wD.

al Te

d form

ine 18

the

ith r

ough

tent

n of

e an

crucial for the projects economics (Alber, 2000). In this

Grima et al., 2000; Okubo et al., 2003). Nevertheless,

they showed very promising results, demonstrating theirstrong potential in coping with this particular issue. In

the majority of these research eorts, the main objective

projects constructed in complex geological formations

articial neural network (ANN) capable of learning

from the tunnelling experience and generalise solutions making prognosis for new input data. Hence, the main

aim is to produce a tailor-made model, utilised during

the construction period, capable of providing estimates

of the expected tunnelling advance rate. The model can

also be used in another context; to assist in the identi-

Tech* Corresponding author. Tel.: +30-210-7722182; fax: +30-210-pursue of developing the most consistent model, the

paths followed have been numerous (Lislerud, 1988;Laughton and Nelson, 1996; Blindheim et al., 2002). This

derives from the fact that a variety of input parameters

and methodological approaches have been used.

Beyond mathematical formulae and analytical solu-

tions, methods utilising articial intelligence have not

been introduced until recently (Bruines, 1988; Alvarez

(Barla and Pelizza, 2000) and especially in urban areas

where the low construction depth and the externalloading from the buildings increase risk conditions

(Duddeck, 1996; Eisenstein, 1999).

This paper deals with the modelling of the TBM

performance emphasising on the identication of the

performance oscillations throughout the tunnelling pe-

riod. This is made possible by the development of anKeywords: TBM tunnelling; Articial neural networks; Advance rate modelling

1. Introduction

The performance analysis of tunnel boring machines

(TBM) and the development of accurate assessmentmodels have been, and still are, the ultimate goals of

many researchers (Tarkoy, 1973; McFeat-Smith and

Tarkoy, 1979; Bruland et al., 1988; Bruland, 1999; Sharp

and Ozdemir, 1991; Nelson, 1993; Barton, 2000), as the

reliable estimation of the excavation rate is proved to be

is to model the tunnelling process and make the per-

formance assessment, based on the experience gained

and the data gathered from past projects. However, even

though probing risk conditions and identifying vulner-able areas that may disrupt the work progress have been

incorporated in the models of many researchers (Ein-

stein et al., 1992; Sineld and Einstein, 1996), they have

not yet been fully addressed, leaving room for further

research. These problems are more intense in tunnellingModelling TBM performance

A.G. Benardos *,

School of Mining and Metallurgical Engineering, Nation

Received 29 September 2003; received in revise

Available onl

Abstract

Assessing TBM performance is an important parameter for

presents an attempt to model the advance rate of tunnelling w

model developed for this particular task is implemented thr

the identication and understanding of both the way and the ex

model described in the paper is customised for the constructio

ANN generalisations provided precise estimations regarding th

2004 Elsevier Ltd. All rights reserved.

Tunnelling and Underground Space7722156.

E-mail address: abenardos@metal.ntua.gr (A.G. Benardos).

0886-7798/$ - see front matter 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.tust.2004.02.128ith articial neural networks

C. Kaliampakos

chnical University of Athens, GR 15780 Athens, Greece

30 January 2004; accepted 11 February 2004

March 2004

successful accomplishment of a tunnelling project. This paper

espect to the geological and geotechnical site conditions. The

the use of an articial neural network (ANN) that allows

that the involved parameters aect the tunnelling process. The

an interstation section of the Athens metro tunnels, where the

ticipated advance rate.

nology 19 (2004) 597605

Tunnelling andUnderground SpaceTechnologyincorporating Trenchless

Technology Research

www.elsevier.com/locate/tustcation of dicult ground conditions that may disrupt

dataset, estimates can be drawn for another specic data

input. Thus, the trained network can generalise and give The input signal (Yin) is introduced to the activationfunction of the Y neuron and signalled to the neurons ofthe output layer, Z1; Z2 following the general form:y f Yin taking into account the weighting of theconnection links, namely, v1 and v2.

The type of ANN used in this paper are the feed-

forward neural networks, which are the most widely

used. They are commonly applied to problems where a

set of input vectors should be corresponded to another

specied set of output vectors.

The training procedure consists of a sequential data

feed into the network, followed by the comparative

evaluation of the corresponding output provided by the

d Unestimates for uncertain conditions or even incomplete

data (Sietsma and Dow, 1991). The main disadvantageof ANNs is that an explicit determination of the pa-

rameters weighting is not an easy task or it may not

even be possible in large and complex network archi-

tectures (Menhrotra et al., 1997).

