Introduction

In recent years, tunnel boring machines (TBMs) have been widely used in various projects around the world. As the competition among various contractors is increasing, the project engineers have to always search for optimization processes to increase projects’ performance. In this regard, for the TBM, specific energy was one of the main parameters that has been extensively studied for the optimization. The literature shows various laboratory tests using the linear cutting machine (e.g., Abu Bakar et al. 2014; Cho et al. 2013; Eskikaya et al. 2005; Gertsch et al. 2007; Ozdemir et al. 1978; Rostami 1993, 1997; Roxborough and Phillips 1975; Sanio 1985; Snowdon et al. 1982; Tuncdemir et al. 2008; Choi et al. 2014; Ma et al. 2016a, 2016b; Pan et al. 2018a, Gong et al. 2015, 2016a, 2016b, 2016c) and the rotary cutting machine (Farrokh et al. 2015; Qi et al. 2016; Gong et al. 2016b) have been utilized to investigate the relationships between specific energy and cut and cutter geometry characteristics. Besides, numerical simulations have been also widely used to study the issues of specific energy and cutter forces (Innaurato et al. 2007; Liu et al. 2002; Ma et al. 2011; Gong et al. 2006a, 2006b; Labra et al. 2016; Liu et al. 2016a, 2016b, 2016c; Park et al. 2018).

These studies indicate, in order to reach an optimum excavation, the ratio of cutter spacing to penetration (S/p) shall be varied to reach minimum specific energy (SE). At this SE, the rolling force required to generate a unit volume of the excavated rock is comparably lower. One note is that in practice, rolling force is much lower than the normal force (less than 20% of the normal force as noted by Pan et al. (2018a, 2018b, 2019), Thyagarajan (2018), Tumac and Balci (2015), Abu Bakar et al. (2014), Gertsch et al. (2007), Cho et al. (2010), and Balci (2009). This is because the normal force firstly causes the radial cracks to develop beneath the cutters. Then the rolling force dislodges the fractured rock from its place. The energy to create the radial cracks is much higher than the energy to dislodge the fractured rock. This leads to a higher normal force.

For this reason, the rolling force value is not a major concern in performance optimization as long as its value falls within its permissible limit defined by the maximum cutterhead torque. As an example, in an 8.75-m hard-rock TBM project, the rock type was granite and granodiorite with 100–250 MPa uniaxial compressive strength. The normal force on the 17-inch cutters reached around 220 kN which is close to the maximum cutter load capacity; however, the rolling force reached only around 10 kN with a total cutterhead torque of 1250 kNm. This is around 10% of the maximum installed cutterhead torque (14500 kNm) in this project. In the field, the operators try to maximize the TBM penetration up to a point at which the total thrust and/or torque reach a maximum allowable value. This value is usually defined by the TBM project managers to prevent any damage to the main bearing of the cutterhead. One major shortcoming of the laboratory tests is that the number of cuts is limited and it is not possible to observe the actual behavior of the cutters when the over-break or under-break phenomena happen. In reality, the TBM cutterhead cut the tunnel surface several hundred times at a specific set of spacing and penetration. In this case, when a rock bridge is generated and the groove is deepened, the cutter flanks will ultimately force the bridge to break. This will not happen in a couple of cutting actions. One of the major problems in numerical simulations is that the surface of the rock is not preconditioned (a process in large-scale testing to create a rough surface before conducting the main test), and this affects the final results.

In addition to these explanations, specific energy issue seems to create only one part of the puzzle of the TBM performance optimization, and other major design issues are needed to be taken into account (e.g., cutter spacing and the specification of the cutterhead layout design in various ground conditions). In this regard, field data analysis is the best way to enhance such optimization as it relies on the actual data and it covers various conditions that might not be easy to be simulated in the laboratory or by numerical modeling.

In this paper, first, an explanation is presented for the database compiled by the author during the past 10 years to investigate the parameters maximizing the field TBM penetration and advance rate. Second, the correlations between cutter penetration, cutter spacing, uniaxial compressive strength, and rock type are studied to find the range of optimum cutter spacing maximizing TBM penetration. Last, a study is conducted on the designs of the TBMs with a relatively high advance rate to identify suitable layout designs utilized in various rock types. The new findings provided in this study will help the industry to enhance the specifications of hard-rock TBMs during the design phase of a project with a major goal to increase its performance during the phase of operation.

