study of various models for estimation of penetration rate of hard rock tbms

Tunnelling and Underground Space Technology 30 (2012) 110–123

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Tunnelling and Underground Space Technology

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Study of various models for estimation of penetration rate of hard rock TBMs

Ebrahim Farrokh a,⇑, Jamal Rostami a, Chris Laughton b

a EME Department, The Pennsylvania State University, University Park, USAb Laughton Associates, Texas, Austin, USA

a r t i c l e i n f o

Article history:Received 1 December 2010Received in revised form 28 October 2011Accepted 7 February 2012Available online 21 March 2012

Keywords:Penetration ratePenetration rate per revolutionSpecific penetrationField penetration rateSpecific excavation rate

0886-7798/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.tust.2012.02.012

⇑ Corresponding author. Tel.: +1 814 863 7606; faxE-mail address: [email protected] (E. Farrokh).

a b s t r a c t

Various approaches for predicting penetration rate of hard rock tunnel boring machines (TBMs) havebeen studied by researchers since the early stages of TBM application in the 1950s. These studies resultedin the development of several penetration prediction models. For evaluation and validation of a model, itis important to test its predictive capability on new projects. A model should include parameters formachine specifications and ground conditions. The model validation process can reveal problems thatan existing model may have in providing an accurate estimate for a given combination of specificationsand conditions.

This paper offers a brief review and discusses the capabilities of some of the more commonly used TBMperformance prediction models. To evaluate the accuracy of these models, the predicted rates are com-pared with recorded TBM penetration rates in a database of recently completed tunnels. Comparisonbetween predicted and recorded rates indicates that most of the existing models tend to overestimateTBM performance. This comparison highlights the on-going difficulties the industry continues to experi-ence in estimating penetration rate. Even the use of normalized penetration rate indices has not been ableto provide higher accuracy expected in related predictions.

This paper discusses the development of new models to support an improved level of predictive accu-racy in penetration rate estimating. These models are based on the analysis of a comprehensive databaseof more than 300 TBM projects records. Analyses of performance information within this database pro-vided for the development of simpler models that are focused on quantifying the influence of primaryfactors, such as tunnel diameter, UCS, RPM, and rock type. These new models are introduced to providealternative ways of penetration prediction. These models are especially useful at the planning stage of atunneling project where TBMs can be used. These models also serve to provide secondary checks for othermore in-depth analyses of TBM performance for an initial assessment of required boring time (inverse ofpenetration rate), and an estimate of utilization rate in an activity-based TBM model.

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1. Introduction

TBM performance has a dominant impact on tunnel completiontime and cost. A key component in the successful planning of TBMtunneling is the accurate prediction of TBM performance parame-ters, notably the penetration rate (PR, the rate of TBM penetrationduring boring times) and the advance rate (AR, the rate of TBM pro-gress during a work time period). Over the past few decades, sev-eral studies have been carried out to develop more accurate andcomprehensive TBM performance prediction models. Early appli-cations of TBMs were mainly undertaken in relatively massiverocks. In such rock masses research modelers focused primarilyon evaluating the influence of intact rock properties on PR for a gi-ven set of TBM parameters. As the use of TBMs and related manu-facturing technology has evolved, the range of application of the

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TBM has expanded. TBMs are now frequently used in a wider rangeof rock mass conditions. Since joints and discontinuities within arock mass may impact TBM performance, a need for an improvedpenetration rate predictive model for TBMs operating in fracturedrock units became evident. Many of the earlier models could notaddress the impact of discontinuities on TBM PR. Consequently, at-tempts were made to either modify existing models or developnew models that included rock mass parameters. These modifiedand new models can be categorized into four classes as shown inTable 1. In developing a practical model, researchers focused onincluding the rock mass parameters that were known to have thestrongest influence on TBM performance.

One of the main challenges in developing predictive methodsfor TBM performance is accounting for the interaction betweenTBM and rock mass. To better model the complexity of thisinteraction, some researchers developed new tests and indices thatwere specifically devised for TBM tunneling prognosis. Specialtesting to derive parameters for boreability, drillability, and

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Table 1Empirical or field-based TBM performance prediction models and their advantages and disadvantages.

Example Typical advantages Typical disadvantages

Simple models Graham (1976) � Easy to apply � Might underestimate due to lack ofjoint parameters� Limited range of application

Multiple parametersmodels

CSM (Rostami, 1993, 1997), NTNU (Bruland, 1998),QTBM (Barton, 1999)

� Accounting for both rock mass andTBM parameters� Relying on good database

� Several parameters� Complex relationships� Using uncommon tests

Probabilistic models Laughton (1998) � Accounting for randomness andapproximation

� Lack of detailed information from alike-case tunnel

Computer-aidedmodels

Neural network models (e.g. Alvarez et al., 2000,Alvarez, 2000)

� Relying on good database � Complex underlying structure� Over fitting� Usually not available in public domain

E. Farrokh et al. / Tunnelling and Underground Space Technology 30 (2012) 110–123 111

indentation were all developed to provide for an improved predic-tion of cutter penetration under a given set of TBM–rock interac-tion conditions, such as the one described for NTNU modeling byBruland (1998). Other researchers have gone one step furtherand have attempted to recreate the process of rock fragmentationin a laboratory setting through the use of disc cutters. The use offull scale linear cutting tests, such as those described by Rostamiand Ozdemir (1993), Rostami (1997, 2008), Sato et al. (1991), Sanio(1985), and Ozdemir et al. (1978) provide researchers with an en-hanced ability to match field parameters to deliver more accurateTBM performance predictions. Only a few laboratories around theworld are equipped to perform such tests. Where such testing isnot possible, TBM performance predictions may need to be basedon an adjustment of performance data taken from sites where arock with similar strength properties was bored. These adjust-ments may introduce significant errors into the estimating process.The amount and likelihood of errors being introduced depend onaccuracy of the underlying model assumptions, and the qualityand quantity of TBM related and ground conditions data.