The ANN operation is based on the following:

Data processing occurs in a number of simple pro-cessing units (neurons), which have signal inputs

and outputs. The neurons bonding is made through connection

links, each one of them having a correspondingthe work cycle and impair the TBMs performance.

Both outputs, modelling of the TBMs advance rate and

identication of the risk-prone areas, are essential

knowledge for the engineers in order to ensure the -

nancial and scheduling credibility of the tunnellingproject.

In the following paragraphs an overview of the

ANNs is given, along with the presentation of the

methodological approach, in a more detailed manner.

Furthermore, a case study of the proposed methodology

is introduced, using an interstation section of the Athens

Metro tunnels as an illustrative example.

2. Articial neural networks

The development of ANN started as an attempt to

understand the operation of the human brain and mimic

its assessment capabilities. In other words, to be able to

decide and act under uncertainty or even deal with sit-

uations having limited previous experience. ANNs aremathematic models consisting of interconnected pro-

cessing nodes (neurons) under a pre-specied topology

(layers).

Neural networks have a strong similarity to the bio-

logical brain and therefore a great deal of their termi-

nology is borrowed from neuroscience. Their basic

characteristic is the ability to perform massively parallel

computing of the input stimulus (data), contrary to thecustom mathematic models that are based rather on a

serial process of mathematical and logical functions

(Fausett, 1994). Another advantage of the ANNs is their

exibility in data processing, as no deterministic math-

ematical relationship of the examined components is

required. Instead, once the data is introduced, in a

causeeect mode, the network identies the existing

relationships, learns and mimics their behaviour by ad-justing the strength of the links between the neurons

(connection weights). Thus, they cannot be programmed

but they are rather taught through case experience. As a

result, soon after the ANNs training, given an existing

598 A.G. Benardos, D.C. Kaliampakos / Tunnelling anweight that multiplies the signal. Each neuron applies an activation function to the sig-nal input to control the signal output.

In general, a typical ANN topology is consisted by a

set of layers; the input layer, one or more hidden layers

and the output layer. Each one of them includes a

certain number of neurons, specied by the ANN ar-

chitecture. Accordingly, each neuron is linked to neigh-

bours with varying coecients of connectivity thatrepresent the weighting of these connections. The to-

pology of a simplied ANN is presented in Fig. 1.

In this simple model, there is one hidden layer having

only one neuron. Each neuron of the hidden layer(s) is

interconnected to all others found in the input and

output layers. The hidden layers are the most important

element of the network as this is the particular part

where the network learns the interdependencies of themodel. This learning procedure is accomplished by ad-

justing the connection weights, impelling the overall

network to generate the matching results. In this man-

ner, changing the connection weights (training) causes

the network to learn the solution for a given problem.

In the topology of Fig. 1, each neuron of the input

layer (X1;X2;X3), sends out its weighted signal to the Yneuron found in the hidden layer. The combined inputsignal in the Y neuron has the following form:

Yin w1 x1 w2 x2 w3 x3;where, xi is the signal of the ith input neuron, wi theweighting factor of the ith neuron.

Fig. 1. Illustration of an articial neural network structure (after

Fausett, 1994).

derground Space Technology 19 (2004) 597605ANN and the actual result. The network adjusts the

usually a great number of epochs is required for the

residual error to converge below a pre-specied thresh-

d Unold. A schematic illustration of a feed-forward ANN

training is given in Fig. 2.

The goal is to train the network so as to achieve a

balance between its capability to memorise the traininginput vectors and its capability to generalise, i.e. to

produce outputs for input vectors that are similar but

not identical to the ones used for the training. In other

words, the ANN should avoid data overtting phe-

nomena, but should have the ability to produce a con-

sistent generalisation.

3. Model synthesis

The model concentrates on the tunnel construction

period in soft ground environments. The whole ideaweighting of the connection links in a continuous eort

to produce the results that would best correspond to thetraining dataset. A complete pass of all the input data

through the network consists a training epoch and

Hidden Layers

Data

inpu

t

Comparison with actual

data

Adjustment of connection weighting

Fig. 2. Training procedure of a feed-forward ANN with two hidden

layers.

A.G. Benardos, D.C. Kaliampakos / Tunnelling anfollows the ANN philosophy, that is, to analyse the

experience gained from the tunnel boring process and to

correspond it to a set of selected data. This causeeect

request is used in the ANN so as to identify the inter-actions between the data and to come up with the exact

weighting of the parameters involved, which will nally

determine the generalisation accuracy.

