In recent years different methods have been introduced to analyse and assess excavation operations of various TBM systems. These methods are divided in two groups: One, those based on mathematical equations and shear force of each cutter. Two, those based on production data and empirical relationships. This paper compares and analyses three methods: two experimental types, QTBM (Barton 1999) and Rock Mass Excavability (RME) (Bieniawski and Celada 2006), as well as using a mathematic model introduced by the Colorado School of Mines (CSM). A case study is presented featuring the 16km Karaj-Tehran water supply tunnel. This study concluded that mathematical models are not suitable because they are highly dependent on the results of special laboratory tests and are not representative of the rock mass characteristics. In jointed or non-homogeneous rock masses such as on this project, the experimental/empirical methods, are more credible as they are based on field data. QTBM considers less the effect of boring machine characteristics and joint filling factor. According to our analyses, and the conditions of the Karaj – Tehran water supply tunnel project, the RME method is more valid than the other approaches.

TBMs have a good reputation for high advance rate. Since 1990, usage of mechanised tunnel methods has increased. Hence, prediction capability of operations and performances in these machines, especially in long length projects, has received much attention. Peter Tarkoy in 1987 developed an empirical relationship between hardness and TBM penetration rate. Cassinelli et al. (1982) used a rock structure rating (RSR) system for evaluation of TBM performance. Nelson (1983) studied TBM performance at several tunnelling projects mainly in sedimentary rock formations, comparing the instantaneous penetration rate achieved in different rock properties. Aeberli and Wanner (1978) studied the effects of schistosity on TBM performance. Barton (1999, 2000) reviewed a wide range of TBM tunnels to establish databases required to estimate penetration rate, advance rate and utilisation of the TBM.

For this purpose, Barton slightly modified the Q rock classification system and produced a new equation, defined as QTBM which is used in this paper. The CSM has developed a semi-theoretical model, based on the measurement and evaluation of cutting forces on an individual cutter (Ozdemir, 1977). Rostami and Ozdemir (1993a, 1993b) improved this model theoretically by estimating cutting forces as a function of intact rock properties, including uniaxial compressive and tensile strength of rock, and cutter geometry. The disadvantage of this model was that it did not quantitatively consider rock mass properties, including planes of weakness, fracture orientations and rock brittleness. Yagiz (2001, 2002) modified the CSM model by adding brittleness of intact rock and fracture properties of rock masses as indices for this the model.

The Norwegian Institute of Technology (NTNU) has developed a comprehensive empirical performance prediction model which considers intact rock and rock mass properties as well as machine parameters (Lislerud, 1988; Bruland, 1999).

In this model, the machine specifications along with laboratory measured indices, (drilling rate index, brittleness index, and cutter life index), and rock fracture data, are used to estimate the penetration rate (Norwegian Institute of Technology, 1995).

Rostami, Ozdemir and Nilson compared CSM and NTNU (also known as NTH) method for hard rock TBM Tunneling (Rostami and et al, 1996). Based on the results, the CSM model can be used to estimate the basic penetration and provide the ability to improve machine design and the NTH model can be applied to adjust the CSM estimate and incorporate the effects of discontinuities and rock mass.

In 2006 Bieniawski et al introduced the Rock Mass Excavability (RME) Index at the ITA Congress in Korea. Its purpose is to evaluate rock mass excavability in terms of TBM performance and to serve as a tool for choosing the type of TBM most appropriate for tunnel construction in given rock mass conditions. In this method specific correlations between the RME and the average rate of advance (ARA) were developed for double shield TBMs, based on data from tunnels constructed in Spain and in Ethiopia. In addition, specific correlations between RMR and the ARA were proposed for open and single shield TBMs. In this paper, the authors analysed the validity of three methods: QTBM, RME and a mathematical model introduced by CSM. In addition, the prediction capability of advance rate on the Karaj – Tehran water supply tunnel was assessed. Because consumption of drinking and industrial water will increase in future decades, many projects including this tunnel have been designed and are being implemented. This 16km long tunnel was excavated by a 4.56m diameter TBM which supplies 16m3/sec water from Amir-Kabir dam to Tehran refinery (treatment system) no.6.

Experimental Models
Q classification is on base drill and blast tunneling and introduced by Barton. After some field research, he developed the tunnel quality index model as follows after some field researches. Also, Barton (1999) developed a prediction model by means of some other parameters to estimate the advance rate of tunnel boring machines:


The NTNU model was developed by Norwegian University of Science and Technology from the 1970s.