Simple models are easy to use since they include only a few basicparameters (e.g. rock compressive and tensile strength), but theycan only offer a limited range of application; many of the parame-ters that influence TBM performance in more variable ground con-ditions, such as rock mass properties (e.g. RQD and rock type), areunaccounted for in the modeling process. Probabilistic models offera more complex methodology for estimating performance. Thesemodels should only be used when it can be demonstrated thatthe detailed information (e.g. probability distribution functionsfor various parameters) of a similar tunnel is available to supportthe prediction of TBM performance on a new project. These modelsuse performance data collected from similar case histories. If thereare significant differences in ground conditions or technologychoices between the new drive and case histories within thedatabase, substantial errors are likely in using the model. Anotherpotential problem, which is also common for computer-aidedmodels, is that in practice, these models are rarely used for TBMperformance prediction purposes, even though they offer severaladvantages over the other methods (e.g. having a higher correlationcoefficient and taking complex formula structures whereverneeded).

Multiple parameters models use more project specific data(compared to simple models), and they are easier to apply (com-pared to probabilistic and computer-aided models). Therefore,these models are among the most-favored models used in TBMperformance prediction. This paper compares the results of com-mon TBM performance prediction models through the evaluationof their predictive abilities. For this purpose, a testing database of17 recent tunnel projects was used to represent the new projects.This database includes information on key performance parame-ters for various geological zones encountered along the tunnel.The paper also discusses the development of a new model that

can be used for the estimation of penetration rate. The new modelis generated on the basis of the analysis of data from more than300 TBM projects records (named as general database) fromaround the world. In other words, the TBM performance recordsin the general database are used to generate the new formulaeand the testing database projects are treated as new projects wherean estimate is needed (i.e. the results of predictions are comparedwith the actual field performance to evaluate the validity and accu-racy of the predictions and to objectively assess the predictivecapabilities of a proposed set of new formulas).

2. Description of the TBM field performance databases

Two separate databases were compiled from the review of var-ious technical sources. The first database (general database) wasassembled with the objective of developing a new performancemodel. The second database was developed to support model val-idation work.

2.1. General database

The database on TBM field performance contains different levelsof information which defines the tunnel, rock mass conditions, andTBM performance parameters over the full length of a tunnel drive,within discrete geological zones, or short tunnel reaches. The gen-eral database contains data on more than 260 tunnel projects andincludes over 300 data sets. This database is the continuation of anexisting database developed at the University of Texas at Austin(UTA) (Nelson et al., 1994). Additional projects were added to theoriginal sets from other available sources found in the literature.This database contains diameter from 1.63 to 11.74 m. TBM pro-jects compiled in the database were completed between 1966and 2004. An effort was also made to complete missing data fieldswithin the database by checking many sources and published liter-ature. In comparison to the original UTA databases, the updateddatabase contains more detailed information and several new,more recently completed tunnel projects. This new database in-cludes bored tunnel records with a total length of over 1500 km.Table 2 lists main parameters included in this database.

The original database of Nelson et al. (1994), included data on640 TBM projects. Data from the UTA database was compiled fromdiverse sources, including literature survey, manufacture records,and detail project records. Parameters for the database were re-corded either as directly reported in documents or as estimatedbased on references (Laughton, 1998). The original database con-tained four levels of information. The first three levels contain pro-gressively more detailed information for a tunnel project overshorter spatial increments. Each zone is categorized based on a gen-eral geological structure and similar rock material characteristics.This increased level of detail continues down to a mining cell, which

Table 2Summary of the parameters included in the developed database.

Layout parameters Rock mass parameters Equipment parameters Performance parameters

Project Name Rock type TBM type Project timeLocation Geological variability General spec. of TBM Support TypeApplication type Quartz content General spec. of BU Penetration RateTunnel diameter UCS TBM condition Advance RateZone length RQD/CFF Type of mucking system Utilization factorSlope Water condition Thrust Cutter wear rateConstruction access Extreme mining areas Power Activity time distributionTunneling hole through year Torque

RPMCutter sizeCutter diameter

112 E. Farrokh et al. / Tunnelling and Underground Space Technology 30 (2012) 110–123

is defined as a 10 m length within the tunnel. The fourth databaselevel provides information required to model the TBM mechanicalavailability and the performance of key mining cycle activities;penetration, mucking and support installation. A schematicrepresentation of the first three database levels is shown in Table3. Part of the general database used in current study is a subset ofUTA database where more complete entries were available.

Each data level can be linked to the other levels by means of aDrive Reference Number (DRN) that is unique for each tunnelingproject. For this study, only level two of the database was used.The data in this level contains average parameters for the zonesof the tunnel or the different geological units along the tunnel. Itcontains 209 records and includes data on tunnel geometry, TBMcharacteristics, and geological parameters reported as numericaldata, ranks, and categories. This database account for a total lengthof over 800 km bored length.

