Evolutionary Reliability-based Tunneling Design Techniques

8/12/2019 Evolutionary Reliability-based Tunneling Design Techniques

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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

EVOLUTIONARY

RELIABILITY-BASED TUNNELING DESIGN TECHNIQUES

A. A. Ahmed

Professor of Geotechnical and Structural EngineeringFaculty of Engineering, Ain Shams University, Cairo, Egypt

Email: [email protected]

H. A. Ali

Assistant Professor of Geotechnical and Structural Engineering

Faculty of Engineering, Ain Shams University

S. M. ElAraby


Faculty of Engineering, Ain Shams University

T. M. ElKateb


Faculty of Engineering, Ain Shams UniversityS. M. Noureldin

Ph.D. Candidate, Faculty of Engineering, Ain Shams University

Business Development Manager/ Projects Engineer,

ECG Engineering Consultants Group S.A.

P.O. Box 1167 Cairo 11511 Egypt

Email: [email protected]/[email protected]

ABSTRACT

Dependence on factors of safety and engineering experience/ judgment have been used

to be the conservative tools to deal with uncertainty. Probabilistic techniques have been

recently implemented to rational engineering design to quantify uncertainties associated

with tunneling. These techniques have various forms, such as statistical-based limit

equilibrium, and deterministic numerical analyses with random input engineering

parameters.

This paper presents a review of recent advances in probabilistic geotechnical/ tunneling

design. This covers the geostatistical techniques used to predict the stratigraphic

conditions and geotechnical parameters. The applicability of the above techniques is

investigated with emphasis on their advantages and limitations in addition to identifying

trends for future improvement.
mailto:[email protected]:[email protected]/mailto:[email protected]:[email protected]:[email protected]/mailto:[email protected]


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This paper also extends to the application of statistical techniques in geotechnical back

analysis in tunneling projects to develop representative engineering parameters for

tunneling design. The approximation of the limit state surface is essential to achieve an

efficient statistical/ reliability analysis of geotechnical systems, especially, for those

systems that cannot be developed explicitly with acceptable accuracy. For nonlinearproblems, the use of regression functions lead to high estimation errors. This paper

demonstrates the utilization of Evolutionary Artificial Intelligence Framework (EAIF)

to estimate probabilistic tunneling parameters values. The proposed technique

overcomes most of the shortcomings associated with the currently used analytical

reliability techniques.

KEYWORDS

tunneling, reliability-based design, Artificial Intelligence (A.I), ANN, uncertainty,

probability, geostatistics, decision making.

1 DETERMINISTIC VERSUS PROBABILISTIC DESIGN APPROACH

Dimensions, environmental factors, material properties, operational parameters,

construction technology, and external loads are design variables incorporating

uncertainties that may be characterized with statistical models. The deterministic

approach defines a worst case or an extreme value to meet in the design and introduces

conservatism by specifying a factor of safety to cover unknowns.

The probabilistic approach utilizes the uncertainty/ statistical characterization of input

design parameters to determine their implication on the output forecast parameters

(probability of failure/ uncertainty of an output forecast).

The application of a factor-of-safety to cover uncertainties has a successful history;however, the main shortcoming of this approach is that the factor of safety may be too

large, or in some cases, too small. Because it has worked in the past, there is no

guarantee that it will be satisfactory in the future. The whole approach of worst case

extremes can lead to unsafe or uneconomic designs. To select a factor-of-safety, solely

on the basis of being a successful approach in the past, should be thoroughly revised.

The Safety Factor reflects the condition of the problem, the engineer's judgment, and the

degree of conservatism incorporated into the parameter values. A primary deficiency

incorporated with this approach is that the design parameters (material properties,

strengths, loads, etc.) must have single/ deterministic values (deterministic approach),

while these values are, in fact, should be treated as uncertain/ non-deterministic.

The Reliability/ Probabilistic approach extends the safety factor concept to incorporate

uncertainty in the design parameters. This uncertainty can be quantified through

statistical analysis of existing data or judgmentally assigned. Even if judgmentally

assigned, the probabilistic results will be more meaningful than the deterministic

approach because the engineer provides a measure of the judgment uncertainty in each

parameter.

2 CURRENTLY USED RELIABILITY APPROACHES

Application of reliability principles was primarily developed to perform probabilistic

slope stability analysis using different approaches, such as analytical approaches and

MCS. Analytical approaches were primarily apprehensive with obtaining closed form


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solutions for the statistical properties of the factors of safety which do not provide

information about the output probability distribution. Besides, it becomes highly

complicated when taking into account different sources of uncertainty. Noureldin [13]

described the shortcomings of the currently used approaches that can be summarized as

follows:

a) In many complicated and nonlinear problems where the analyses involve the use ofnumerical procedures such as the finite element method, it is difficult to express the

problem explicitly in terms of the random variables, and therefore the limit state and

the performance functions can only be expressed implicitly rather than in a closed-

form-solution (Goh and Kulhawy, 2003).

b)The currently used techniques are considered difficult to be implemented, as toachieve accurate results, thousands of finite element analysis runs are needed.

c)The variation of the input parameters undergoes mathematically defined parametercombinations which should be randomly set.