Description of the TBM field performance databases

A field performance database of hard-rock TBM projects has been compiled by gathering information from different sources. This database was set up to include the information of cut and cutter geometry information and to include their influential parameters (e.g., UCS and quartz content) within a geological zone of a tunnel drive. It consists of more than 300 tunnel projects. This database contains TBM diameters ranging from 1.63 to 11.52 m. TBM projects compiled in the database were completed between 1980 and 2015 with a total length of around 1500 km by three types of hard-rock TBMs (open, single-shield, and double-shield) manufactured by 8 different companies. Fig. 1 shows the distribution of the main parameters included in this database. As seen, the range of these parameters shows the database cover the majority of the values that occur in TBM tunneling projects. It is also evident from the distribution curves that the majority of the data are symmetric around the mid-point, meaning that the database information is not skewed towards a certain range of parameters. The boxplots show excavated diameter, UCS, cutter spacing, and cutter penetration have a range of 1.63–11.52 m, 5–350 MPa, 57–105 mm, and 0.8–17.7 mm; an interquartile range of 3.5–5.55 m, 55–140 MPa, 73–83 mm, and 4–7.1 mm; and a median of 4.12 m, 103 MPa, 78.5 mm, and 5.5 mm, respectively.

Fig. 1.
figure 1

The distribution of the main parameters included in the database

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Also, the distribution curves and box plots of total thrust (Th), cutterhead revolution per minute (RPM), power (P), and calendar monthly advance rate (MARc) show they have a range of 1176–20374 kN, 0.6–16.75, 175–3150 kW, and 90–1619 m/month; an interquartile range of 5475–8872 kN, 6–11.5, 596–1200 kW, and 265–587 m/month; and a median of 7120 kN, 9.65, 783 kW, 380 m/month, respectively.

One note to consider is that there are many missing data (parameters) for various tunnel records in the database, which make it heterogeneous. This means that only a limited number of records can be used when considering a certain combination of input parameters, thus reducing the population size used in the statistical analyses. In order to reduce the uncertainty in the database values, the data is cross-checked from multiple sources of information.

Data analysis using the database

Optimum cutter spacing

In order to find the optimum cutter spacing, its variation across its influential factors is studied to find the maximum field cutter penetration. In the following sections, three major influential factors of rock type, uniaxial compressive strength (UCS), and quartz content (Qtz) are studied. In addition, the common range of values for spacing over penetration (S/p) are studied for the range of maximum penetrations in various rock types, quartz contents, and different categories of UCS. It is important to note that the size of cutters in this analysis is 17 inches.

Cutter spacing and rock type

Figs. 2–5 show the correlation between cutter spacing and penetration for four major categories of rock types, including the following:

  • Sedimentary rocks (e.g., mudstone, shale, siltstone, sandstone, limestone, dolomite)

  • Metamorphic rocks (e.g., marble, schist, phyllite, slate)

  • Granitic rocks (e.g., granite, granodiorite, gneiss)

  • Volcanic rocks (e.g., basalt, tuff)

Fig. 2.
figure 2

Correlation between cutter spacing and cutter penetration for sedimentary rocks

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Fig. 3.
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Correlation between cutter spacing and cutter penetration for metamorphic rocks

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Fig. 4.
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Correlation between cutter spacing and cutter penetration for granitic rocks

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Fig. 5.
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Correlation between cutter spacing and cutter penetration for volcanic rocks

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As seen, in all figures, penetration across different spacing categories generally tends to increase, and then the trend direction reverses. It is also seen that the maximum value of the penetration in various categories of rock types coincides with different cutter spacing values. Considering the optimum cutter performance at its maximum penetration, the corresponding cutter spacing values can be identified as the optimum cutter spacing in various categories of rock types as shown in Table 1. In this table, Q3 and Q4 refer to the third and fourth quartiles. If we use the fourth quartile of the cutter penetration to recognize the optimum cutter spacing, it is seen that in sedimentary rocks which are usually softer, the optimum spacing can be raised to 90 mm, whereas in granitic rocks, the optimum spacing is below 85 mm. One note is that considering the rock type as the only parameter to identify the optimum cutter spacing, the achieved range is a bit large; hence; it is necessary to study the effect of other influential parameters to narrow this range.

