A model for the prediction of tunnel boring machine performance
SAFFET YAGIZ1
1Pamukkale University. (e-mail: syagiz@)
Abstract: A key factor in the successful application of a Tunnel Boring Machine (TBM) in tunnelling is the
ability to develop accurate penetration rate estimates for determining project schedule and costs. Rate of
penetration (ROP), defined as the distance the machine advances in a given time in rock, is a complex process
that not only depends upon intact and rock mass properties (strength, fractures, and texture of rock) but also
machine specifications including thrust and torque requirement. The Earth Mechanics Institute (EMI) of the
Colorado School of Mines (CSM) has developed a model to predict the performance of TBM in hard rock
conditions. The model is primarily bad on intact rock properties and machine specification. Although the
model has proven reliable in massive rock conditions, its accuracy has been limited in brittle rocks exhibiting a
high degree of fracturing. Therefore, this rearch was conducted to investigate the effect of rock mass fracture
and brittleness on TBM performance. In order to accomplish the goal, extensive mapping of the tunnel was
conducted to make a record of the joints and fractures along the 16-kilometer long Queens Water Tunnel in
New York City. A large number of cores were taken from inside the tunnel where rock exhibited varying
degrees of fracturing to conduct geomechanical tests including uniaxial compressive strength, tensile strength,
and punch penetration tests. Additionally, the field TBM data from the tunnel was analyd in detail.
Conquently, the data collected for the machine, rock properties and geology were then subjected to a multiple
regression analysis together with the basic penetration rate derived from the existing model. As a result of this
rearch, a new model was propod for TBM performance prediction.
Résumé: Un facteur principal dans l'utilisation réussie d'une aléu de tunnel (TBM) dans le perçage d'un
tunnel est la capacité de développer des évaluations précis de taux de pénétration pour déterminer le
programme et les coûts de projet. Le taux de pénétration définissant comme une distance que la machine
avance dans un temps donné dans la roche est un processus complexe qui dépend non ulement au moment
intact et les propriétés de mas de roche (force, ruptures, et la texture de la roche) mais usinent également des
caractéristiques comprenant la condition de poussée et de couple. L'institut de mécanique de la terre (EMI) de
l'école du Colorado des mines (CSM) a développé un modèle pour prévoir l'exécution de TBM en état dur de
roche. Le modèle est principalement basé sur les propriétés de roche et les spécifications intactes de machine.
Bien que le modèle ait prouvé fiable en états massifs de roche, son exactitude a été limitée dans les roches
fragiles montrant un degré élevé de rupture. Par conséquent, cette recherche a été conduite pour étudier
l'affectation de la rupture et de la fragilité de la mas de roche sur l'exécution de TBM. Afin d'accomplir le
mais tracer étendu du tunnel a été conduit pour noter les joints et les ruptures le long du 16-kilometer
longtemps les Reines arront le tunnel à New York. Un grand nombre de noyaux ont été pris de l'intérieur du
tunnel où la roche a montré des degrés variables de rupture pour effectuer les essais geomechanical comprenant
la résistance à la pression uniaxiale, résistance à la traction, et essais de pénétration de poinçon. En plus, les
données du champ TBM du tunnel ont été analysées en détail. En conséquence, la machine rasmblée, la roche
et les données géologiques ont été alors soumis à une analy de régression multiple ainsi que le taux de
pénétration dérivé du modèle existant. En raison de la recherche, un nouveau modèle est purpod pour la
prévision d'exécution de TBM.
Keywords: Excavations, rock mechanics and tunnels
INTRODUCTION
The key parameters for the TBM tunnel project are intact and rock mass properties and also machine specifications. The Colorado School of Mines (CSM), Earth Mechanics Institute (EMI), developed the CSM model for TBM performance prediction over the cour of 25 years. To establish the detailed databa for the development of the model, EMI has collected extensive field data and conducted full-scale laboratory cutting tests to rve as a basis for model development and validation. This data collection effort was complemented by extensive theoretical analysis of rock failure under the action of TBM cutters. All the efforts successfully led to the development of the initial formulation of the CSM model in late 1970s by Ozdemir. Subquently, Rostami and Ozdemir (1993) modified the model in the early 1990s. At the CSM, an empirical modified CSM model has been developed for describing rock fractures and brittleness and quantifying their effect on TBM perf
ormance. Incorporating the adjustment factors into the existing CSM model basic penetration rate has led to more accurate TBM performance prediction for given rock conditions (Yagiz, 2002). This paper is bad on the geotechnical study that was performed at the CSM and the field data gathered from 16-kilometer Queens water tunnel, which was excavated in fractured hard rock by using High Power TBM in the City of New York.