The models inputs are based on data relating to the

geological and geotechnical characteristics of the sub-

surface and the specic site conditions. Although ma-

chine characteristics (e.g. thrust, torque) are very

important for the overall TBM performance, in the casewhere tunnelling is performed in soft rock or complex

ground formations, the properties of the ground me-

dium tend to be the most inuential ones, as they govern

the type and extend of possible failures. Subsequently,

encountering ground conditions dierent from theTBMs working envelope, aect the achieved tunnelling

rate (Deere, 1981) and can give rise to claims (Buchi,

1998). Thus, the model considers the geological setting

to be the most dominant factor for the TBM perfor-

mance, as many researchers have also noted (Tarkoy,1981; Nelson, 1993; Sapigni et al., 2002).

In this way, it is assumed that the characteristics of

machine operation remain unchanged and all possible

problems and downtime are a direct eect of the geo-

technical conditions. Even though downtime is also in-

icted by machine failures, logistics support problems,

etc., the real question is how the TBM performance is

aected by ground conditions and the aforementionedassumption is made exactly so as to be able to evaluate

this particular issue. Having that in mind, the data

gathering procedure concentrates on obtaining infor-

mation about the subsurface conditions encountered

and the scheduling data, yet excluding all machinery

occurred failures (e.g. power failures, belt replacements,

etc.).

The selection of the parameters used in the model wasmade having in mind their capability to credibly repre-

sent the ground behaviour, hydrogeological environ-

ment and site-specic conditions (Benardos, 2002).

These parameters are easily collected in the site-investi-

gation phase and are available to all design stages of the

project, without the need for implementing special in-

vestigation techniques. More specically, these param-

eters, are rock mass fracture degree as represented by RQD

(P1), weathering degree of the rock mass (P2), overload factorstability factor (N) (P3), rock mass quality represented by RMR classication

(P4), uniaxial compressive strength of the rock (UCS) (P5), overburden-construction depth (P6), hydrogeological conditions represented by the water-

table surface relative to the tunnel depth (P7), rock mass permeability (P8).

Many of them have already been proposed as indi-

cators of the tunnelling eciency. For example, the

fracture degree of rock masses is extremely important to

TBM tunnelling (Deere and Deere, 1988), the overload

factor, rst introduced by Peck (1969), can provide in-formation about the face stability conditions. In addi-

tion, the compressive strength is inuencing TBM

performance, while RMR is very important as it denotes

the tunnels stand-up time and is also used in TBM

performance analysis (Sapigni et al., 2002). Finally, as

Terzaghi (1950) noted the hydrogeological conditions

and the presence of water is directly or indirectly linked

to the problems occurring in soft ground tunnelling.From a rst point of view, it appears that there is a

degree of interconnection between the parameters (e.g.

derground Space Technology 19 (2004) 597605 599RDQ is incorporated in RMR), that might bias the

nal results. Nevertheless, each parameter describes a

specic issue and the information provided can further

assist in the deeper understanding and clarication of

the possible problems or mishaps encountered. For

instance, even when there are cases with the sameoverall RMR values, where similar behaviour is ex-

pected, the dierentiation in the fractures and joint

network, consequently and in the RQD values, might

lead to dierent stability conditions; stable conditions

in one case, while experiencing instabilities and col-

lapses on the other.

The case study used for the model development is an

interstation tunnel of the Athens Metro. The geologicalsetting is a system of low-level metamorphic sedimen-

tary weak rock consisted of interbedded marly lime-

stones, calcareous sandstones, siltstones, conglomerates,

phyllites and schists. The formations are intensely

thrusted, folded and faulted with a variable and erratic

degree of weathering and alteration (Kavvadas et al.,

1996). The examined tunnel is located between theKatehaki and Panormou stations (Fig. 3). It is the lon-

gest interstation tunnel in the Athens Metro, until now,

having a total length of 1129.36 m (Attiko Metro SA,

1995a). The examined tunnel length is approximately

1077 m, excluding the rst 53 m (learning curve period).

The area is divided in 11 control areas (segments), in

which the data is collected and the assessment of the

selected geological properties is made (Fig. 3). All datafrom boreholes have been spatially modelled so as to

identify the properties especially within the 12 m thick

Fig. 3. Layout of the examined Athens Metro tunnel.