Table 1. Optimum cutter spacing in various rock types
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Cutter spacing and UCS

Figs. 6–9 show the correlation between cutter spacing and penetration in four major categories of uniaxial compressive strength values, including the following:

  • Below 50 MPa

  • Between 50 and 100 MPa

  • Between 100 and 150 MPa

  • Above 150 MPa

Fig. 6.
figure 6

Correlation between cutter spacing and cutter penetration for UCS below 50 MPa

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Fig. 7.
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Correlation between cutter spacing and cutter penetration for UCS between 50 and 100 MPa

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Fig. 8.
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Correlation between cutter spacing and cutter penetration for UCS between 100 and 150 MPa

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Fig. 9.
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Correlation between cutter spacing and cutter penetration for UCS over 150 MPa

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In these figures, it is also seen that in general, penetration across different spacing categories generally tends to increase, and then the trend direction reverses. The maximum value of the penetration in various categories of UCS values coincides with different cutter spacing values. Considering the optimum cutter performance at its maximum penetration, the corresponding cutter spacing values can be identified as the optimum cutter spacing in various categories of UCS values as shown in Table 2. Similar to the previous section, if we use the fourth quartile of the cutter penetration to recognize the optimum cutter spacing, it is seen that in the category below 50 MPa which refers to softer rocks, the optimum spacing can be raised to 95 mm, whereas in harder rocks with UCS value above 150 MPa, the optimum spacing is below 80 mm.

Table 2. Optimum cutter spacing in various categories of UCS values
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Empirical models to evaluate optimum cutter spacing

In this section, the database is filtered to have the fourth quartile of the cutter penetration in various rock types and UCS categories. The result is considered the optimum rock cutting condition database.

In this database, tunnel diameter ranges from 2.7 to 11.74 m, UCS ranges from 5 to 230 MPa, cutter penetration ranges from 2 to 17.7 mm, and cutter spacing varies from 70 to 91 mm. Hence, the data covers almost the full spectrum of various cutting parameters. This is very important when an empirical formula is meant to be generalized. Table 3 shows the corresponding codes used to represent different categories of rock type and quartz content.

Table 3. Description of various rock type and quartz content categories
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The correlations between optimum cutter spacing and its three major influential parameters of UCS, rock type code, and quartz content code show the optimum cutter spacing decreases when UCS, RT, and Qtz increase. The simple regression formulas are only useful when the data for more robust models (e.g., multiple regression formulas) are not available. In order to evaluate Sopt, with higher accuracy and to consider the combined effects of all discussed parameters, different multivariate regression analyses were run on the database information using Minitab 16. In this study, the filtered database comprises 33 samples (training dataset) which were used for the development of the statistical model, and 10 randomly selected data of TBM tunneling projects which were not used in the development of the model (validation dataset) were considered for the validation process.

The final result is presented in Eq. 1 and Table 4. As seen, the R2 of this equation is relatively high.

$$ {S}_{opt}=87.85-0.0239\ UCS-1.663\ RT-1.027\ Qtz\kern2.25em \left[{R}^2=75\%\right] $$
(1)

where Sopt is optimum cutter spacing in mm.

Table 4. Minitab regression coefficient statistics for Sopt prediction
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The comparison of the predicted versus actual cutter spacing values for both training and validation datasets is shown in Fig. 10. As seen, predicted values are in good agreement with the actual data. The obtained results were evaluated based on the statistical measures such as mean absolute deviation (MAD), root mean squared error (RMSE), relative root mean squared error (RRMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE)(Table 5). The results indicate the error terms are relatively small.

