fuzzy model is introduced for the prediction of ROP. This fuzzy model was implemented on fuzzy logic toolbox of MATLAB ver. 7. (R200b) software package. The model includes four input variables and one output variable. Figure 5 shows input and output variables, where UCS, BI, DPW and alpha angle are referred to as input and ROP is referred to as output. In order to develop the fuzzy model, four steps were performed, which are described in the following sections. Fuzzification of input and output variables Triangular membership functions were adopted for describing input and output variables because of their simplicity and computational efficiency. The triangular membership function as described in Eq. () is used to convert the linguistic values in the range of 0. 8 9 0 ifx a >< x a >= lðxþ ¼ b a if a x b c x ðþ c b if b x c >: >; 0 ifc x where a, b, c are the parameters of the linguistic value and x is the range of the input parameters. The graphical

Predicting penetration rate 27 Fig. 5 Input and output variables of the fuzzy model Fig. 6 Fuzzy representation of input and output variables: a UCS; b BI; c DPW; d alpha angle; e ROP representations of the membership functions of different input and output variables are shown in Fig. 6. In this figure, VVL stands for very very low, VL for very low, L for low, M for medium, H for high, VH for very high, VVH for very very high. Also, Table 3 shows the linguistic variables, their linguistic values and associated parameters. Design of fuzzy inference system Mamdani fuzzy inference system was chosen in this study. The Mamdani algorithm has become one of the most common and widely used algorithms for solving many real-world problems, because of its simplicity. The Mamdani FIS was proposed by Mamdani to control a steam

28 E. Ghasemi et al. engine and boiler combination by the set of linguistic control rules obtained from experienced human operators (Mamdani and Assilian 975). The Mamdani fuzzy model takes the following form: If x is A i and x 2 is A i2 and...x r is A ir then y is B i ðfor i ¼ ; 2;...; kþ ð2þ where k is the number of rules, x i is the input variable, A ir and B i are the linguistic terms and y is the output variable. Design of rule base The next stage in designing the fuzzy model is the construction of the if then rules, which are used to represent the fuzzy relationships between input and output fuzzy Table 3 Representation of membership functions and their parameters Variables Linguistic variables Linguistic values Parameters Inputs UCS Very low [8.3 8.3 32.8] Low [29.5 37.4 46.5] Medium [42.5 52.8 62.9] High [58.2 65.7 76.5] Very high [72.4 99.7 99.7] BI Very low [25 25 33] Low [30 33 38] Medium [35 40 45] High [42 46 55] Very high [53 58 58] DPW Very low [0.05 0.05 0.35] Low [0.25 0.40 0.75] Medium [0.55 0.80.45] High [.20.60.80] Very high [.70 2.00 2.00] Alpha angle Very low [2 2 4] Low [ 20 3] Medium [27 36 47] High [43 55 68] Very high [65 89 89] Output ROP Very very low [.27.27.55] Very low [.49.6.76] Low [.7.8 2.00] Medium [.94 2.0 2.23] High [2.6 2.30 2.53] Very high [2.4 2.65 2.90] Very very high [2.8 3.07 3.07] variables. In this study, a total of 272 rules were utilized for constructing the rule base of the fuzzy model. These rules were made based on training datasets and cover all possible manners. Table 4 presents some samples of fuzzy if then rules in the model. Defuzzification process In the last stage, each result in the form of a fuzzy set is converted into a crisp (real output) value by the defuzzification process. In this model, the COA method, that is a commonly used method of defuzzification, was employed for the defuzzification process (Grima and Babuska 999). The developed fuzzy model can provide an estimation of ROP when proper and acceptable input data are entered into the model. For example, as can be seen in Fig. 7, when input parameters are UCS = 82.4 MPa, BI = 39 kn/mm, DPW = 0.8 m and alpha angle = 66, the predicted output ROP is.97 m/h (whereas according to Table 5 actual ROP is 2 m/h). Table 4 Samples of if then rules Description of if then rules IF UCS is VH and BI is VH and DPW is M and Alpha is L IF UCS is VH and BI is VH and DPW is H and Alpha is L IF UCS is H and BI is VH and DPW is H and Alpha is M IF UCS is VH and BI is VH and DPW is L and Alpha is H IF UCS is M and BI is H and DPW is H and Alpha is H IF UCS is H and BI is H and DPW is M and Alpha is L IF UCS is L and BI is M and DPW is VL and Alpha is VH IF UCS is L and BI is H and DPW is H and Alpha is VH IF UCS is L and BI is L and DPW is H and Alpha is VL IF UCS is VL and BI is L and DPW is H and Alpha is L IF UCS is M and BI is L and DPW is M and Alpha is H IF UCS is M and BI is L and DPW is M and Alpha is H IF UCS is M and BI is L and DPW is VL and Alpha is M IF UCS is H and BI is L and DPW is VL and Alpha is VH IF UCS is VH and BI is VL and DPW is M and Alpha is M THEN ROP is H THEN ROP is M THEN ROP is H THEN ROP is VVH THEN ROP is M THEN ROP is M THEN ROP is VH THEN ROP is H THEN ROP is L THEN ROP is VL THEN ROP is M THEN ROP is L THEN ROP is M THEN ROP is H THEN ROP is L