Table 3Database levels and schematics of distance increments in each level (modified from Nelso

Database level Distance increments

Level 1Geology description for the whole tunnel

The whole tunnel drive

Level 2Geological variation characterized by zoneparameters

Tunnel

zone

Zone 1

Level 3Geological variation characterized by zone and unitcell parameters

Unit cell within a tunnel

zone

U

This database was one of the first databases compiled for thepurpose of predicting TBM advance rate. The database parametersdefined rock type and related rock mass parameters referenced byreference to the recommendations of the International Society ofRock Mechanics (ISRM), including the Basic Geotechnical Descrip-tion (BGD), and common rock mass classification systems (Laugh-ton, 1998). It should be noted that in categorizing the rock types inthis database, only the dominant rock type in each zone was noted.

2.2. Testing database

To verify the predictive capability of existing or new models atesting database including 17 hard rock TBM projects was devel-oped. These projects provided detailed information for TBM perfor-mance in each geological zone. TBM diameter for these projectsranged from 2.6 m to 11.8 m. As would be expected, the format

n et al., 1999).

Tunnel Drive

Zone 2 Zone 3 Zone 5Zone 4

nite Cell within Tunnel Zone


and the extent of reported TBM operational parameters and geo-logical data varied significantly from project to project. Table 4shows the summary information reported for these projects, nota-bly including description of the TBM type, diameter and sitegeology.

3. Objective or target parameter

A general review of previous TBM penetration rate modelsshows that, depending on the analytical approach adopted, differ-ent target penetration parameter were used to support the model-ing of TBM penetration rate. Typically, the models predictperformance parameters such as PR and PRev (penetration perrevolution of the cutterhead). Other indexed parameters used insome of the prediction models include Specific Penetration (SP),and Field Penetration Index (FPI). These parameters are definedin Table 5.

The purpose of using SP (Alber, 2000) is to combine the thrustand cutter head rate of rotation with penetration rate so that thepenetration rate can be normalized against variations in rock massstrengths (As shown by Alber, 2000). Alber (2000) noted a generalcorrelation between rock mass strength and SP without includingany strength factor for the correlation. FPI was also introduced tobe a normalized measure of penetration rate, specified in termsof applied thrust on cutters for a specific PRev in different geolog-ical conditions (Hamilton and Dollinger, 1979; Nelson et al., 1983;Klein et al., 1995). Nelson et al. (1983) offered a relationship be-tween FPI and total hardness (Ht). Klein et al. (1995) presented cor-relations between FPI and intact rock and rock mass parameterswith the primary goal of presenting different classes for differentground conditions in four tunnels. More recently, Hassanpouret al. (2009a,b) and Khademi et al. (2010) used FPI as an objectivevariable in a multiple regression setting to offer a new way of esti-mating the rate of penetration. In fact, SP is the inverse of FPI. Theadvantage of using these combined or normalized parameters isthat they can be applied on machines of various sizes. These

Table 4General information of the tunnel projects in testing database.

No. Project name Tunnel length(km)a

TBM type

1 Ghomroud (Iran) 22.8 DS2 Karaj (Iran) 15.7 DS3 Zagros (Iran) 5.3 DS4 Golab (Iran) 0.7 DS5 Maen (Italy) 1.7 Open6 Pieve (Italy) 6.3 DS7 Varzo (Italy) 6.2 DS8 Queens (USA) 0.2 Open9 Milyang (S. Korea) 0.6 Open

10 Manapouri (Newzealand) 1.7 Open11 S. Manhattan (USA) 5.6 Open12 KCRC D 320-First Tube (Hong Kong) 1.3 Mixed

Shield13 KCRC D 320-Second Tube (Hong Kong) 1.4 Mixed

Shield14 Frasnadello-Pilot (Italy) 1.6 Open

15 Antea-Pilot (Italy) 0.7 Open16 Frasnadello-Main (Italy) 1.6 SS

17 Antea-Main (Italy) 0.7 SS

Total 73.6

DS: double shield, SS: single shield.a With available data.b Data from authors (Farrokh et al., 2006, 2011; Farrokh and Rostami, 2007, 2008, 20

parameters also account for the rate of cutterhead rotation(RPM), which is typically directly related to cutterhead diameter.

Stevenson (1999) introduced Specific Excavation Rate (SER) asthe excavated volume per revolution divided by thrust per cutterto combine SP and the tunnel cross-sectional area. One benefit ofusing a normalized penetration rate is to allow the inclusion of aTBM-–rock mass interaction factor. Laughton (1998) maintainedthat SP is not an appropriate parameter for TBM performance pre-diction purposes as it does not reflect the true non-linear nature ofthe PRev:Fn (penetration-cutter load) trend. Fig. 1 shows a typicalnonlinear relationship between PRev and Fn (cutter load) and atypical assumption for SP (straight line). As can be seen, the slopesof these two lines might be different drastically. As such, the accu-racy of TBM penetration rate estimates based on SP or FPI may con-tain a significant error if an SP from one tunnel drive is useddirectly to predict TBM performance on a new tunnel drive wherea different cutter load is to be applied. This refers to the fact thatfor the estimation of the actual PR from these indices, the modelrequire an assumed level of the cutter load. However, the applica-bility of a certain cutter load on a given TBM requires a close exam-ination of TBM power and torque capacity. In other words, thecutter load rating of a given cutter size cannot be reliably usedfor PR estimation since in reality the TBM may not have sufficientpower to turn the head at the required thrust level. The differencebetween the results are especially high if the applied cutter load isnear the range of the threshold thrust where there is a change ofslope in the PRev-Fn curve.