Fig. 10.
figure 10

The comparison between the actual and predicted values for the a training and b validation datasets

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Table 5. Results of the statistical measure for the evaluation of Sopt
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S/p and rock type

In the literature, the optimal spacing over penetration (S/p) is referred to as the combination of spacing and penetration at which the energy consumption becomes lower. This is usually defined based on the results of large-scale laboratory tests (i.e., linear cutting machine or rotary cutting machine tests). Based on these tests, the optimal ratio of spacing to penetration (S/p) generally varies between 10 and 20 for different rocks (Ozdemir et al. 1978; Rostami 1993; Gertsch et al. 2007; Farrokh et al. 2015). In soft rocks with brittle behavior; this is closer to 10, whereas, for hard rocks with brittle behavior, this ratio is closer to 20–25 (as noted by Farrokh et al. (2015) for a granitic rock). As rock becomes more ductile, chip formation at larger spacing becomes more difficult. Hence, lower ratios of S/p are more appropriate for ductile rocks. As an example, Bilgin et al. (2016) showed a range of S/p=10–15 would lead to optimum specific excavation energy in siltstone.

As noted before, specific energy is not a major concern as the rolling force (which is the major component of the specific energy) is commonly low (majorly less than 20% of the normal force as noted by Pan et al. (2018a, 2018b, 2019), Thyagarajan (2018), Tumac and Balci (2015), Abu Bakar et al. (2014), Gertsch et al. (2007), Cho et al. (2010), Balci (2009), and Rostami (1993)) and the performance of the TBMs are not usually limited by the rolling force. In practice, the optimal set of S and p refers to a situation in which the production of the larger chips is higher (e.g., portion of chips with the size of over 2 cm as noted by Farrokh and Rostami (2007)). This can be translated into a situation in which the cutters perform at their maximum penetration for a long period. For this, in order to identify the optimum S/p values, we need to filter the database utilized in the previous section on the basis of the maximum achieved penetration values. In this paper, the database is filtered according to the limits of the fourth quartile of the cutter penetration achieved in various categories of the influential parameters (i.e., UCS, rock type, and quartz content). Fig. 11 shows the variation of S/p across various categories of rock type, quartz content, and UCS.

Fig. 11.
figure 11

Correlation between S/p, rock type, quartz content, and UCS

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Table 6 summarizes the descriptive statistics of S/p in various categories of the noted parameters. As seen, the optimum S/p tends to be lower in softer rocks with lower UCS values and lower quartz content (between 8 and 11.6), while in harder rocks with higher UCS values and higher quartz content, S/p is typically over 15 (between 15 and 26). This is consistent with the results of previous studies (Farrokh et al. 2015; Ozdemir et al. 1978). One note is that in designing optimum spacing and penetration, optimum spacing should be selected first (e.g., by using the optimum ranges discussed in the previous sections). This is because in evaluating the maximum cutter penetration at maximum cutter load capacity, the cutter spacing should be known first. The maximum possible penetration can be evaluated according to the cutterhead operational constraints (e.g., using the Colorado school of mines (CSM) model (Rostami 1997)). When the pair of S and p are achieved, the ratio of S/p is calculated and is checked to evaluate whether it is within its optimum range. If it falls outside its optimum range, it is necessary to adjust the cutter spacing and repeat this process to reach an optimum S/p ratio.

Table 6. Optimum S/p in various categories of UCS values
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Empirical models to evaluate (S/p)opt

Using the optimum rock cutting condition database (filtered database) described in the “Empirical models to evaluate optimum cutter spacing” section, the correlations among major identified influential factors and optimum ratio of cutter spacing over cutter penetration (S/p)opt are investigated.

The correlations between (S/p)opt and its three major influential parameters of UCS, rock type, and quartz content show (S/p)opt increases when UCS, RT, and Qtz increase. In order to evaluate (S/p)opt, with a higher accuracy, different multivariate regression analyses were run on the database information using Minitab 16. The final result is presented in Eq. 2 and Table 7. In this study, the filtered database comprises 55 samples (training dataset) which were used for the development of the statistical model, and 10 randomly selected data of TBM tunneling projects which were not used in the development of the model (validation dataset) were considered for the validation process.

$$ {\left(\frac{S}{p}\right)}_{opt}=4.83+0.04\ UCS+2.486\ RT\kern6em \left[{R}^2=70\%\right] $$
(2)
Table 7. Minitab regression coefficient statistics for \( {\left(\frac{S}{p}\right)}_{opt} \) prediction
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Based on this analysis, among the input variables, Qtz was not statistically significant to the model (p-value>0.05) and was removed from the final formula.

