Inverse Design of NATM Tunnels by Neural Networks

8/12/2019 Inverse Design of NATM Tunnels by Neural Networks

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12thICSGE10-12 Dec. 2007

Cairo - Egypt

Ain Shams University

Faculty of Engineering

Department of Structural Engineering

Twelfth International Colloquium on Structural and Geotechnical Engineering

INVERSE DESIGN OF NATM TUNNELS BY NEURAL

NETWORKS

F. M. EL-NAHHAS

Professor, Head of Department of Structural Engineering,Ain Shams University

H. E. A. ALI

Associate Professor, Department of Structural Engineering,


S. M. EL-ARABY

Assistant Professor, Department of Structural Engineering,


H. E. ABDELBARY

PH.D. Research Student, Department of Structural Engineering,


ABSTRACT

Tunnels are often designed using uncertain geotechnical data. Insufficient boreholes,

natural variation, difficulties in extracting undisturbed samples and lack of realistic

testing procedures are common impediments rendering precise prediction of the

associated deformations and lining stresses practically unachievable. Faced with these

uncertainties, geotechnical engineers usually opt to re-appraise the assumed parameters

by inverse analysis using the monitoring measurements. The parameters obtained from

such analyses can then be realistically implemented in subsequent geotechnical

assessments.

In this paper, artificial neural networks (ANNs) are used in an attempt to simulate theback analysis of the tunnels to obtain realistic parameters that can be used in the finite

element analysis to achieve more accurate design of tunnels. A large database of actual

models for a real case study of Tunnel in Algeria is used to develop and to verify the

ANN model. The designed tunnel deformations determined by utilizing ANNs through

the finite element analyses are compared with the measured deformations. The results

indicated that ANNs are useful technique for inverse design of tunnels.

KEYWORDS

Tunnels, NATM, Neural Networks, Rock Excavation, and Inverse (back) Analysis.


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1 INTRODUCTION

In order to improve tunnel ground support behaviour and reduce costs associated with

over-design or rehabilitation due to under-design, there is always a need for better

modelling capability of support and lining behaviour prior to construction. Hence, the

need exists to model the rock mass behaviour well past the yielding point, not just thetypical elastic stress modelling that currently occurs in tunnelling [1].

Incompatibility often prevails between the predicted and the real behaviour of the model

and only during construction, it is possible to re-evaluate the input data and to

continuously refine the numerical model using the field measurements and inverse

analysis techniques. In this study, the inverse analysis conducted by the artificial

intelligence techniques (in particular Artificial Neural Networks, ANN) is investigated.

Over the last few years, the use of Artificial Neural Networks (ANNs) has dramatically

increased in many engineering fields [2], [3]. In particular, ANNs have been applied to

various geotechnical engineering problems, including the design of tunnel andunderground openings [4], and have demonstrated considerable degree of success in that

field.

2 CASE STUDY

The case study involves The Bouira Tunnel, which forms part of the construction lot

Lakhdaria-Liaison RN5 of Autoroute Est-Ouest and is located near the village of

Djebahia in the north of Algeria. It is a twin tube motorway tunnel with three lanes and

walkways on both sides in each tube, as shown in Fig 1. The tubes are running parallel,

with a distance between tunnel axes of 34.5m. Excavation cross section varies between

153 and 156m2.

Fig. 1: Cross-Section of the Bouira Tunnel at East Portal

The tunnels are running below a pass located at the end of Oued Djelada bordered by

Djebel Harchaoua (Elevation +770 m) in the southwest and by Djebel Guenadir(Elevation +720 m) in the Northeast, as shown in Fig 2 [5]. The village of Ain Cheriki

is situated on this pass which shows an elevation of approximately 560m. The majority

of the tunnel alignment runs in a straight line from Northwest to Southeast before

turning to the east at the eastern tunnel portal. Overburden varies between 8 to 68m.

Table (1) shows the chainages of the portals for each tunnel.