Table 6 shows some examples of the significant differences thatcan exist between nominal cutterhead thrust and RPM capacitiesand operating values in various geological settings. Even in rela-tively hard rock (Diorite, Meta-Volcanic) common operating thrustand RPM values can be far away from the design values. Part of thereason for such large discrepancies is related to the fact that thereare interactions between the strength of the rock, the thrust level,and TBM cutterhead design parameters. This issue is addressed inthe Colorado School of Mines (CSM) model (Rostami and Ozdemir,1993; Rostami, 1997). This model was based on the results of

TBM diameter(m)

Geology Reference

4.5 Metamorphic rocks b

4.65 Pyroclastic rocks Hassanpour, 20096.73 Limestone, Marl, Shale Hassanpour, 20094.5 Diorite, Schist b

4.2 Meta gabbro, Meta basite, Schist Sapigni et al., 20024.05 Schist, Granite, Diorite Sapigni et al., 20024.05 Gneiss Sapigni et al., 20027.06 Granite Ramezanzadeh,2.6 Granite, Andesite Kim, 2010

10.05 Gneiss Kim, 20103.84 Gneiss, Schist b

8.75 Granite Ramezanzadeh, 2005

8.75 Granite Ramezanzadeh, 2005

3.9 Dolomite, Limestone andArgillite

Barla and Pelizza, 2000

3.9 Dolomite Barla and Pelizza, 200011.8 Dolomite, Limestone and

ArgilliteBarla and Pelizza, 2000

11.8 Dolomite Barla and Pelizza, 2000

09).

Table 5TBM penetration rates.

Description Typical unit Formula

PR Penetration rate m/hPRev Penetration rate per

revolutionmm/rev (1000 PR)/(60

RPM)SP Specific penetration (mm/rev)/(kN/

cutter)PRev/Fn

FPI Field penetration index (kN/cutter)/(mm/rev)

Fn/PRev

SER Specific excavation rate (m3/rev)/(kN/cutter)

A � SP

A: Tunnel cross section area, Fn: Normal force per cutter.

PRev, mm

Line Slope=

SP, mm/kNPRev Predictor

Operating Point

Critical Thrust Fn, kN

Thrust InterceptValue

Fig. 1. Relationship between penetration per revolution (PRev) and cutter normalforce (Fn) (modified from Laughton, 1998).

Table 6TBM operational parameters in different settings.

Tunnel name Rock type RPM Fn (kN) (Gross)

Designmax

Applied Designmax

Applied

GhomroudIII&IV

Limestone 12 11 �220 170

GhomroudIII&IV

Slate 12 6 �220 90

GhomroudIII&IV

Meta-Volcanic

12 10.3 �220 130

GhomroudIII&IV

GraphiteSchist

12 8 �220 100

Karaj Tuff 11 7 �220 150Zagros Limestone 11 6 �220 100Golab Diorite 12 8.6 �220 125Maena Serpentinite 11 �220 155Milyang Granite 13 10 �195 160Queens Granitic

Gneiss8.3 8.3 �320 250

a Obtained from Sapigni et al. database (2002).


full-scale cutting tests, where the relationship between PRev andFn follows a curve that is closer to actual cutting behavior of a disccutter.

The different relationships between the rock strength, cutterthrust, and TBM parameters were very well defined by Frenzelet al. (2008) and are shown in Fig. 2. A key reason for observinglower thrusts in the field might be related to the TBM encounter-ing weaker rock mass conditions. In this regard, a big problem forshielded TBMs is that the Fn value used in the predictive calcula-tion is a gross value and does not include any friction losses. The

net Fn delivered to the cutterhead may be significantly less thanthe nominal cutter load calculated from applied machine thrust.As Laughton (1998) notes, SP and FPI are preferred for the evalu-ation of TBM performance in the field, where TBM is operatedover the critical thrust (e.g. massive rocks with higher UCS value).In softer, more jointed rock masses, using these thrust-normal-ized indices are not necessarily the critical performance factorsand there are several other parameters that can come into play,which overshadow the effects of the TBM operational thrust orcutterload. Therefore, normalized factors, FPI and SP, should beused with caution before providing a penetration rate estimatefor a new project.

Meanwhile for the development of alternative models, PR canbe used in statistical studies to allow for an analysis of the realrelationship between the various parameters, including TBM diam-eter. This is the approach that is used in the following sections ofthis paper.

4. Evaluation of existing penetration rate models

The purpose of the study described in this section is to test thecapability of some of the more commonly used or recently devel-oped TBM performance prediction models as applied over a rangeof tunnel diameters and rock mass conditions. Table 7 summarizesmore commonly used TBM performance prediction models. Thesemodels have been developed since the early 1970s.

Among the models in Table 7, 12 models (with given formulae)were selected for evaluation. These models were selected based onthe availability of the required information logged in the testingdatabase of TBM field performance. The graphs in Fig. 3 comparethe actual and predicted PRs for the selected models. A 45� dashedline (1:1line) represents the line where predicted and actual ratesare the same. Points plotted above the dashed line indicate anover-estimate of PR by predicting models.