BACKGROUND
Several models have been introduced over the years for prediction of TBM performance. The TBM performance prediction models are mostly bad on an empirical or a mi-theoretical approach. The interrelationship between cutter wear, machine operation, continuous mucking, and support installations requires an evaluation of many factors affecting TBM performance. Tunnel boring is a complex process and it is difficult to account for all rock properties in a single formula. The rock cutting process involves the indentation of a rock surface by a cutting tool as it is driven forward, leaving behind it a groove and fractured and crushed rock.
All mechanical rock-cutting tools share the same principles and, conquently, many efforts have been made to develop performance prediction models and theories offering explanations into the for
ce-penetration behavior of rocks (Roxborough (1975), Ozdemir (1977), Cook et al. (1984), Sanio (1985), Snowdon et al. (1983), Peng et al. (1989)).The analytical solution for indentation of mechanical tools into the rock begins with an analysis of stress in an elastic media under the point load. Swain and Lawn (1975) provided the most comprehensive description of indentation fracture in rock to express the fracture phenomenon in rock cutting. Paul and Sikarski (1965) propod a theoretical model for wedge penetration, omitting the crushed zone occurrence pha and emphasizing the brittle chip occurrence pha for brittle isotropic rock. Wijk (1982) modified Paul and Sikarski’s proposal to account for the interaction between penetrations. Cook et al. (1984) performed a ries of acoustic emission tests to obrve crack growth in hard rock loaded by an indentor. Graham (1976), Farmer and Glossop (1980), Snowdon et al. (1983), and Sanio (1985)achieved strong correlations between rock compressive strength and the specific energy defined as the amount of energy needed to excavate a unit volume of rock. The influence of joints and planes of weakness were examined by Roxborough (1975), Ozdemir and Miller (1978), Sanio (1985), and Sato et al. (1991). All obrved “a significant reduction in cutting forces in prence of joints in the rock except for a joint orientated normal to the cutting surface.”Tarkoy (1987) developed an empirical relationship between total hardness and TBM rate of penetration. Cassinelli et al . (1982) ud a rock structure rating (RSR) system for correlation with TBM performance. Nelson (198
3) studied TBM performance at veral tunnelling projects mainly in dimentary rock formations by comparing the instantaneous penetration rate achieved with different rock properties. Aeberli and Wanner (1978) studied effects of schistosity on TBM performance. Barton (1999, 2000) reviewed a wide range of TBM tunnels to establish the databa for estimating rate of penetration, utilization and advance rate of TBM. In order to estimate the TBM penetration rate, Barton slightly modified the existing Q rock classification system and produced a new equation,defined as Q TBM that was ud for estimating rate of penetration.The Norwegian Institute of Technology (NTNU) has developed a comprehensive empirical performance prediction model that considers intact rock and rock mass properties as well as machine parameters (Lislerud, 1988; Bruland,1999). In the model, the machine specifications (including cutter size, type and number, machine thrust and torque requirements) along with laboratory measured indices, (drilling rate index, brittleness index, and cutter life index), and rock fracture data, are ud to estimate the rate of penetration (Norwegian Institute of Technology, 1995).