Table 1: The Tunnel Portals are Located at the following Chainages:

Tunnel Western

Portal

Chainage (m)

Eastern Portal

Chainage

(m)

Total

Length

(m)

T1 182+985 184+230 1245

T2 183+025 184+208 1183


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Cut and cover sections have originally been planned for the western portal for T1

between chainage PK 182+985 to PK 183+040 and for T2 between chainage PK

183+025 to PK 183+075. The rest of the tunnels have been planned to be excavated

using the New Austrian Tunnelling Method (NATM).

Fig. 2:The Geological Map for Bouira Tunnel

2.1 The Tunnel and Geology

The area in which the tunnel alignment is situated forms part of folded mountain chain

(Rifo-Tellin Chain), which extends over the entire length of the Maghreb and is part

of the Alpine chain. In the area of northern Algeria it is named Tell Atlas. According

to Pique [6] the region of interest should be part of the external zones of the Rifo-

Tellian mountain chain. The external zones are further divided into the ultra-Tellian

nappe, the Tellian units sensu strictu and the peni-Tellian and southern units. Due to the

lack of the regional geologic maps, an exact allocation of the region of interest to one ofthese geological units is not possible up to now. This area has been exposed to

polyphase, complex tectonic deformation resulting in folding and faulting. Due to the

continuing convergence of Africa and Eurasia the area is at present still submitted to

active compressive faulting [6]. Three lithological formations of Senonian age are

described as follows:

- Foliated marl, strongly fractured and folded, at the base and the middle of the

excavation.

-Compact marl and hard limestone, intercalations of compact marls and of hardlimestone with a thickness of several meters.

-Clay / alterated Marl, light colored, dense marls, very superficially weathered.The longitudinal geological section, as shown in Fig 3, shows the three lithogies: sound

marl, foliated marl and clay/alterated marl. All three lithological unites may be

considered as a succession of clay and deformed marl of Senonian age.


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Fig. 3:The Longitudinal Section of the Tunnel with Geology

2.1 Monitoring

Two types of monitoring sections are considered. Monitoring section type A contains 5

points for convergence measurements and monitoring section B with 5 points for

convergence measurements and multiple rod extensometers. Distance between

monitoring sections type A is generally 100m. Three monitoring sections type B are

considered for each tunnel, Geoconsult 2004 [7]. Fig.4 shows the plan and cross-section

for the monitoring system.

Fig. 4: Schematic showing Instrumentation through Bouira Tunnel


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3.1 Calculation Steps

Table 2 shows calculation phases and the construction stages used in the finite element

simulations. The twin tunnels were explicitly modelled in the finite element simulations

while the study was carried out on tunnel (T1), as the construction of tunnel (T2) was

not started at the time when the field data measurements were recorded.

Table 2: PLAXIS Calculations Phases and the Corresponding Construction Stages

Calculation Phase Construction Stage

0 Initial Condition

1 T1 Heading Excavation

2 T1 Heading Support

3 T1 Bench Excavation

4 T1 Bench Support

3.2 Rock Parameters and Excavation Sequence

The elastic-plastic Mohr Coulomb model was used to characterise the rock constitutive

behaviour in PLAXIS simulation of the tunnel construction. Mohr Coulomb model

involves five input parameters, i.e. E and for soil elasticity; and c for soil plasticity

and as an angel of dilatancy.

A parametric study was carried out as shown in Figures 8 to 19 to obtain the most

influential parameters on the tunnel design. Based on the parametric analysis, Table 3

shows the range of the effective parameters that was used through the analysis to obtain

the horizontal deformations in order to learn the neural network model.