In 1995, Palmstrom introduced the RMi system to explain the conditions of rock mass. Based on this model, the penetration speed is estimated with a combination of the characters of rock drillability and rock mass joint as well as machine factors.

The purpose of the RME index, first presented in 2006, is to evaluate rock mass excavability in terms of TBM performance and to serve as a tool for choosing the type of TBM most appropriate for tunnel construction in given rock mass conditions.

Mathematical models
CSM introduced a mathematical model by the Earth Mechanics Institute (EMI) for advance estimation and penetrating rates based on 25 years of theory, experimental and operational studies.

In the late 1970s, work by Ozdemir and subsequently by Rostami and Ozdemir (1993) modified the model based on extensive theoretical analysis of rock failure under the action of TBM cutters. An empirical modified CSM model has been developed to describe rock fractures, brittleness and to quantify their effect on TBM performance. Incorporating these adjustment factors into the existing CSM model basic penetration rate has led to a more accurate TBM performance prediction for given rock conditions (Yagiz, 2002).

This model is based on the forces applied to disc cutters for a certain penetration, advancing force momentum and the necessary power of cutter head. To estimate the amount of forces applied in disc, shearing tests must be carried on a real scale and accurately. This type of test contains all controlling parameters. Some of these parameters are: rock strength, rock brittleness, disc cutter details, spaced joints, continuity and joint gradients (slopes).

Validation study on methods

CSM Methodology
One of the most sensitive parameters of the CSM model is the penetration force of each disc cutter. This parameter can be estimated by laboratory testing. If it is not determined accuratly, the results of calculation will be wrong. The Colorado School of Mine has proposed many equations to calculate the penetration rate, the most important of which are the Cassinelli equation (Eq 2), the Innaurato equation (Eq 3) and the Graham equation (Eq 4).


At the Karaj-Tehran water supply tunnel, the penetration rate is calculated by all three methods as shown in Figure 1.

Innaurato equation in two regions lacks validity (negative value). In the Cassinelli equation, the rock strength has not been considered and it only classifies the rock structure. Furthermore, in both equations that have been introduced based on databanks in the years 1986 and 1991, the rotation speed of cutter head has been considered based on early 1990s technology. As mentioned above, the application of these two equations in modern projects will not be valid highly.

The Graham equation has a greater validity than others as it is frequently used in the USA and Norway in CSM methodology. This equation considers simultaneously the characteristics of rock mass and machine. This will be used to calculate Karaj-Tehran water supply tunnel project.

The CSM model evaluates the utilisation of any region without considering time. Furthermore, the standard values that have been presented based on the data bank have extensive ranges. This reduces the accuracy of the calculations. Also, the section in the CSM model that is used for performance calculation, cannot estimate accurately for the time being, because, the results of _ eld studies are dependent on the machine technology, As technology has advanced the model has become outdated. The model is therefore not able to make accurate predictions.

QTBM Methodology
This method by Barton (1999) involves six parameters shared by two models designed to undertake any conventional (Q) and TBM excavation (QTBM) except the index of Rock Quality. The RQD index in QTBM model, as opposed to earlier model must be measured on direction of the tunnel axis. The RQD parameter can be measured through drilling with a diamond bit and by using equation 5.


The SIGMA parameter can be calculated with the related UCS and tension strength of rock (or I50) and Q. The numerical value of the SIGMA parameter is closely related to the angle between the discontinuity and tunnel axis. A parallel or semi-parallel structure with the tunnel axis (perpendicular to face) not only can alleviate the penetration rate (PR) but also decreases the utilisation (U) rate. Since, longer sections of rock need to be supported, the operations on the face are harshly crushed and fall. Also, the presence of the synchronous jointed structure that is normal in tunnel axis (parallel to face) will influence positively on PR, U and advance rate (AR). This structure shows a better stability in boring the rock with TBM.

The Cutter Life Index (CLI) depends on the rock condition in addition to the alloy materials applied. The presence of abrasive minerals such as quartz increases cutter wear and reduce its life. This index is presented in estimating figures by cutting tools manufacturers. However, exact measurements are necessary to test abrasion and drillability (Salehi, 2007).

It is evident that there is a direct correlation between the strength of rock mass and vertical stresses. Barton has included the eq4in the equation in order to consider the bidimensional mode of stress. It must be noted, considering the value of parameter eq4in 100m depths or the equivalent by tangential stress is generalised and less precise. So, it must be considered when using numerical value of eq4.