CSM has developed a mi-theoretical model, bad on the measurement and evaluation of the cutting forces on an individual cutter (Ozdemir, 1977). Rostami and Ozdemir (1993b, 1993c). They improved this model theoretically by estimating cutting forces as a function of intact rock properties, i
ncluding uniaxial compressive and tensile strength of rock, and the cutter geometry. The shortcoming 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 mass as indices into the model.DATABASE DEVELOPMENT FOR THE MODELLING
As mentioned previously, the mi-theoretical model developed by CSM is mostly bad on intact rock strength,expresd as uniaxial compressive and tensile strength. In order to render the CSM predictor model more accurate in predicting TBM performance, particularly in fractured rock mass conditions, the model was modified and developed by accommodating the rock mass fracture properties and orientations, and the rock brittleness as additional quantitative indices into it. In order to obtain the objectives, extensive geotechnical and mechanical field data from a 16-kilometer hard rock tunnel in New York City was collected and analyd in detail to examine the influence of various rock mass properties and brittleness on TBM performance. The following are the main results from the geotechnical and mechanical investigations, which were ud as input parameters for the model development.Geotechnical investigation
In order to investigate engineering rock properties that affect TBM performance and to establish a da
taba, an intensive rock coring, sampling, and testing programme was conducted both in the field and in the laboratory. Inten rock sampling was undertaken at 151 points along the tunnel where fractures comprising faults, shear zones, and joint ts were encountered. Using the data, correlations between rock mass and intact rock properties and TBM penetration rate could be developed. After rock cores were retrieved and logged in detail, rock samples were prepared for testing according to ASTM and industrial standards. Uniaxial compressive strength (UCS), Brazilian tensile strength (BTS) tests were conducted for each station along the tunnel where fractures were encountered according to ASTM (American Society for Testing and Materials, 1995) D3967 and D4543 respectively. Punch penetration tests as ud for investigation of intact rock brittleness, were performed according to recommended industrial standards (Dollinger, et al. 1998; Atlas-Copco-Robbins, 1995).
Along the tunnel alignment, fractures, faults and shear zones were obrved and orientation and fracture conditions were quantified for u in the databa. The alpha angle that fractures make with tunnel axis, expresd as a function of fracture orientation and tunnel direction was calculated as follows:
α = arcsin (sin αf – sin(αt - αs )
Where αs is the strike and αf is the dip of the fracture; and αt is the bearing of the tunnel axis. Fracture class designation has been ud for fracture classification in terms of spacing for databa development in Table 1.Developed intact and mass rock properties part of the databa was given in Table 2.Table 1. Fracture class designation with corresponding spacing of fracture (modified from Bruland, 1999)
Rock class Fracture spacing Description
O Greater than 1.60 m Totally massive rock interval with few joints or fissures. Seldom found in
complexly deformed terranes except for granoblastic metamorphic rocks and equiangular, crosscutting igneous rocks. Fracture spacing must be greater than
1.60m
O - I 1.60 m Massive rock interval with fracture spacing of 1.60m
I-0.80 m Relatively massive rock interval with fracture spacing of 0.80m
I 0.40 m Fractured rock interval with fracture spacing of 0.40m
II 0.20 m Well fractured rock mass with fracture spacing of 0.20m
III 0.10 m Highly fractured rock mass with fracture spacing of 0.10m
IV 0.05 m or less Highly brecciated with cloly spaced anastomosing fractures exhibiting
spacing of 0.05m or less. Commonly associated with zones of stress relief,
fault breccia, and fault gouge.Table 2. An example of intact and mass rock data collected along the tunnel
Orientation Stations (m)Tunnel Bearing (deg)UCS (MPa)BTS (MPa)
Brittleness
Index -Strike (deg)Dip
(deg)Fracture Class Designation Fracture Spacing (m)Alpha Angle (degree)269N47E 2009.3 4.95N20E 68SE
I-0.8025280N47E 1999.3 4.95N22E 58SE
O-I 1.6021301N47E 1999.1 4.95N25E 68SE
O >1.6020473N47E 1909.0 5.02N48W 42SW
II 0.2042600N47E 1899.0 5.02N05W 54NE
O >1.6040929N47E 1689.8 5.17N57W 34SW
O-I 1.6041989N47E 1749.9 5.20N88W 55NE
O >1.60351021N47E 17810.1 5.17N19W 74NE
I 0.40611026N47E 18110.1 5.15N08W 86NE
II 0.20551045N47E 18410.2 5.12N23W 54SW I 0.4049
TBM field data analysis
The TBM operational data for the Queens Tunnel was analyd and evaluated for the entire length of the tunnel where the fractured rock mass was encountered. All data derived from the control system of the machine was recorded on a standard personal computer (PC), which was connected t
o the control system via modems, or via a local connection; logging was done automatically. The data was stored on the PC hard drive, which could then be printed in text or graphical form. The data was easily accessible for analysis by another program, such as a spreadsheet or a databa program. Separate daily files, in which the pertinent variables were stored, were created on the hard drive. In order to analy the TBM field data, an Excel macro program was written to open the two daily raw data files and retrieve the data according to the shift schedule. As a result of data evaluation, the average of penetration rate, total thrust, cutterhead power, cutterhead torque, and cutter load was calculated (Table 3).