The comparison of the predicted versus actual \( \left(\frac{S}{p}\right) \) values for both training and validation datasets is shown in Fig. 12. As seen, predicted values are in good agreement with the actual data.

Fig. 12.
figure 12

The comparison between the actual and predicted values for the a training and b testing datasets

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The performance of the developed model is also assessed in terms of the values of various statistical measures (Table 8). The results indicate the error terms are relatively small showing a close relationship between the measured and predicted values.

Table 8. Results of the statistical measure for the evaluation of \( {\left(\frac{S}{p}\right)}_{opt} \)
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Layout design study

In order to study the layout design of the TBMs with good MARc values, there was a need to set up a criterion to filter the database to a lower number of projects. For this purpose, the criteria of MARc values over its median are used. In order to account for the tunnel diameter parameter, this database is also divided into nine categories of less than 5 m, 5–10 m, and over 10-m diameter for three types of open TBM (Open), single shield TBM (SS), and double shield TBM (DS). In each category, the distribution of the MARc and its median is used to filter out the lower MARc from the higher MARc. With this criterion, 50 projects are filtered out to be studied as case studies with good performance. The following sections provide data analysis conducted on this reduced database.

Cutterhead layout

Table 9 and Fig. 13 show a categorization of the general layout design configurations of the cutterheads with respect to various identified rock types for the reduced database. In this table, radial layout refers to a pattern in which the cutters are located along specific radial alignments. Evenly distributed layout refers to a pattern in which the free space around the cutters is distributed more or less evenly to prevent having large free spaces in certain areas of the cutterhead (e.g., near the cutterhead periphery). The radial complex layout is a mix of two formerly explained patterns.

Table 9. Categorization of the general layout design with respect to rock type
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Fig. 13.
figure 13

Distribution of the general layout design with respect to rock type

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As seen, for flysch and molasse, because of the extension of the openings towards the center of the cutterhead, the radial and complex radial are more used due to the presence of space constraints. For granite and gneiss, the evenly distributed or complex radial patterns are more used. For tuff and shale with an RMR of over 60–70, the evenly distributed layout is used with great success.

Fig. 14 shows a comparison between the advance rates of different shielded TBMs in various rock types with a similar TBM diameter range (8–12 m). As seen, radial design is used more for flysch and molasses, while evenly distributed is used more for tuff with great success (e.g., 722 m/month for a 12.3 m double shield TBM). In the category of granite and gneiss, the evenly distributed layout is used for hard and blocky grounds with success. As a reference, in the Hallandsas tunnel project, in Granitic blocky ground, both radial and distributed layout are used, and the distributed pattern proved to be a high success in increasing cutter life (i.e., number of hours a cutter excavates before its replacement) and increasing advance rate (Burger and Dudouit 2009).

Fig. 14.
figure 14

The advance rate for TBMs of 8–12-m diameter in different geological conditions and with different cutterhead layouts (distributed for evenly distributed and complex radial; G for granite and gneiss; L, M, and T for limestone, marl, and tuff)

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Bucket number and bucket extension

Table 10 and Fig. 15 show a categorization of major information of cutterhead openings and buckets for the projects in the reduced database.

Table 10. Categorization of the general cutterhead opening design with respect to rock type and TBM diameter
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Fig. 15.
figure 15

Distribution of the percentage of bucket opening with respect to rock type

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As seen, as the TBM diameter increases, the number of buckets increases. The information also indicates that in softer rocks such as molasse, marl, and flysch, the percentage of opening extension shall be well above 50% of the cutterhead radius in order to allow a smooth flow of the excavated material from the cutterhead towards the conveyor belt. The information of this table can be used as a preliminary guideline to allocate sufficient buckets with an appropriate opening extension to maximize TBM performance.