Fig. 8: Effect of the Unloading Ratio for Fig. 9: Effect of the Unloading Ratio for

Heading Excavation on the Vertical and Bench Excavation on the Vertical and

Horizontal Total Deformations Horizontal Total Deformations


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Fig. 10: Effect of the Ko of Foliated Marl Fig. 11: Effect of Ko of Marl Shale on

on the Vertical and Horizontal Total the Vertical and Horizontal Total

Deformations Deformations

Fig. 12: Effect of the Ko of Shear Zone Fig. 13: Effect of E of Foliated Marl of

on the Vertical and Horizontal Total on the Vertical and Horizontal Total


Fig. 14: Effect of the E of Marl Shale Fig. 15: Effect of E of Shear Zone




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Fig. 16: Effect of the C of Foliated Marl Fig. 17: Effect of Phi of Foliated Marl



Fig. 18: Effect of the C of Marl Shale Fig. 19: Effect of Phi of Marl Shale



Based on the previous parametric study, it was found that the following parameters have

the most influential on the horizontal and vertical deformations of the tunnel; Unloading

Ratio for Heading Excavation, Unloading Ratio for Bench Excavation (The Unloading

Ratio is the ratio between the part of the stresses released due to the excavation and theremained stresses that will be imposed on the lining), Youngs Modulus E for

Foliated Marl Layer, Youngs Modulus E for Compact Marl Layer, Cohesion C for

Compact Marl Layer and Friction for Compact Marl Layer.

Table 3, based on this parametric study, shows the range of the influential parameters

that was used through the analysis to obtain the horizontal deformations in order to train

the neural network model.


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Table 3:Range of the most Influential Parameters

Parameters Range Units

Unloading Ratio for

Heading Excavation

0.2 0.75 -

Unloading Ratio for

Bench Excavation0.2 0.75 -

Youngs Modulus E for

Foliated Marl Layer400 900 MPa

Youngs Modulus E for

Marl Shale Layer

100 600 MPa

Cohesion C for Marl

Shale Layer

50 100 kPa

Friction for Marl ShaleLayer

11 - 22 Deg.

The following figures from 20 to 25 showing the obtained deformations corresponding

to the variations of the most influential parameters after the heading excavation (step

no.1)

Fig. 20: Effect of the Unloading Ratio for Fig. 21: Effect of the Unloading Ratio

Heading Excavation on the Vertical and for Bench Excavation on the Vertical

and Horizontal Deformations Horizontal Deformations


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Fig. 22 Effect of the E of Foliated Marl Fig. 23 Effect of the E of Marl Shale

on the Vertical and Horizontal on the Vertical and Horizontal


Fig. 24: Effect of the C of Marl Shale Fig. 25: Effect of Phi of Marl Shale

on the Vertical and Horizontal on the Vertical and Horizontal


4 DEVELOPMENT OF NEURAL NETWORK MODEL

The Pioneering work in developing ANN models shows that neural network concepts

can be extended to constitutive relations [10], [11]. A neural network is trained using

the input and output values deduced from the finite element analysis to learn the

material behaviour. If the training data contains enough relevant information, the trained

neural network can generalize material behaviour to new loading cases.Among various types of neural networks, multi-layer feed-forward network is known to

be most suitable to describe non-linear functions [12], and so far, has been the only type

of neural network used to describe material constitutive behaviour.

The simulation of the neural network model through this work was carried out by

personal computer-based software NeuroSolutions Version 4.3 (2003) developed by

NeuroDimension, Inc [13].

The data used to calibrate and validate the neural network model were obtained from the

parametric study of the most influential parameters affecting on the tunnel design as

well as the corresponding deformations associated with the tunnel excavation. As

explained earlier, the data cover a wide range of variation in soil parameters and


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sequence of excavation (unloading ratio). The database comprised a total of 77

individual cases.