Table 3. An example of TBM field data for Queens Water Tunnel
TBM Field Performance and Power
Stations (m)Thrust (ton)Cutter Load (ton)Torque (ton-m)Cutterhead
Power (HP)
TBM Field Penetration Rate (m/hr) (mm/rev)269151130991150
2.190.432801535301021187
2.120.41301151230951106
1.880.374731587321361580
2.810.556001685341491728
2.200.439291725351321533
2.370.479891783361621884
2.340.4610211429291401628
2.900.5710261737351721998
3.040.6010451586321812098 3.070.60
Evaluation of the existing CSM model
The CSM Earth Mechanics Institute (EMI) developed the CSM model for TBM performance prediction over the cour of 25 years. To establish the detailed databa for the development of model, EMI has collected extensive field data and conducted full-scale laboratory cutting tests to r
ve as a basis for model development and validation. This data collection effort was complemented by extensive theoretical analysis of rock failure under the action of a TBM cutter.
A databa of measured cutting forces using disc cutters in different rock types has been developed and continuously updated at the EMI (Rostami, 1991). The Linear Cutting Machine (LCM) full-scale test was ud for establishing this databa for a variety of rock types. LCM tests were accompanied by physical property testing of the same rocks to measure the uniaxial compressive and Brazilian tensile strength of the samples.
The databa was initially ud to derive formulas for cutting forces. The data was collected including spacing between cuts, penetration rate, cutter diameter and tip width, compressive, and tensile strength of rock to calculate individual cutter load so that the normal force acting on the rock surface could be calculated. Multiple variable regression analysis was performed to find the best combination of parameters to develop a relationship between the cutter load and the input parameters. As a result of findings, formulas of TBM performance prediction in the model are as follow.
F
n
=8.76.T0.8.R0.79.φ0.6.S0.28.σc0.63.σt0.2
φ=Cos-1((R-p)/R)
P o=C.T-1/6.R-1/6.φ−1/3.S1/3.σc2/3.σt1/3
F
n
= (T.R.P o/φ).(1-Cosφ)
F
r
=(T.R.P o/φ).(1-Sinφ)
T
h =ΣF
n
.n
T
r = ΣF
r
.R=0.3.D
c
.F
r
where; F
n
is the normal force in pounds, S is the spacing between the cuts in inches, p is the penetration in inches, P o is
the ba pressure in the crushed zone at the point underneath cutter, σ
t and σ
c
is the Brazilian tensile strength and the
uniaxial compressive strength in pounds per square inches respectively, T is the cutter tip width, D
c is the cutter
diameter and R is the cutter radius in inches.
After that, calculating the maximum rotational speed (RPM) is governed by the diameter of the cutter and the power (P
c
) requirement of the cutter head as follows:
RPM=(V
max /π.D
c
)
P
c =T
r
.RPM
With all the parameters fixed in a certain rock type using a specific TBM, penetration (p) is the only unknown
variable that can be incread until maximum thrust, torque or power is reached. Obviously, maximum thrust (T
h ),
torque (T
r ) and power (P
c
) of the machine for rock cutting are known. Therefore; from known parameters and
formulas, rate of penetration can be calculated by using iteration method.
In the model, all the input parameters and result output can be either in English or SI units. However, the best results can be achieved using the English unit system since the original equation of the model was bad on English units, which can be converted to SI units as required. Typical existing TBM performance prediction model output is given in Table 4.
Table 4. An example of the existing CSM performance prediction model output
TBM Field Performance and Power
Stations (m)Thrust
(ton)
Cutter Load
(ton)
Torque
(ton-m)
Cutterhead
Power (HP)
CSM-Model
Penetration Rate
(m/hr) (mm/rev)
269151130991150 2.980.58
2801535301021187 3.120.61
301151230951106 2.980.58
4731587321361580 3.340.65
6001685341491728 3.340.65
9291725351321533 3.340.65
9891783361621884 3.340.65 10211429291401628 2.500.49 10261737351721998 3.340.65 10451586321812098 3.340.65
Databa establishment and statistical approach
In order to modify the existing TBM performance prediction model, intensive field and laboratory rearch was conducted at the EMI for analysing the affect of fractures and brittleness of the rock on
TBM performance. In the
USA, the Queens Water tunnel in New York City was investigated from both a mechanical and geotechnical point of view to identify the influence of the rock fractures and brittleness feature of rocks on the TBM performance.