It should be noted that the upper cluster of the CSM model plot isattributed to pump limitations (e.g. max. propel rate of the hydrau-lic thrust cylinders during the stroke extension). This means thatwith the proper information on the applied cutter load, the esti-mated PR can be adjusted. The three models of Cassinelli et al.(1982), Innaurato et al. (1991), and Yagiz (2002) tend to underesti-mate TBM performance. One potential problem of these particularmodels may be related to the absence of any parameter that wouldaccount for a variation of tunnel diameter. The absence of a diame-ter parameter may be a result of the limited number of casehistories that were referenced in the development of these models.The penetration rates of larger diameter TBMs are generally lowerthan those of smaller TBMs. Yagiz (2002) modified the CSM modelusing field data collected on the performance of a relatively large-diameter TBM tunnel (Queens Tunnel with the diameter of7.06 m) and does not include a parametric adjustment for TBMdiameter. As such, the corresponding graph in Fig. 3 shows the var-iation of this model for the Queens TBM or its equivalent in otherground conditions. The results of the remaining comparisonsshown in Fig. 3, indicate that these models also generally tend tooverestimate the PR. The percent differences between predictedand observed values can be more than 100%. Some likely causesof the tendency of models to overestimate PR are listed as follows:

� Limited database use in the development of the models.� Exclusion of influential parameters, such as tunnel diam-

eter, from the model due to the limited range of TBMdiameters in the original databases used for developmentof the models or the omission of key physical relation-ships between TBM parameters (i.e. RPM and hence PRare strongly related to TBM diameter).

Fig. 2. Operating limits of a TBM with 1700 disc cutters at different rock strengthsafter Frenzel et al. (2008).

Table 7TBM performance models.

Author/model Year Comment

Tarkoy 1973 For limestone, shale, sandstone, quartzite, orth0.076–3.716 m/h

Roxborough andPhillips

1975 For UCS of 70–205 MPa, Tensile strength of 5.5

Graham 1976 PRev = 3940 Fn/UCSOzdemir et al. 1978 Based on The Robbins Company data in granitFarmer and Glossop 1980 Based on six tunnel projects’ data. PRev = 624Cassinelli et al. 1982 Using RSR. PR = -0.0059 RSR + 1.59Snowdon et al. 1982 A Formula to demonstrate relationship amongLislerud et al. 1983 Based on excavation records in Norway in shaNelson et al. 1983 Based on information of four tunnels in sedimBamford 1984 Based on data of tunneling in claystone on theSanio 1985 Effect of foliation on penetration rateHughes 1986 For sandstone and penetration of up to 10 mmBoyd 1986 On the basis of cutterhead power, specific eneSato et al. 1991 Followed Sanio’s work and used the same appInnaurato et al. 1991 Updated version of the method presented by C

provided on the number of bored tunnels. PR =Rostami and

Ozdemir1993 CSM model. On the basis of LCM tests

Sundin andWanstedt

1994 For granite, micaschist, gneiss with UCS range

Howarth 1986 Based on information of excavation in sandstoRostami 1997 Updated CSM model. On the basis of LCM testBruland 1998 NTNU model. PRev = [Mekv/M1]b

Barton 1999 QTBM model. PR = 5 Q�0:2TBM

Cheema 1999 Based on information of one project to modifyAlvarez 2000 Neuro-Fuzzy modelingYagiz 2002 Based on information of one project to modify C

BI = 0.0157 PsRibacchi and Lembo

Fazio2005 SP = 250 UCS�0:66

cm

UCScm = UCS exp((RMR � 100)/18)Ramezanzadeh

et al.2005 Based on information of 11 projects to modify

Gong 2005 Based on information of one projectHassanpour et al. 2009a and

2009bBased on information of two projects. FPI = 0.4

RMCI = 0.01 UCS RQD2/3

Khademi et al. 2010 Based on information of one project. FPI = 4.16

Nomenclature: PR: penetration rate, PRev: penetration per revolution, SP: specific penetraUCS: uniaxial compressive strength of intact rock, TS: tensile strength, UCScm: rock masRQD: rock quality designation, Mekv: equivalent cutter thrust (kN/cutter), M1: critical cutcoefficient, a: the angle between the tunnel axis and the planes of weakness, Ps = peak slrock fracture index, BI: brittleness index, Jc: RMR joint condition partial rating, QTBM: Baindex, LCM: linear cutting machine.


� Use of inappropriate, inferred, estimated, or inaccurateparameters.

� Lack of adequate TBM operating information, especially inweaker rock masses.

� Use of too many parameters. In applying the model inter-actions between the many parameters may result in unre-alistic result. The need for multiple parameters may alsooblige the estimator to guess at multiple missing inputvalues.

� The mere fact that the predictions are based on themachine’s installed capacities (cutter load, power, etc.)whereas in reality machines are operated at lower thrustlevels to cope with other field parameters.

To provide an example of the latter problem, consider the modelintroduced by Khademi et al. (2010). The bivariate analysis showsthat UCS by itself accounted for 70% of the variation of the FPI. Add-ing three more parameters led to only a marginal increase in R2

from 0.7 to 0.77. This means that the effects of the additionalparameters were largely overshadowed by UCS. It is worth noting

oquartzite, schist, dolomite with total hardness of 2–242 and penetration rate of

–13.8 MPa, Cutter tip width of 11.4–19 mm, Cutter diameter range 382–432 mm

e, quartzite, schist, and shaleFn/TS

normal force, rolling force and penetration per revolutionle, limestone, gneiss, basaltentary rocksThompson project in Australia for bedding spacing range 0.3–0.5 m