4.1 Inputs and Outputs of the ANN-based Model

Ten input parameters were used in the ANNs model, as follows:- Horizontal and vertical deformations for point no.1 (P1)- Horizontal and vertical deformations for point no.2 (P2)- Horizontal and vertical deformations for point no.3 (P3)- Horizontal and vertical deformations for point no.4 (P4)- Horizontal and vertical deformations for point no.5 (P5)While the output layer consists of the following:

- Unloading Ratio for Heading Excavation

- Unloading Ratio for Bench Excavation

- Youngs Modulus E for Foliated Marl Layer

- Youngs Modulus E for Compact Marl Layer

- Cohesion C for Compact Marl Layer

- Friction for Compact Marl Layer

4.2 Data Division and Processing

It is common practice to divide the available data into two sub-sets; a training set, to

construct the neural network model, and an independent validation set to estimate model

performance in the deployed environment [14]. However, dividing the data into only

two subsets may lead to model overfitting. As a result, and as discussed later, cross

validation [15] is used as the stopping criterion in this study and, consequently, the

database is randomly divided into three sets: training, testing and validation. In total,

70% of the data are used for training and 15 % are used for validation set and 15% for

the testing set.

4.3 Model Architecture

Determining the network architecture is one of the most important and difficult tasks in

the development of ANN models. It requires the selection of the number of the hidden

layers and the number of the nodes in each of these. It has been shown that a network

with one hidden layer can approximate any continuous function, provided the sufficient

connection weights are used [16]. Consequently, one hidden layer is used in this study.

The utilized network paradigm is a Multi-Layer Perceptron type (MLP) consisting of

multiple layers of PEs connected in a feedforward pattern. Back-propagation of errors

technique is used to train the MLP. The calculated backpropagation components of errorpass backwards from the end of the network to the beginning. The gradient search

components adjust the weights contained in the synapses and axons. The network is

constructed using the medium complexity setting which have one hidden layer. The

criterion axon reads the desired file from the attached file component and determines

the error in the network. The output axon generates the actual network outputs. The

input axon does nothing but accept the input from the file component.

The number of the nodes in the input and output layers are restricted by the number of

the model inputs and outputs. The input layer of the ANN model developed in this work

has ten nodes; one for each of the model inputs [i.e., horizontal and vertical

deformations for point no.1 to point no. 5 (P1 to P5). The output layer has six nodes

[i.e., unloading ratio for heading excavation, unloading ratio for bench excavation,


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youngs modulus E for foliated marl layer, youngs modulus E for compact marl

layer, cohesion C for compact marl layer, friction for compact marl layer]. Inorder to obtain the optimum number of hidden layer nodes, it is important to strike a

balance between having sufficient free parameters (weights) to enable representation of

the function to be approximated, and not having too many so as to avoid overtrainingand to ensure that the relationship determined by the ANN can be interpreted in a

physical sense. Overtraining is not an issue in this study, as crossvalidation is used as

the stopping criterion. However, as just discussed, physical interpretation of the

connection weights is important, and hence the smallest network that is able to map the

desired relationship should be used. In order to determine the optimum network

geometry, ANNs with one, two, three and four hidden layer nodes are investigated.

Fig. 26:The Skeleton of the Neural Network Model

4.4 ANN Model Training

The process of optimizing the connection weights is known as training or learning.

The method most commonly used for finding the optimum weight combination for

feedforward neural networks is the back-propagation algorithm [17], which is based on

first-order gradient descent. Feedforwards networks trained with the backpropagationalgorithm have already been applied successfully for many geotechnical engineering

problems [18] and [19], and are thus used in this work.

In this study, the general strategy adopted for finding the optimal parameters that

control the training process is as follows; for each trial number of hidden layer nodes,

random initial weights and biases are generated. The neural network is then trained with

different combinations of momentum terms and step sizes in an attempt to identify the

ANN model that performs best on the testing data. The momentum terms used in this

study are 0.2, 0.4, 0.6, 0.8 and 1.0 whereas the step sizes used are 0.01. 0.05. 0.1. 0.3.

0.6 and 1.0

4.5 Stopping CriteriaStopping criteria are those used to decide when to stop the training process. They

determine whether the model has been optimally or suboptimally trained. As discussed

earlier, the crossvalidation technique [15] is used in this work as the stopping criterion,

as it is considered to be the most valuable tool to ensure that overfitting does not occur

[20] and as sufficient data are available to create training, testing and validation sets.