3 UNCERTAINTY IN SOIL DESIGN PARAMETERS

Uncertainty in soil design parameters is a function of inherent soil variability,

measurement error and model uncertainty. These components can be combined

consistently using the fol lowing probabil is t ic approach [15 and 16]:

a)Assume that the design parameter (d) is predicted from a test measurement (m)using the probabilistic transformation model:

d= T(t + w +e, ) (1)

Where d is the design parameter predicted from a test measurement

m,

t is the deterministic trend,

w is the inherent variability,

e is the measurement error, and

is the model error.

b)Linearize the Equation about the mean of (w, e, ) using a first-order Taylor seriesexpansion [2]:

dT(t,0) + w T/w|(t,0) + e T/e|(t,0)+ T/|(t,0) (2)

c)Estimate the mean and variance of d by applying second-moment probabilistictechnique:

MdT(t,0) (3)

sd2[T/w|(t,0)]

2sw2

+ [T/e|(t,0)]2se

2+ [T/|(t,0)]2s

2


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Where: mdand sd are the mean and variance of drespectively,

sw is the variance of inherent soil variability,

se is the variance of measurement error, and

s is the variance of model error.

d)The spatial average of d is defined as:1

( )bt

z

a z d

a

z dzL

= (4)

Where: a is the spatial average,

ztand zb are the top and bottom coordinates of the depth interval,

and

La= zb- zt is the averaging length.

the variance of the spatial average (sa)2is given by [18]:

sd2[T/w|(t,0)]

22(La) sw2

+ [T/e|(t,0)]2se

2+ [T/|(t,0)]2s

2 (5)

Where: 2() is the variance reduction function, which depends on the

length of the averaging interval (La)

The following approximate variance reduction function is proposed for practical

application [18]:

2(La) = 1 for La v (6)

2(La) = v/La for La > v (7)

Where: v is the vertical scale of fluctuation.

The above general probabilistic approach is applied to determine the typical range of

variability for soil design parameters.

Correlation coefficients between field tests results and soil geotechnical parameters are

essential for estimating the parameters required for the design development. The

following parameters are the main parameters in concern:

a)Shear strength,b)Friction angle, andc)Stiffness modulus.SPT is abundant in nearly all the geotechnical investigations of tunneling projects in

Egypt due to being simple and economic, as well as proving to be strong positively

correlated to the soil strength and to the elasticity parameters. The SPT N-value

recorded during the geotechnical investigation of Greater Cairo Metro - Line No. 2, is

used for predicting the soil design parameters.


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4 GEOSTATISTICAL ANALYSIS OF LOT 42, GREATER CAIRO METRO,

LINE NO. 2

The case study in concern is Lot 42 which a part of Phase 2A extending from El-Dokki

to El-Gezira. Being a mega national Project, the Egyptian National Authority ofTunnels (NAT), conducted an extensive geotechnical investigation program for the

subsurface conditions along the project route. The investigation incorporated deep

boreholes with a majority of SPT tests; the following evaluation of the subsurface

conditions is based on the data gathered throughout that investigation. The site strata

comprise the following (Figure 1):

1. FILL: Appears at the ground surface and extends to a depth of about 1.0 m. The fillcontains asphalt, sand, clay and limestone pieces.

2. CLAY: A medium to stiff silty clay or clayey silt layer exists below the fill andextends to a depth of about 7.00 m below ground surface.

3. SAND: A medium dense to very dense fine to medium sand layer underlies the clayand extends to the end of the borings.

4. GROUNDWATER: Groundwater appears at about 3.50 m below the groundsurface.

The SAND layer exhibited refusal at a depth of 18.50 m till the end of the boring. The

SAND layer exhibiting refusal was treated as a separate sand layer, with geostatistical

parameters corresponding to that of Dense Sand in the available literature review

sources.

Fig. (1): Soil Log at Lot 42 Location


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Fig. (2): SPT N-Value of SPT Vs Depth

Figure (2) through Figure (4) and Table (1) illustrates the Sand Layer geostatistical

analysis results. The above mentioned approach is used to investigate uncertainties

associated with the predictions of the following soil design parameters along with the

available guide values found in the literature.

Table (1): SPT N-Value Statistical Parameters at Tunnel Location

Parameter Value

Mean 29S2 16

S2W 11

S2e 5

Standard Deviation 4

COV 13.79%

COVw 11.44%

COVe 7.71%

Scale of Fluctuation () 2.00 m *

Autocorrelation Distance 0.50 m

* This result conforms to the results obtained by Jones et al. (2002) 2.40 m


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Fig. (3): Autocorrelation Function (ACF) for Sand

Fig. (4):Estimation of Measurement Error


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4.1 Friction Angle:

Estimation of can be deduced using the following equation obtained from Peck et al.[14], using uncorrected SPT N-values.