/revrgy, and tunnel cross section arearoach, but on a rotary cutting machineassinelli, see above. Based on 112 homogeneous sections. No information isUCS�0.437 � 0.047 RSR + 3.15

65–200 MPa, point load range 1–9 MPa, CAI = 1.9–5.9, toughness of 2.2–3.3

ne and marble with Fn = 3.16 kN and RPM = 14s. PRev = f (Fn, Fr)

CSM model

SM model. PR = 0.859 + RFI + BI + 0.0969 PRevCSM; RFI = 1.44 Log(a) � 0.0187 JS;

CSM model. PRev = PRev0:37CSM exp(1.8–0.0031 JS-0.0065a)

25 RMCI + 11.28

1 + 0.091 UCS + 0.077 RQD + 0.117 Jc + 1.077 Log(a)

tion rate, FPI: field penetration index, Fn: cutter normal force, Fr: cutter rolling force,s uniaxial compressive strength, RSR: rock structure rating, RMR: rock mass rating,ter thrust (kN/cutter), that is necessary thrust to achieve 1 mm/rev, b = penetration

ope index (obtained from punch penetration test), Fs/Js = fracture/joint spacing, RFI:rton rock mass quality rating for TBM driven tunnels, RMCI: rock mass cuttability

Fig. 3. Results of comparison for the selected models.


that even with very detailed information on selected sections of atunnel drive; some models still fall short of yielding satisfactoryresults. From this perspective, although all these models werecalibrated to field performance data at one level or another, theirpredictive power is limited. These models can only be expected to

provide realistic predictive results when the new set of conditionsis very similar to the conditions on which the models were based.

The Neuro-Fuzzy model developed by Alvarez et al. (2000) isanother analytical approach for PR prediction. This model usedfour major rules as described by Alvarez et al. (2000). Each rule


is a linear combination of five parameters. These rules were ob-tained based on the Takagi–Sugeno fuzzy method (Takagi and Su-geno, 1985) in combination with the least square method. Fig. 4depicts the recreated Neuro-Fuzzy model rules (r1–r4) using Excelspreadsheet formulae expressions:

� r1: If CFF is low and UCS is medium and RPM is medium andThr/c is medium and Dsize is large, then PR = �0.7288 �CFF � 0.01444 � UCS + 0.1076 � RPM + 0.001287 � Thr/c + 0.006937 � Dsize + 0.937.� r2: If CFF is medium to high and UCS is medium and RPM is high

and Thr/c is medium and Dsize is medium, then PR = �1.95 �CFF + 0.05495 � UCS + 0.13 � RPM + 0.03825 � Thr/c + 0.04546 � Dsize � 24.65.� r3: If CFF is very high and UCS is very low and RPM is low and

Thr/c is low and Dsize is small, then PR = �9.639 � CFF +0.1399 � UCS + 3.332 � RPM + 0.0511 � Thr/c � 0.009726 � Dsize + 1.319.� r4: If CFF is medium to high and UCS is high and RPM is high

and Thr/c is low and Dsize is large, then PR = �1.459 �CFF + 0.06171 � UCS + 1.943 � RPM + 0.3512 � Thr/c � 0.2676 �Dsize � 8.085.

In these formulas, CFF is the core fracture frequency, UCS is theuniaxial compressive strength in MPa, RPM is the cutterhead revo-lutions per minute, Thr/c is the thrust per cutter in kN, and Dsize isthe cutter diameter size in mm. The calculation methodology isexplained in detail in Alvarez and BabusÏka (1999).

When applying these rules within the testing database, therules applied in isolation do not generate reasonable PR values.The application of rules number 2–4 are particularly suspect asthey yield results that are mostly negative. Furthermore, for certainset of parameters this model yields negative value (see Fig. 5). Theoccurrence of negative results may indicate that although the fuzzy

Fig. 4. Recreated example of the Neuro-Fuzzy model rec

logic models may yield better overall performance accuracy, theinterpretation and use of such models might be more problematic.

5. Proposed new model

Two different objective parameters were used to develop a newmodel for the estimation of TBM penetration rate under a given setof ground conditions. The first analysis involved the analysis ofpenetration per revolution (PRev). Obviously, the penetration rate(PR) can be obtained from multiplication of PRev and cutterheadrevolution per minute (RPM). The second analysis entailed the di-rect analysis of penetration rate (PR). As noted at the beginning ofthe paper, the different tunnel records within the database wereheterogeneous. Only a limited number of records could be usedin performing the above analyses, thus reducing the populationsize that was used in the statistical analyses. As for statistical pro-cess used in this study, the first step involved bivariate analysesbetween penetration rate and other parameters to identify influen-tial parameters. Second step included multiple regression analysesto develop a best fit combination of key parameters that demon-strate the strongest correlation to PR. Finally, the prediction capa-bility of the new model was verified using the testing databaseinformation.

5.1. Modeling approach

The compiled database includes numerical, ranked, and cate-gorical data. Dealing with categorical data in the statistical analysiscan be problematic. In one form, it is possible to assign differentnumbers to different categories to convert the qualitative ordescriptive ranking information into quantitative values (ranking)as used by Alvarez et al. (2000). Fig. 6 shows a histogram of TBMdiameters in the database. As can be seen, the 3–6 m diameter

reated in an Excel sheet from Alvarez et al. (2000).

Fig. 5. An example of the recreated Neuro-Fuzzy model (Alvarez et al., 2000) yielding negative value.


range is common for a large number of projects, and it is the mostpopular range in the database. The graphs in Figs. 7–9, show thattunnel diameter is related to TBM characteristics and performance.