The testing set measures the ability of the model to generalize, and the performance of

the model using this set is checked at many stages of the training process, and training is

stopped then the error of the testing set starts to increase. The testing set is also used to

determine the optimum number of hidden layer nodes and the optimum internal

parameters (step size, momentum and initial weights).


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4.6 ANN Model Validation

Once the training phase of the model has been successfully accomplished, the

performance of the trained model is validated using the validation data, which have not

been used as part of the model building process. The purpose of the model validation

phase is to ensure that the model has the ability to generalize within the limits set by thetraining data, rather than simply having memorized the input-output relationships that

are contained in the training data.

5 INVERSE MODELING: UPDATING TUNNEL DESIGN USING

REALISTIC ROCK PARAMETERS

After testing the trained network, it was shown that the correlation coefficient (R2)

between the networks output and the desired value is reached up to 0.88, 0.61 and 0.67

for data sets of training, cross validation and testing, respectively, which indicates a

successful performance as shown in (Table 4).

Table 4: Performance of Network for Different Output Parameters

R2

Data Set Unloading

Ratio for

Heading

Excavation

Unloading

Ratio for

Bench

Excavation

E for

Foliated

Marl

Layer

E for

Marl

Shale

Layer

C for

Marl

Shale

Layer

forMarl

Shale

Layer

Training 0.66 0.69 0.48 0.43 0.46 0.88

Cross

Validation0.30 0.61 0.03 0.06 0.35 0.55

Testing 0.51 0.003 0.46 0.53 0.67 0.29

In Figures 27 to 44, the actual values for the most influential are plotted against the

networks output for different data sets of training, testing and cross validation.

Fig. 27 Fig. 28


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Fig. 29 Fig. 30

Fig. 31 Fig. 32

Fig. 33 Fig. 34


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Fig. 35 Fig. 36

Fig. 37 Fig. 38

Fig. 39 Fig. 40


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Fig. 41 Fig. 42

Fig. 43 Fig. 44

5.1 Comments on the results

As shown in the aforementioned figures, it is clear that the influential parameters in

tunnel design can be predicted by using a Neural Networks model. The training of the

Neural Networks model is the key of obtaining more accurate results. This effect is

appeared in Figures 29, 30, 35 and 42. In order to improve the accuracy of the results, a

larger database should be used to train the model.

5.2Validation of the modelThe neural network model is validated by comparing the results of the model with thedeformation and stress measurements that are deliberately excluded from the learning

database, as indicated in Table 4 and Figures 27 through 44.

As this work is a part of an ongoing research for using the artificial neural networks in

the back analysis of tunnels, the authors believe, at this stage, that the accuracy of the

prediction can be enhanced by adopting the results of well-trained neural networks into

the learning database. This hypothesis shall be investigated/validated at the concluding

stage of this research.


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6 SUMMARY AND CONCLUSIONS

At present, tunnels tend to be designed with considerable uncertainties. In this paper, a

neural network approach was presented to determine realistic soil/rock parameters that

to be used in the tunnel design.

A two hidden layer MLP was trained using data sets supplied by FE models. The

number of neurons, step sizes and momentum of the layers were optimized using

genetic algorithms during the training process. The testing of the trained network

showed that the neural network model can predict successfully the soil/rock parameters

that will be used in the FE model in the tunnel design.

7 ACKNOWLEDGMENT

The Authors would to thank Mr. Issam Ghalayini and Dr. Sherif Wissa, Directors of the

Geotechnical and Heavy Civil Engineering Department - Dar Al-Handasah (shair and

partners) for their kind help and permit to use data from their files on the Bouira tunnel.

8 NOTATIONS

Ko At Rest Coefficient of Earth Pressure

E Elasticity of Modulus [MPa]

C Cohesion [kN/m2]

Angle of Friction [deg.]

R2 Coefficient of Correlation

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Inverse Design of NATM Tunnels by Neural Networks

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