Predicting penetration rate 29 Fig. 7 Fuzzy rule viewer for proposed fuzzy model Performance of fuzzy model As mentioned before, 30 datasets, which were not incorporated in the model, were used for testing and validating the model. To evaluate the performance of the model, the predicted ROP values were compared with the measured ones, which can be seen in Table 5. The coefficient of determination (R 2 ) between the measured and predicted values is a good indicator to check the prediction performance of each model. Furthermore, in this study, variance account for (VAF; Eq. (3)) and root mean square error (RMSE; Eq. (4)) indices were calculated to control the prediction performance of the model. When R 2 is, VAF is 00 and RMSE is 0, then the model is excellent. VAF ¼ varða i P i Þ 00 ð3þ varða i Þ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u X N RMSE ¼ t ða i P i Þ 2 ð4þ N i¼ where A i and P i are the measured (actual) and predicted values, respectively, and N is the number of testing samples. The VAF and the RMSE indices for the proposed fuzzy model were 89.06 and 0.3, respectively. Also, determination coefficient (R 2 ) of the model is 0.8930. Evidently, the obtained indices indicate that the proposed FL model can provide a good prediction for ROP. Figure 8 illustrates the effects of each input parameter on ROP based on the results obtained from different runs of the FL model. It can be concluded from Fig. 8 that the proposed fuzzy model can efficiently predict the ROP in all ranges within the database. The relationship between UCS and ROP is approximately linear and increasing UCS leads to a gradual decrease in ROP. Furthermore, the relationship between BI and ROP is linear and increasing BI leads to a gradual increase in ROP (Fig. 8a, b). DPW shows a nonlinear relationship with ROP. As the DPW drops to 45 cm or less, ROP decreases. Because in this condition, the operator may change the TBM operational parameters (for example, the machine thrust can be decreased), so ROP is subsequently decreased. However, when the DPW is between 45 and 80 cm, the ROP increases. Furthermore, when the DPW is higher than 80 00 cm, then, it has no effect on the ROP, because the TBM does not see the