PR and PRev were chosen as the objective parameters. Theseparameters are commonly reported more than the other perfor-mance measures such as FPI, SP, and SER. Conversion of the PRevvalues to FPI or SP based on machine’s installed power and cutterload could be erroneous due to operation of the machines belowtheir nominal capacities and lack of measured parameters for cal-culation of these indices. Fig. 10 depicts the correlation betweensome of the most important dependent variables and the penetra-tion rate (PR) or penetration per revolution (PRev). Coefficients ofdetermination (R2) of the bivariate analyses (Fig. 10) show thatPR-UCS has the strongest correlation. It should be noted that‘‘R2(adj)’’ is the adjusted R2 for the number of parameters in themodel, and the number of data points used for regression analysis.

Fig. 6. Histogram of tunnel diameter in the database.

As can be seen in Fig. 10, PR and PRev are at maximum at lowerUCS levels. As UCS increases, PR and PRev decrease. This is a logicaltrend and is in agreement with several research studies such asthose reported by Laughton (1998), Robbins (1992), Hassanpouret al. (2009a,b), and Khademi et al. (2010). However, this is notthe whole story since with lower UCS values, the operators tendto reduce the thrust thus the correlation in the graphs is not asstrong as it should truly be.

Since different rock textures (cementation and grain size andshape) affect the penetration rate, such properties should also betaken into account in PR studies. In these analyses, seven rock typecategories, as proposed by Hoek and Brown (1980) and Stevenson(1999), were adopted. These rock types are listed in Table 8. Thefirst four classes are for ‘‘Sedimentary Rocks.’’ The fifth, sixth, andseventh classes are for ‘‘Metamorphic Rocks, Granitic Rocks, andVolcanic Rocks’’ respectively. It should be mentioned, Gneiss

Fig. 7. Relationship between installed or nominal torque and tunnel diameter.

Fig. 8. Relationship between nominal RPM and tunnel diameter.

Fig. 9. Relationship between installed or nominal thrust and tunnel diameter.


(GN) is inherently metamorphic, but it is typically closer to granitein terms of its behavior, especially where foliation is less pro-nounced. For this reason, it was categorized as GN in this analysis.

As can be seen in Fig. 10, when the rock type is taken into con-sideration in the analysis, a good relationship can be establishedbetween rock strength and PR/PRev. The graphs show that in gen-eral a higher PR/PRev is achieved in sedimentary rocks, and a lowerPR/PRev is achieved in igneous rocks. These results are in agree-ment with the results proposed by Laughton (1998) and Robbins(1992) for different rock types.

Core fracture frequency (CFF) data was the only rock massparameter that was available for all the records from Nelsonet al. database (1994) and some of the records of the general data-base. Basically, this factor is in close relationship with RQD andrefers to the frequency of rock mass fractures. Table 9 shows theapproximate relationship between CFF and RQD and the numericalcodes used for subsequent analyses.

5.2. Multivariate regression analysis

Multivariate regression analyses with PRev as the objectiveparameter were performed using Minitab 16 (Minitab Inc., 2010).These analyses allowed PR results to be projected over differentmachine sizes, with PRev being multiplied by RPM to determinePR. Based on these analyses, best-fit linear regressions were

identified and reported. A transformation of the objective parame-ter was made wherever it was necessary to correct for normality inthe regression model (i.e. Ln(PRev) for Eq. (1), and Ln(PR) for Eq.(3)). The results of these analyses are shown in Fig. 11 and Eq. (1).

PRev¼Expð0:41þ0:404 �D�0:027 �D2þ0:0691 �RTc

�0:00431 �UCSþ0:0902 �RQDcþ0:000893 �FnÞ R2¼63% ð1Þ

PR ¼ PRev � RPM � 601000

ð2Þ

where D is tunnel diameter in m, RTc is rock type numerical code(1 for G and GN, 2 for MV, 3 for SLK, 5 for C), UCS is uniaxial com-pressive strength in MPa, RQDc is RQD numerical code (Table 9),and Fn is disc cutter normal force in kN.

It should be noted that at larger diameters, the TBM face areaincreases significantly allowing for a more efficient cutting process,higher penetration per revolution can be achieved. Since the casehistories typically do not report the operating thrust; we assumethat the TBMs operated close to the design thrust values – a real-istic assumption in harder rocks. The installed thrust capacitywas used in the calculation of thrust per cutter (Fn).

Eq. (2) can be used to convert PRev to PR. Fig. 12 depicts com-parative results of Eqs. (1) and (2) results with the actual valueswithin the test database.

As can be seen in Fig. 12, the modeled PR values show good cor-relation with actual values. Furthermore, the new model yieldsgood improvement in predictive capacity over the other modelsevaluated. Fig. 13 shows the regression analysis performed onthe general database for PR evaluation using the logarithm of thePR (Ln(PR)). The resulting PR can be expressed by a power functionas in Eq. (3).

The regression equation is:

PR ¼ Fn0:186 � RQD0:133c � RT0:183

c � RPM0:363 � D5:47 � expð0:046 � D2Þ5:64 � UCS0:248 � expð1:58 � DÞ

R2

¼ 58%

ð3Þ

where D is tunnel diameter in m, RTc is rock type code (1 for G andGN, 2 for MV, 3 for SLK, 5 for C), UCS is uniaxial compressivestrength in MPa, RQDc is RQD code (Table 9), Fn is disc cutter nor-mal force in kN, and RPM is revolution per minute.