600 A.G. Benardos, D.C. Kaliampakos / Tunnelling and Underground Space Technology 19 (2004) 597605Fig. 4. Spatial modelling of the RQD values in the area of the examined tunnel.

For each segment, a corresponding value for every

principal parameter is taken. Allocating a representative

value for the parameters is accomplished by the spatial

modelling of the parameters value and by the incor-

poration of statistical distribution that mimics the pa-rameters behaviour in each segment (Benardos, 2002).

In Fig. 4 the spatial modelling of the RQD values is il-

lustrated, for the whole analysis area.

In the next step, the data is categorised in four in-

terval scale classes, from 0 to 3, where 0 denotes the

worst case and 3 the best. The limits taken in every class

are representative of the specic site conditions and the

machine characteristics. In the case of the Athens metro,the tunnel is constructed in relative low depth and, in

Table 1

Rating of the principal parameters

Value class Rating

Rock mass fracture degree RQD

60 3

Overload factor (N)

>5 0

35 1

A.G. Benardos, D.C. Kaliampakos / Tunnelling and Underground Space Technology 19 (2004) 597605 6011.253 2

10 0

510 1

05 2

The tunnelling advance rate, achieved in each seg-

ment, is also introduced into the ANN model. Hence,

the input vector of the principal parameters is tallied to

the output vector of the mean achieved advance rate, in

each segment (Table 3), expressed in m/day (AttikoMetro SA, 1995b). Note that all external origin delays

(e.g. strikes, maintenance, etc.) have not been taken into

account.

4. ANN development

In order to proceed with the development of theANN model, the dataset of the whole 11 analysis

segments has been divided into two subsets. The rst

one (training subset A) is used for the ANNs training,

whereas the second (test subset B) is used for the

validation of the models generalisation capability.

Special focus is given on the second subset (B), as the

network consistency should be ensured for the whole

spectrum of cases. Thus, a set incorporating the mostrepresentative cases, in terms of the achieved advance

The LevenbergMarquardt algorithm, selected for

training the ANNs, is a variation of the classic back-

propagation algorithm that, unlike other variations that

use heuristics, relies on numerical optimisation tech-

niques to minimise and accelerate the required calcula-tions, resulting in much faster training (Demuth and

Beale, 1994). More specically, the direction in which

the search is made is described by the following equa-

tion:

xk1 xk A1k gk;where, Ak is the Hessian matrix of the error function atthe current values of weights and biases and gk is thegradient of the error function.

Since the error function has the form of a sum of

squares the Hessian matrix can be approximated as

A JT J ;and the gradient as

g JT e;where, J is the Jacobian matrix, which contains rstderivatives of the network errors with respect to the

weights and biases, and e is a vector of network errors.

602 A.G. Benardos, D.C. Kaliampakos / Tunnelling and Underground Space Technology 19 (2004) 597605rate, has been selected. Apparently, segments no. 2, no.

7 and no. 9, are selected as they represent the worst, the

best and an average case. Consequently, the two subsets

are comprised by the data collected in the following

segments: A {1, 3, 4, 5, 6, 8, 10, 11} and B {2, 7, 9}.The neural network toolbox of the Matlab software

package has been used for building the ANN code andperforming the training and testing of the model.Fig. 5. ANN code development in the MaFinally, the search direction is given by

xk1 xk JT J l I 1 JT e:In the case where the scalar l is zero, this is just

Newtons method, using the approximate Hessian ma-

trix. When l is large, this becomes gradient descent witha small step size. Newtons method is faster and more

accurate near an error minimum, so the aim is to shifttlab Editor/Debugger environment.

ror v

d Underground Space Technology 19 (2004) 597605 603towards Newtons method as quickly as possible. Thus,

l is decreased after each successful step (reduction inperformance function) and is increased only when a

tentative step would increase the performance function.

In this way, the performance function will always be

reduced, at each iteration, of the algorithm.

The ANNs performance is assessed in terms of the

Fig. 6. Training er

A.G. Benardos, D.C. Kaliampakos / Tunnelling anrelative error level (D) achieved, between the actual andthe predicted advance rate (AR), following the expres-

sion:

D ARactual ARpredictedARactual

:

This criterion can provide a clear aspect regarding the

ANN behaviour and moreover makes possible the

comparison between the ANN results and other meth-ods or theoretical models focusing on advance rate

prediction.