30 E. Ghasemi et al. Table 5 The comparison between measured ROP and predicted ROP values by different predictive models No. UCS (MPa) BI (kn/ mm) DPW (m) Alpha angle (deg.) Measured ROP (m/h) Predicted ROP (m/h) LMR NLMR PSO FL 68.3 58.6 4 2.37 2.62 2.83 2.54 2.33 2 74. 58 2 35 2.34 2.49 2.68 2.42 2.34 3 84. 57 0.4 49 3.07 2.84 3.06 2.77 2.97 4 94.5 52 0.4 33 2.3 2.59 2.78 2.52 2.34 5 82.4 39 0.8 66 2 2.30 2.54 2.8.97 6 64. 46 0.8 9 2.09 2.32 2.46 2.25 2.09 7 40 43 0. 46 2.46 2.62 2.86 2.67 2.65 8 25 27.6 83 2.2.99 2.27.93.84 9 34.2 34 2 4 2.7.94 2.7.9 2.23 0 30 32.6 5.87.79.9.76.72 38.6 3 0.4 58 2.43 2.26 2.5 2.23 2.3 2 38.8 3 0.8 55 2.3 2.6 2.4 2.0 2.34 3 37.2 30 0.8 67.88 2.7 2.44 2..85 4 33.3 30 0.8 47 2.4 2.2 2.36 2.07.85 5 34.3 32 0.4 40 2.42 2.23 2.46 2.22 2.33 6 43.4 33.6 33 2.28.93 2.4.88 2.34 7 45.5 38 0.8 52 2.35 2.33 2.57 2.27 2.3 8 59.3 36 0.8 78 2.6 2.3 2.57 2.2 2.65 9 57.9 33.6 0.5.66.8.59.5 20 73. 3 0.8 33.84.96 2.6.88.93 2 76 30 2 7.6.8 2.06.7.62 22 76.8 30.6 77.88.9 2.6.79.85 23 44.8 29 2 70.84.87 2.3.8.74 24. 29 0.8 0.46.83.35.79.38 25 20.7 29 0.8 68.94 2.20 2.47 2.5 2.09 26 9.7 29 0.2 60.97 2.3 2.57 2.33.97 27 25. 28.6 25.65.79.98.76.84 28 36.2 26.6 62.56.87 2.3.8.49 29 39.3 26 2.27.45.43.4.39 30 55.9 25.6 45.8.72.95.65.85 fractures or weakness after some point (about a meter) as seen in Fig. 8c. The alpha angle has a polynomial relationship with the ROP (Fig. 8d). When the alpha angle is less than about 50, the ROP increases and the maximum ROP occurs between 50 and 65. When the alpha angle exceeds 65, the ROP decreases. All these results show good conformity with published researches (Bruland 999; Yagiz 2002, 2008; Gong and Zhao 2009). Comparison of fuzzy model performance with previous models Yagiz (2008), Yagiz et al. (2009) and Yagiz and Karahan (20) have presented three equations for predicting ROP based on the Queens Water Tunnel database. These equations were developed using linear multivariate regression (LMR) analysis (Eq. 5), nonlinear multivariate regression (NLMR) analysis (Eq. 6) and particle swarm optimization (PSO) techniques (Eq. 7). ROP ¼ :093 0:003 UCS þ 0:029 BI 0:29 DPW þ 0:437 LogðaÞ ð5þ ROP n ¼ 0:076 0:39 UCS n þ 0:524 BI n 0:234 DPW n þ 0:634 a 0:205 n ROP ¼ 2:827 0:004 UCS þ 0:029 BI 0:406 DPW 0:584 :6756a 0:27 ð6þ ð7þ In Eq. (6), the subscript n indicates normalized parameters. In this section, the performance of these equations is compared with the proposed FL model. To do this, 30

Predicting penetration rate 3 datasets, which were used for testing the FL model in the previous section, are used. The comparison between the predicted ROP using LMR, NLMR and PSO equations and the measured ROP values can be found in Table 5. Furthermore, the differences between the predicted values by the FL, MLR, NLMR and PSO models from the measured values are presented graphically in Fig. 9. These plots indicate that the deviation intervals (-0.2 to?0.37) of the predicted values for FL are smaller than the deviation intervals of MLR (-0.37 to?0.35), NLMR (-0.60 to?0.33) and PSO (-0.36 to?0.40). The performance indices (R 2, VAF and RMSE) for all predictive models were listed in Table 6. Furthermore, the relationship between measured ROP and the corresponding values predicted by the FL, MLR, NLMR and PSO models were given in Fig. 0. According to the RMSE, VAF and R 2 values, the performance of the MLR, NLMR and PSO models is nearly the same whereas the constructed FL model shows a higher prediction performance in comparison with them. Discussion and conclusions The purpose of the study was to develop a fuzzy model for the prediction of the ROP in hard rock tunnels. The fuzzy model considers the intact and mass rock properties including UCS, BI, DPW and alpha angle as input parameters. The model was trained with experimental data obtained from the Queens Water Tunnel using the fuzzy logic toolbox of MATLAB. Mamdani algorithm and triangular fuzzy membership functions were used to predict the ROP. Also, the use of the trapezoidal membership function for marginal conditions was examined but no change was observed in the obtained results. Furthermore, the proposed model was constructed based on 272 if then fuzzy rules and the COA method for defuzzification. The most important findings of this study are as follows: Fig. 8 The effect of each individual input parameter on ROP: a ROP versus UCS; b ROP versus BI; c ROP versus DPW; d ROP versus alpha angle. The results of different predictive models for ROP showed that the LMR, NLMR and PSO equations have lower prediction performance in comparison with a FL model.