In the QTBM model, utilisation of machine at the any is dependent on the tunnel diameter, CLI, rock mass quartz content and porosity. Indeed, the QTBM model knows the self support of the tunnel as well as excavation capability impressed by four mentioned parameters. Utilisation is exercised in reducing factor form. In other words, U is considered as a negative exponent of special time range.

NTNU Methodology
This method uses parameters such as joint characteristics, rock mass strength, cutter thrust, and also contributes to the AR. However, this method considers equivalent value of parameters as well, rather than using their numerical values.

In this model, the joint characteristics of rock mass are introduced by six parameters. In the NTNU model, the classification of joints was based on their spacing and all parameters such as joint condition and drilling rate index (DRI) as computed by joint equivalent factor.

In the NTNU model the base penetration rate can be computed by using the numerical value of joint and cutter thrust equivalent factors. The data bank in this method shows some parameters such as the cutting tool spacing and diameter with constant values. Therefore, in cases where the parameters of a project differs from the data bank, correction coefficients are used. By applying the correction coefficient the pure or operational penetration rate is calculated.

Performance of a machine is expressed by the time of the service and the length of drive within a selected time range.

RME Methodology
Since RME introduction in 2006, continued improvements were made to the RME index as more case histories were collected for double shield TBMs and new data obtained for open TBMs and single shield TBMs from tunnels constructed in Germany, Switzerland and Spain. As a result, the score for ci has changed from 0-15 points to 0-25 and for the discontinuities has decreased from 0-40 to 0-30 points, as shown in Table 1 and Figure 2. Note that the graphs enable more accurate determination of the RME values than the Table 1 (Bieniawski et al, 2008).

The RME is calculated using five input parameters having these initial ratings:

  • Uniaxial compressive strength of intact rock material, eq4aci: 0 – 15 rating points;
  • DRI: 0 – 15 points;
  • Number of discontinuities present at tunnel face, their orientation with respect to tunnel axis and homogeneity at tunnel face: 0 – 40 points;
  • Stand up time of the tunnel front: 0 – 25 points; and
  • Water inflow at tunnel front: 0 – 5 points.

The sum of the ratings of the above parameters varies between 0 – 100 rating points and it is expected that the higher the RME value, the easier and more productive the excavation of the tunnel.

To prevent errors in the prediction, this approach avoids calculating the ARA from the PR which normally varies between 6 and 60mm/min (Bieniawski and et al, 2008); this is so because while PR can be accurately measured in the TBM controls, the actual daily ARA depends on a number of factors which constitute uncertainties. They are, for example, the mechanical condition of the machine, the excavation strategy adopted by the TBM crew and the percentage of TBM utilization exclusively dedicated to excavation. ARA is closer to the average speed concept of the TBM than the peak output in a day.

In RME method it is possible to predict ARA by classifying types of TBMs and uni-axial compressive strength of the rock material. It is evident that a TBM working in a rock mass having eq5= 20MPa will obtain much higher advance than one working in terrain with eq5=130MPa.

For this reason, and based on research and tunneling data, it was decided that the most meaningful correlations between RME and ARAT for the common TBM types are when two ranges of the uniaxial compressive strength of intact rock are selected: the strength eq5 greater or lesser than 45MPa.

Comparison of the methods
The capability of advance rate (AR) prediction models for consideration of effective parameters is shown in Table 2. Careful quantifying of some parameters (especially in utilisation like effect of labour force) is subjective. Clear quantification is required to achieve accurate advance rate prediction.

QTBM method, involves the CLI index as the only parameter re_ ecting machine characteristics, shown in Table 3. This is a two-dimensional factor and is expressed by the geological properties in excavation area. So, to introduce the capability and operation of the TBM cannot be a good decision. In the Barton method, the factors which are effective in operation and affected by geological conditions and manpower operations, have been ignored. Geological conditions are the only parameters that have been included except for joint filling. This defect is seen in an earlier version of the rock quality index (Q).

Parameters in the QTBM method are estimated by observation and use of tables and equations. The CLI parameter is necessary to estimate by complicated tests (Abrasion value steel (AVS) and Sievers’ J- value (SJ)).

The NTNU model shows that the boring machine features are of greater importance. The most important parameters of this model are computed in an indirect way and through equivalent factors and correction coefficients. However, these coefficients and rates are limited and the effects of ground water conditions were ignored. Also, the thrust factor and DRI have great effect in this method. However, the numerical value of this index is determined indirectly resulting in considerable variation in the calculated results.