After completing the geotechnical site investigation, geomechanical laboratory testing and TBM field data analysis was undertaken in order to obtain the relationship between the parameters (including spacing of fractures, alpha angle that fractures makes with tunnel axis and rock brittleness). The, taken together with TBM field penetration rate and the existing CSM predictor model basic penetration rate allowed the establishment of the databa. This databa was ud for developing a modified penetration rate equation and adjustment factors including fracture and brittleness indices to improve the accuracy of the model specifically for fractured rock conditions. As mentioned previously, the existing model could not accept input parameters appropriate to the rock fractures and brittleness properties that are two of the main effects on TBM performance in the field.
One of the• commercial software packages for standard statistical analysis was ud to perform the multiple variable regressions among the rock and machine parameters in the databa. Actually, the
relationship achieved between the variables is a linear function. In other words, the program finds the best-fit regression between the parameters in a linear combination, as follows:
F = f (x 1, x 2, ….) = a 1.x 1 + a 2.x 2 + ….
where:
F = Objective parameter
x 1, x 2, … = Independent variables a 1, a 2, … = Calculated coefficients
The non-linear relationships between the parameters can be determined by defining a new t of variables (new columns) in the program from the original t of variables. For example, a new variable x j can be empirically defined as a function of the original parameter x i (x j = f (x i )). This allows defining other parameters in various forms, such as polynomials, exponential, and logarithmic functions of the original parameters. In order to determine the correct power or constant coefficients to be ud for each variable in an equation, the new variables can be t to different powers of the original parameters (e.g. instead of using x i , its square or square root is ud). An alternative to this method is logarithmic analysis, using the logarithm of each parameter in a linear relationship. This al
lows for obtaining the correct power for each parameter using the characteristics of logarithmic function. Altogether, u of the logarithmic method allows the development of veral combinations of parameters in different mathematical forms. In order to develop the best linear relationship between the parameters and the objective parameters, input parameters need to be defined as they are or as functions of logarithms. Using the regression analysis, the following equation was developed, relating the field penetration rate to rock mass properties, rock brittleness and the basic penetration rate provided by the CSM model. Thus, the predictor equation is:
ROP = 0.859-0.0187.F s +1.44.Log (α)+0.0157.P s +0.0969.CSM (b-rop)
where, F s is the spacing between the fractures in inches, Ps is dimensionless, CSM (b-rop) is the CSM model basic rate of
penetration in ft/hr, and α is the alpha angle in degree.
In the equation, the variables were then grouped according to their reprentative parameters. Spacing of fracture and alpha angle that tunnel axis makes with plane of weakness or fractures was taken as rock fracture index (RFI)since both of them are rock fracture properties. Peak slope (P s ) calculated from punch penetration tests was named as brittleness index (BI) with a constant coefficie
nt so that the adjustment could be made in the model according to the indices. The regression coefficient achieved for this equation is 82%. As a result, RFI and BI are formulated as follows:
ROP = 0.859-RFI+BI+0.0969.CSM (b-rop)
where 0.859 is a constant coefficient, RFI = 1.44.Log (α)- 0.0187.F s and BI = 0.0157.P s .The achieved equation was introduced as a function of TBM specification including machine thrust and torque,machine power, cutter diameter, cutter tip width, depth and spacing between the cuts; intact rock properties including uniaxial compressive and Brazilian tensile strength, brittleness index; and also rock mass properties including spacing of fractures and fracture orientation.
Influence of rock properties on TBM performance
It is widely considered that the uniaxial compressive strength of the rock is the most significant parameter for TBM performance estimation. However, if the rock mass is heavily fractured and has significant shear zones, intact rock strength alone is insufficient for reliable performance estimation since it is not reprentative of rock mass properties.Thus, machine performance prediction on this basis would differ significantly from obrved performance. In this rearch, special attention was given to rock mass properties and their influence on the performance of TBM since the machine perf
ormance could be influenced by rock mass strength, fractures properties of rock mass and rock brittleness with machine specification.
As a result of the statistical analysis among the variables that were evaluated for performance prediction, it is obrved that the rock fracture properties and brittleness behaviour of the rock are two main parameters that control TBM performance in rock mass. Correlation and effect of RFI and BI on TBM performance are shown in Figure 1and 2 below respectively. After the formula was adjusted with the two indices, achieved regression coefficient (r)between field TBM performance and predicted ROP that achieved from the modified model was 0.82 (Figure 3).