Integrative data analysis for the layout design (Table 9) and opening design (Table 10) shows a larger opening extension limits the random distribution of the cutters. In hard and blocky grounds where the even distribution of the cutters is important, opening extension becomes shorter to allow even distribution of the cutters to crush the free blocks easier (e.g., TBMs used for Hallandsas project (Burger and Dudouit 2009) and Lotschberg project (Classen et al. 2003)). In soft and massive rocks, the even distribution of the cutters is not important as much; hence, the openings are extended towards the cutterhead center to allow higher muck volume handling from the face (e.g., TBMs used for Islisberg and Genova high-speed line tunnels (Herrenknecht web site 2021)). When the cutterhead encounters a mixed face (e.g., stratified hard and soft rocks), a complex radial layout with alternating short and long buckets is used to allow both even distribution of the cutters on the cutterhead and higher muck volume handling capacity (e.g., TBMs used for Adler, Murgenthal, and Perschling tunnels (Herrenknecht web site 2021)).

Number and size of the cutters and manholes

Fig. 16 shows a summary of the information of the number of gage cutters in the curved section of the cutterhead (Ng), number of manholes (Nm), number of total cutters installed on the cutterhead (N), number of center cutters (Nc), and cutter diameter (d) for the reduced database (“Layout design study” section). Among these parameters, the optimum number of gage cutters (Ng) is the most important parameter to optimize the cutting process in the curved section of the cutterhead. This is because, in the peripheral area, the efficient normal force in the direction of the inclined cutters is much lower than the normal force applied to the face cutters.

Fig. 16.
figure 16

Number and size of the cutters with respect to cutterhead diameter

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TBM thrust, torque, RPM, and power

TBM design characteristics include total thrust (Th), cutterhead torque (Tq), power (P), and revolution per minute (RPM). The simple regression analyses conducted to verify the influential factors of these parameters revealed that two major parameters of the total number of cutters on the cutterhead (Ntbm) and cutter diameter (d) are highly correlated with the cutterhead design characteristics.

In the tunneling industry, empirical models are used widely due to their ease of application and due to their practical basis. In order to evaluate Th, Tq, RPM, and P, different multivariate regression analyses were run on the database information using Minitab 16. In this study, the database is randomly divided into a training dataset (with 117 samples) and a validation dataset (with 20 samples). The training dataset was used for the development of the statistical models, and the validation dataset was considered for the validation process. Eqs. 3–6 and Table 11 show the Minitab outputs for the best-fitted models for the evaluation of these design parameters based on different step forward regression analyses. It should be noted that the criterion of p-value less than 0.05 is used to mark the high significance of a parameter in multiple regression analysis and to include it in the final formula.

$$ Th=1.618\ {N_{tbm}}^{0.8373}\ {d}^{1.963}\kern3.75em \left[{R}^2=81\%\right] $$
(3)
$$ Tq={N_{tbm}}^{2.1596}\ {d}^{2.252}/1067\kern3.5em \left[{R}^2=85\%\right] $$
(4)
$$ RPM=5.59\ {d}^{1.393}/{N_{tbm}}^{0.9838}\kern3em \left[{R}^2=77\%\right] $$
(5)
$$ P={N_{tbm}}^{1.1791}\ {d}^{3.146}/438\kern5em \left[R2=74\%\right] $$
(6)

where Th is the total thrust in kN, Tq is the cutterhead torque in kN-m, P is the cutterhead power in kW, RPM is the cutterhead revolution per minute, Ntbm is the number of cutters installed on the cutterhead, and d is the cutter diameter in inch.

Table 11. Minitab regression coefficient statistics for Th, Tq, RPM, and P prediction
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As seen, the coefficients of determination of these formulas are relatively high, making them suitable for a preliminary evaluation of the TBM design characteristics. In these formulas, when Ntbm increases, the total normal force and rolling force capacities of the cutterhead become higher; hence, the installed thrust and torque also become higher. On the other hand, in higher Ntbm, in order to limit the maximum linear speed of the gage cutters, the installed RPM is lowered. For all three parameters of Th, Tq, and RPM, when d increases, these parameters become higher. This is because, for larger cutters, the load and linear speed capacities are higher which allows the TBM to apply higher Th, Tq, and RPM.

The comparison of the predicted versus actual values for both training and validation datasets is shown in Fig. 17. As seen, predicted values are in good agreement with the actual data.

Fig. 17.
figure 17

The comparison between the actual and predicted values for the a training and b validation datasets

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The performance of the developed models is also assessed in terms of the values of various statistical measures (Table 12). The results indicate the error terms are relatively small showing a close relationship between the measured and predicted values.