A number of test runs have been conducted in order

to come up with the network architecture that produces

the more consistent results. From the various network

architectures that were examined, two particular ANN

architectures (8 9 4 1 and 8 10 7 1) provedto be more promising as they responded quite well to thetraining process. The ANN that was nally selected

followed the rst architecture, namely the 8 9 4 1form. This particular structure type means that the

ANN has a total of 4 layers, with 8 neurons in the input

level, same as the number of the parameters, two hidden

layers with 9 and 4 neurons respectively, followed by 1

neuron in the output layer that eventually generates the

value of the advance rate. The code used for the ANNdevelopment is presented in Fig. 5. The mean squared

error (MSE) of training for this particular ANN model

approximates 1.4 1027 and is attained after 103training epochs, as illustrated in Fig. 6.

The results generated from the trained model were

very satisfactory (Table 4). The relative error between

the model outputs and the validation subset ranges in

s training epochs.the region of 6% and 8%, reaching a maximum of about

8.4%, a level that is quite acceptable. Furthermore, the

ANN behaviour shows that the results are consistent in

all the validation subset segments, element of major

importance for an accurate and eective measurement of

the TBM performance.

In Fig. 7 a surface plot of the model is presented. It

has been constructed in relation with the RMR andUCS parameters for a given RQD value of 0.5; the

values of all other parameters are taken equal to their

mean values. This nomograph can be used as a way of

presenting the eect of the selected parameters on the

TBM advance rate.

Table 4

Comparison between the ANN generalisation output and the actual

advance rate data

Segment ANN generalization

results

Actual data Relative error

2 4.8545 4.54 0.0693

7 17.6875 16.67 0.061

9 9.9424 10.85 )0.0837

d Underground Space Technology 19 (2004) 5976055. Conclusions

The development of articial intelligence methods for

modelling TBM performance has been well accepted

through the scientic community, as the various at-tempts made in that eld proved their eciency. The

ANN system used in this paper demonstrated very sat-

isfactory results in predicting the achieved advance rate

for the case study in question. The resulting remarks can

be drawn hereinafter:

Once trained, the ANN can become a practical o-the-self tool for the prediction of the tunnelling ad-

vance rate. Its ease of use and its straightforwardnessin giving the results can allow its utilisation even for

on-site assessments.

The open source code increases the models exibility,allowing also the insertion of additional data enhanc-

ing the prediction accuracy of the nal results, even

on daily basis.

The prediction of the TBM advance rate can be usedfor the identication of risk-prone areas. As the mod-el is based on geotechnical data, a drop in the ad-

vance rate indicates that the area in question may

Fig. 7. Surface plot of the expected advance rate with respect to RMR

and UCS for a given RQD value.

604 A.G. Benardos, D.C. Kaliampakos / Tunnelling aneventually pose threats to the tunnelling process

and special attention should be paid.

The ANN model can also be utilised for a projectsstrategic development. Thus, it can be used either

for choosing the best tunnel alignment from a num-

ber of alternatives, or selecting the most appropriateground improvement technique if needed to over-

come any diculties or major downtime due to ad-

verse ground conditions. In both cases, scenario

analysis can be performed by changing the values of

the input parameters, with respect to the proposed

tunnel alignment or technique followed. Thus, a di-

rect comparison can be made in nancial terms, re-

garding the best possible selection that wouldensure the projects success.

Finally, it should be noted that in all cases a number

of records should be available in order to come up with

Underground Space Technology 11 (1), 510.

Einstein, H.H., Dudt, J.P., Halabe, V.B., Descoudres, F., 1992.Decision aids in tunnelling principle and practical application.

Monograph, Swiss Fed. Oce of Transportation, Alptransit

Project.

Eisenstein, Z., 1999. Urban tunnelling challenges & progress. ITA 25th

Anniversary Commemorative Book.

Fausett, L., 1994. Fundamentals of Neural Networks. Architectures,

Algorithms and Applications. Prentice Hall International Editions,

New York.

Kavvadas, M., Hewison, L.R., Laskaratos, P.G., Seferoglou, C.,consistent results. Thus, the model can nd its optimal

use in cases of intense urban underground development

(e.g. subways, sewage tunnels, etc.) as the operations are

taking place in roughly the same geological setting, with

the same methods and tools, extensive data is availablefrom past projects and a constant data ow can be ex-

pected from the worksites.

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Modelling TBM performance with artificial neural networksIntroductionArtificial neural networksModel synthesisANN developmentConclusionsReferences