The RME method has the best score for including both influence factors as geotechnical and machine parameters (see Table 3). Parameters in the RME method can be estimated by site investigation (joint properties and ground water conditions) and basic laboratory testing methods (USC). The DRI parameter is necessary for accurate estimation using standard ISRM tests.

In the RME method, the effect of geological conditions is of more importance than the features of TBM system. In this method machine parameters are involved as correction factors. In other words, after assessment of the theoretical advance rate, the machine parameters and performance are affected by three factors (tunnel diameter, crew efficiency, and team adaptation to the terrain).

Case Study
The Karaj – Tehran water supply project, with the length of 16km, is under construction by a TBM. It is a double shield type machine with a 4.566m diameter. According to geological characteristics of this region, the whole excavation area has been divided into nine zones (Table 4, opposite). Figures 3 and 4 show the results obtained for PR, AR as well as the real operation during one year (RME method does not deal with penetration rate). The construction time of project is shown in Table 5 (below).

The values produced by CSM are higher than by the two other models. In CSM, the utilisation has been calculated on the data bank basis, and also according to time periods required for excavation and other services. It should be noted that all the models (except the RME) are using old data available in data banks and if these are not updated, this limits the prediction capability. So, the numbers obtained with the CSM model are restricted in value.

The AR as calculated by QTBM method shows different values at different geological areas. This is acceptable, while NTNU presents a similar AR for all nine regions.

Finally, Figure 5 summarises the best results of the correlation obtained during this investigation between the ARA and the RME index, plotted with the original correlation by Bieniawski et al. (2008). Note that ARA (theoretical and real) is expressed in meters per day (m/d).

The results are also tabulated for convenience in Table 7 (below). A significant conclusion becomes apparent that the present correlation is markedly better, with R2 over 0.9, by comparison with the original correlation of R2 just below 0.7. This means that once the RME is determined on a given tunnelling project, the site-related correlation should be calibrated for the best R2 which can then be used with much confidence for reliable prediction of future rates of TBM advance at that project.

In the CSM model, construction time in the Karaj-Tehran Water supply tunnel project was estimated at 15 months (Table 5). The CSM model is also necessary for some essential tests that should be conducted to identify the cutter thrust and determine the initial PR. But these kinds of tests could not be conducted in the present project. This model considers the geological characteristics in an indirect mode and by using laboratory findings. It is evident that inaccurate quantities of parameters such as cutter thrust produce a less credible result. Furthermore, the CSM model estimates the performance process for all regions independent from time interval (as opposed to Barton model). It is one of the weaknesses of CSM. Generally, the PR as obtained from this model can be relied on if the required tests have been conducted carefully and completely. Among the experimental methods, the NTNU model requires accurate values of DRI and the equivalent factor of cutter thrust. Also, the calculation complications will be intensified because engineering judgment differs as well as different correction factors. Wherein carry out tests is possible to assess the drill ability, bit wear index, equivalent cutter thrust and etc, NTNU method will produce more accurate the results. Because this method considers not only the ground condition but also the characteristics of boring machines. Certainly, the NTNU method cannot find a reliable answer exclusively. Because, a number of influencing factors are not considered, such as ground water conditions and tunnel self support. The required time for execution of the project was estimated 56 months (Table 5).

Factors of QTBM model except CLI do not require intricate tests. As for equation 1, it is observed that this index has been applied inversely to the first power. Hence, approximating this factor with specific limits will not provide gross changes in the results. With its extended data bank based on rock mass quality (Q) and repeated use of it in both mining and civil projects, it is possible to assess accurately the geological factors. The time to implement the project has been calculated at about 52 months by using the Barton model. This method considers less to effect of boring machine specification and joint filling factor.

In the RME method all parameters were assessed by site investigation and standard laboratory tests. The RME method introduced in 2006 utilised the experience with the RMR classification system, because one of the RME input parameters, the stand up time, is determined from the RMR. To prevent errors in prediction, this approach avoids calculating the ARA from the PR.

Moreover, with the RME, one considers a TBM type (open, single or double shield). This feature makes this method more useful in construction issues. Using the RME, the required time for execution of the project was estimated at 21 months, which was the closest result to actual data out of all the methods.

It was concluded that for projects with various joint structures, where tests of drill ability, and abrasion were not implemented, RME is the most suitable method. The data that is available from the Karaj-Tehran water supply tunnel conform more to the RME method capabilities. Furthermore the results showed in Figure 5 and Table 7 confirm the credibility of the RME method.