32 E. Ghasemi et al. Fig. 9 The difference of the predicted values by FL, MLR, NLMR and PSO models with the measured values Residual error of ROP (m/h) 0.4 0.3 0.2 0. 0-0. -0.2-0.3-0.4-0.5-0.6 FL LMR NLMR PSO 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 25 26 27 28 29 30 Sample NO. Table 6 Performance indices (R 2, VAF and RMSE) for models Model R 2 VAF (%) RMSE FL 0.8930 89.06 0.3 LMR 0.7039 70.39 0.22 NLMR 0.6952 6.37 0.34 PSO 0.6968 69.64 0.2 2. It was concluded that the proposed FL model was a suitable and practical technique that can be effectively used in the prediction of ROP with acceptable error rates. The major advantage of fuzzy model in comparison with other models is that human judgment and intuition can be effectively used for the prediction of ROP, which helps in field applications. 3. The outcome of the proposed fuzzy model can be considered as a preliminary estimation of ROP and based on it, the time-scheduling can be more efficient and consequently the project costs decreased. 4. Based on the obtained results, the use of fuzzy logic is a useful and powerful means to assist engineering geologists and tunneling experts in coping with the complexity of geo-related problems such as TBM penetration rates. 5. Based on different runs of the FL model, it was observed that the UCS and BI have linear relationships with ROP while DPW and Alpha indicate nonlinear relationships with ROP. 6. Finally, it should be mentioned that the proposed fuzzy model has been developed based on data from the database of the Queens Water Tunnel and it should not be used directly for ROP prediction in

Predicting penetration rate 33 (a) 3.2 3 R-squared = 0.8930 (b) 3.2 3 R-squared = 0.7039 2.8 2.8 Predicted ROP (m/h) 2.6 2.4 2.2 2.8.6 Predicted ROP (m/h) 2.6 2.4 2.2 2.8.6.4.2 Data points Best linear fit.2.4.6.8 2 2.2 2.4 2.6 2.8 3 3.2 Measured ROP (m/h).4.2 Data points Best linear fit.2.4.6.8 2 2.2 2.4 2.6 2.8 3 3.2 Measured ROP (m/h) (c) 3.2 3 R-squared = 0.6952 (d) 3.2 3 R-squared = 0.6968 Predicted ROP (m/h) 2.8 2.6 2.4 2.2 2.8.6 Predicted ROP (m/h) 2.8 2.6 2.4 2.2 2.8.6.4.2 Data points Best linear fit.2.4.6.8 2 2.2 2.4 2.6 2.8 3 3.2 Measured ROP (m/h).4.2 Data points Best linear fit.2.4.6.8 2 2.2 2.4 2.6 2.8 3 3.2 Measured ROP (m/h) Fig. 0 The relationship between the measured and predicted ROP by: a FL; b MLR; c NMLR; d PSO; models with their coefficient of determination other tunnels. It is clear that this model can be improved using more data from other tunneling projects over time. Acknowledgments The authors would like to express their thanks to the anonymous reviewers for their useful comments and constructive suggestions. The authors are also very much grateful to Mrs. I. Mahboobi for her kind help during the preparation of manuscript. References Acaroglu O (20) Prediction of thrust and torque requirements of TBMs with fuzzy logic models. Tunn Undergr Space Technol 26:267 275 Acaroglu O, Ozdemir L, Asbury B (2008) A fuzzy logic model to predict specific energy requirement for TBM performance prediction. Tunn Undergr Space Technol 23:600 608 Alber M (996) Prediction of penetration, utilization for hard rock TBMs. In: Proceedings of the international conference of Eurock 96, Balkema, Rotterdam, pp 72 725 Alber M (2000) Advance rates of hard rock TBMs and their effects on project economics. Tunn Undergr Space Technol 5:55 64 Ataei M, Khalokakaei R, Hossieni M (2009) Determination of coal mine mechanization using fuzzy logic. Min Sci Technol 9:49 54 Aydin A (2004) Fuzzy set approaches to classification of rock masses. Eng Geol 74:227 245 Azimi Y, Osanloo M, Aakbarpour-Shirazi M, Aghajani Bazzazi A (200) Prediction of the blastability designation of rock masses using fuzzy sets. Int J Rock Mech Min Sci 47:26 40 Bamford WF (984) Rock test indices are being successfully correlated with tunnel boring machine performance. In: Proceedings 5th Australian tunneling conference, Melbourne, vol 2, pp 9 22

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