Table 12. Results of the statistical measure for the evaluation of TBM thrust, torque, RPM, and power
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Discussion

On the basis of the discussed issues in the previous sections for the general hard-rock TBMs’ cutterhead layout design specifications, in order to optimize cutter penetration and TBM cutterhead overall performance, one can utilize the following steps:

  1. 1.

    Calculation of the range of Sopt with respect to rock type, quartz content, and UCS

  2. 2.

    Calculation of Sopt/p range with respect to rock type, quartz content, and UCS

  3. 3.

    Calculation of the range of (S/p)opt using the specified cutter penetration for the project

  4. 4.

    Selection of specific Sopt range for which (Sopt/p) overlaps with (S/p)opt

  5. 5.

    Selection of the optimum cutterhead layout with respect to rock type

  6. 6.

    Selection of the optimum bucket number and bucket extension with respect to TBM diameter and rock type

  7. 7.

    Selection of the optimum number of gage cutters, center cutters, and manholes according to the tunnel diameter

  8. 8.

    Calculation of TBM thrust, torque, RPM, and power

As stated before, in the previous studies, the major goal in the optimization process of TBM performance is set up to reach a specific value of (S/p)opt at which the specific energy is at its minimum value. Minimum specific energy occurs at the minimum rolling force. The experience of applying various rolling force values at various sites shows rolling force variation usually does not change the energy consumption a lot; hence, a complementary criterion is needed to optimize the TBM performance. In practice, maximizing cutter penetration even at a cost of slightly higher energy consumption than the optimum specific energy is acceptable. The criteria, outlined in this paper, have one major goal to firstly evaluate the optimum cutter spacing based on the highest cutter penetration experienced in the field. This can be further enhanced using the new criteria to evaluate (S/p)opt. In addition, it is tried to complement the traditional optimization process with cutterhead layout design characteristics. These are the missing links in the chain of the optimization which were neglected or at least were not discussed deeply in the previous studies. In brief, the current study tries to transfer this major idea that, optimization of S/p, is not enough to optimize the performance, and other design characteristics should be also considered. It is obvious that enhancing proposed strategies need further study in the future, and the author hopes to make a good first contribution in this area.

Conclusions

In this study, with the use of a compiled database of various information on many projects from around the world, an extensive data analysis is conducted to provide optimized information for hard-rock TBMs’ design and performance. Considering a cross-correlation between spacing and penetration in various categories of rock types and uniaxial compressive strength values, the range of optimum cutter spacing maximizing the cutter penetration is identified. Based on the data analyses mentioned, it is found that the maximum cutter penetration in sedimentary, metamorphic, granitic, and volcanic rocks is achieved in the cutter spacing range of 72–91, 71–86, 70–84, and 81–85 mm, respectively. It is also found that the maximum cutter penetration in UCS values below 50, between 50 and 100, between 100 and 150, and above 150 MPa is achieved in the cutter spacing range of 72–91, 71–86, 70–84, and 81–85 mm, respectively.

Once the optimum spacing is selected, the cutterhead design parameters can be evaluated using the provided formulas. As part of the optimization of TBM cutterhead design and performance, the layout design characteristics of TBMs relatively high advance rate are studied in detail. The results show that the radial design is used more for flysch and molasses, while evenly distributed or complex radial patterns are used more for granite and gneiss with great success. For tuff and shale with an RMR of over 60–70, the evenly distributed layout can also be used with a relatively high monthly advance rate (over 400–500 m/month). The data analyses also indicate that in softer rocks such as molasse, marl, and flysch, the percentage of opening extension shall be well above 50% of the cutterhead radius to allow a smooth flow of the excavated material and to increase the TBM advance rate.

In sum, on the basis of an extensive field data and TBM cutterhead design study, using developed tables and formulas, this paper provides a basic guideline for the tunnel industry engineers to select optimum cutter spacing, optimum S/p ratio, number of required buckets, percentage of opening extension, and appropriate layout design characteristics, in order to maximize TBM performance parameters, including cutter penetration and TBM advance rate. The new findings offer a new horizon for the researchers to initiate various types of cutterhead optimization in addition to specific energy in the upcoming field projects and future studies.