Eq.(3) was obtained by performing a log transformation of mostof the model parameters. Fig. 14 shows comparative results of Eq.(3) with actual values from the testing database.

The comparison between the results in Figs. 12 and 14 indicatesthat, overall, PR formula yields better results and using normalizedpenetration rates for the purpose of TBM performance predictionmay yield less reliable results, even when PRev is estimated andadjusted with the use of real RPM. It should be noted that Eqs.(1) and (3) may produce higher errors in estimating PR values inhighly jointed rock masses due to lack of exact RQD value or lackof other rock mass parameters (e.g. joint orientation).

In general, the proposed new models offer better results thanthose of the previously discussed models and indicate a potentialfor better PR prediction. Further study of this approach will requirethe development of new databases that report additional TBM andground condition factors. This effort will require worldwide coordi-nation and close collaboration between project partners, includingcontractors, engineers, and owners. Data to be reported shouldinclude:

– Recent tunnel information for various TBM types.– Detailed rock mass classification information such as RMR or

RQD, Q, and GSI for a range of tunnel sizes and rock types.

Fig. 10. Correlation between PR/PRev and other parameters (rock type abbreviations from Table 8, �for rock type refers to records with missing rock type, �for PRev refers tooutlier).

Table 8Rock type categorization in database (modified from Hoek and Brown, 1980).

Rock type Code

Claystone, mudstone, marl, slate, phyllite, argillite CSandstone, siltstone, conglomerate, quartzite SLimestone, chalk, dolomite, marble LKarstic Limestone KMetamorphic rocks such as gneiss and schist MCoarse igneous such as granite and diorite GFine volcanic such as basalt, tuff, and andesite V


– Detailed specification for various TBM types, for a range oftunnel sizes and rock types.

– Recording and use of actual operational parameters for a rangeof tunnel sizes and rock types.

6. Discussion and conclusions

Comparisons between predicted and actual TBM performanceindicated that most of the existing predictive models, especiallythe simple ones, cannot offer accurate estimates of TBM perfor-mance for new projects. A study of these models indicates thatusing more parameters in a model will not always guarantee im-proved results due to lack of inherent limits of the initial models.

In some cases, existing models do not include important param-eters; as such they cannot adequately distinguish between the

Table 9CFF categorization.

CFF Code Description CorrespondingRQD range

Less than 8 fractures/m S or 1 Low frequency 90–1008–12 fractures/m M or 2 Medium frequency 60–9012–16 fractures/m H or 3 High frequency <60

Fig. 13. Results of linear regression analysis for PR (response is Ln(PR)).

Fig. 11. Results of linear regression analysis for PRev (response is Ln(PRev)).


ground conditions and job constraints that control TBM perfor-mance. To achieve more accurate estimates, a database of TBMfield performance was compiled and subjected to a statistical anal-ysis in order to derive new equations and models for improvingperformance prediction for hard rock TBMs. The proposed modelsoffer better accuracy than existing models. Part of the reason forthe model improvement may be related to the ability to utilize alarger database of TBM field performance records that includes awider range of tunnel diameters and ground conditions. Limitednumbers of rock mass parameters in the database and the lack ofaccurate records of actual TBM operational parameters are amongthe reasons for the scatter in the results of the new model. Expand-ing the existing databases with more parameters and adding moredetails on the different geological zones should allow for moreimprovement in the results and a higher degree of accuracy andreliability in model prediction.

Fig. 12. The comparative results of Eqs.

The analyses of the available data indicate that certain set ofavailable parameters including, tunnel diameter, UCS, RPM, androck type, account for approximately half of the PR and PRev vari-ation. These analyses further indicate that UCS is the single mostimportant rock parameter controlling PRev. Obviously, frequencyand condition of jointing can have a dominant impact on TBM per-formance especially in harder rocks and further study of this phe-nomenon, notably including a quantitative representation of jointspacing and condition may be needed to improve model accuracyin harder rock units.

There are other areas of concern related to the use of TBM de-sign parameters in performance prediction. The TBMs in operationmay only use a fraction of the torque and thrust capacity that is in-stalled in the factory. In the development of new models or themodification of existing models, one should be able to evaluateperformance over a range of physical scales, perhaps zone-by-zoneanalysis, which based on previous experiences can yield the bestresults. Additionally, one should always be mindful of the tradeoffbetween model complexity, accessibility of the relevant data androck property tests for various models, and the desired accuracyand reliability of the model. Given all these issues, the proposedmodels should be used with caution on any new project since theymay lack TBM and ground-related parameters that are specific to aproject. The proposed new formulas can serve the purpose of offer-ing preliminary TBM performance estimates. Used in conjunctionwith anticipated utilization rates, the models can be used to

(1) and (2) using testing database.

Fig. 14. The comparative results of Eq. (3) using testing database.


estimate TBM advance rates for the early stage of a projectplanning process. The model can also be used to calculate theTBM boring time in the models under development for estimationof the utilization rate, based on activity time allocations.

The authors strongly recommend the use combination of mod-els to ensure a higher degree of confidence in the development offinal estimates. Preference should be given to using models thatbest match key project criteria relative to the ground conditionsand TBM type. In summary, the proposed PR predictive modelsprovide alternative methodologies that can be used at the planningstage of a TBM drive when project-specific information is limitedor as a double check on the results of more detailed predictiveapproaches based on the use of existing, more complex models.

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