= 53.881 27.6034 *e-0.0147* N

(8)

The transformation function can be expressed as follows:

-0.0147*(t+w+e)53.881 27.6034d e =

(9)

In which (t+w+e) =N. The mean and variance for this design property () can be

determined as follows:

-0.0147t53.881 27.6034dm e

(10)

-0.0147t2 2 20.4058 ( ) ( )w eds s se

2s + + (11)

The COV ofd

is given by:

-0.0147t2 2 20.4058 ( ) ( )w ed COV COV COV COV e

2 + + (12)

The COV of the spatial averaged

can be obtained as follows:

-0.0147t 22 2 20.4058 ( ) ( )

a w ed COV COV COV COV e L2

+ + (13)

4.2 Modulus of Elasticity of Cohesionless Soils:

Coduto [5], Table (2), and Bowles [3], Table (3), present a list of indicative values for

the elasticity modulus based on the soil type.

Table (2): Typical Values for Youngs Modulus for Sand [5]

Soil Type Es, kPa

Loose sand 10,000-25,000 Medium dense sand 20,000-60,000 Dense sand 50,000-100,000

Table (3): Typical Values for Youngs Modulus for Sand [3]

Soil Type Es, MPa

Sand and gravel Loose 50-150 Dense 100-200

Young's Modulus was correlated from the following equations introduced by Bowles

[3]:

E(kPa) = 500*(N+15) (14)

Where N is the SPT N-value


500 * ( ) 7500d t w e = + + + + (15)


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In which (t+w+e) =N. The mean and variance for this design property can be


500*( 15)dm t + (16)22 2 2

(500 )w ed

2s s s s

+ +

The COV ofd

is given by:

22 2 2 ( / )dw ed COV COV COV s m + + (17)

The COV of the spatial averaged

can be obtained as follows:

2 22 2 2 ( / )a w ed COV COV COV L s m + + d (18)

4.3 Modulus of Elasticity of Cohesive Soils:

Tables (4) and (5) present a list of indicative values for the elasticity modulus based on

soil type:Table (4): Typical Values for Youngs Modulus for Clay [5]

Soil Type/ Condition Es, kPa

Undrained Condition

Clay

Soft 1,500-10,000 Medium 5,000-50,000 Stiff 15,000-75,000

Drained Condition

Soft 250-1,500 Medium 500-3,500 Stiff 1,200-20,000

Table (5):Typical Values of Youngs Modulus for Clay [3]

Soil Type Es, MPa

Clay

Very soft 2-15 Soft 5-25 Medium 15-50 Hard 50-100 Sandy 25-250

Youngs Modulus is correlated by means of the following equations [3]:

E = (150 to 200).C (19)

Where C is the shear strength;


150 * ( )d t w e = + + (20)

In which (t+w+e) =C. The mean and variance for this design property can be



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150*dm t (21)

22 2 2(150 )w ed

2s s s s + + (22)

The COV ofd

is given by:

22 2 2 ( / )dw ed COV COV COV s m + + (23)

The COV of the spatial averaged can be obtained as follows:

2 22 2 2 ( / )a dw ed C O V C O V C O V L s m + + (24)

Figure (5) shows the elasticity modulus variation with depth. Tables (6) and (7)

illustrates the elasticity modulus geostatistical properties at the Case Study Location.

Fig. (5): Soil Log at Lot 42, Variation

of the Elasticity Modulus with Depth

Fig. (6): Simulation Cycle using Hybrid ANN/

MCS System


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Table (6):Elasticity Modulus Geostatistical Parameters at Lot 42, Using the

Correlations Reported By Bowles [3]

Sand Layer (1)

Eref(kPa) Normal Probabilistic Distribution Function

Mean (kPa) 1.25E+04Variance 3.05E+07

S.D. (kPa) 5.52E+03

COV (%) 44.07%

Mean + S.D. (kPa) 1.80E+04

Mean - S.D. (kPa) 7.00E+03

Einc(kPa) 3.55E+03

yref (m) -3.50

Sand Layer (2)


Mean (kPa) 6.49E+04

Variance 3.05E+07S.D. (kPa) 5.52E+03

COV (%) 8.50%

Mean + S.D. (kPa) 7.04E+04

Mean - S.D. (kPa) 5.94E+04

Einc(kPa) 3.55E+03

yref (m) -18.50

Clay

Emin(kPa) 9E03

Emax(kPa) 2E04

** For the Sand layer, the modulus of deformation is assumed to proportionally increase with depth

according to the correlation with SPT N-value.

Table (7): Elasticity Modulus Geostatistical Properties at Lot 42, Using the

Correlations Reported by Phoon [15]

Sand Layer (1)


Mean (kPa) 8.08E+03

Variance 5.16E+07

S.D. (kPa) 7.18E+03

COV (%) 88.89%

Mean + S.D. (kPa) 1.53E+04

Mean - S.D. (kPa) 8.98E+02

yref (m) -3.50

Sand Layer (2)


Mean (kPa) 1.38E+04

Variance 1.45E+08

S.D. (kPa) 1.20E+04

COV (%) 87.08%

Mean + S.D. (kPa) 2.58E+04

Mean - S.D. (kPa) 1.78E+03

yref (m) -18.50

** For the Sand layer, the modulus of deformation is assumed to proportionally increase with depth

according to direct correlation with SPT N-value.


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4.4 Transformation (Model) Error:

It should be noted that the transformation (model) error of the correlation equations is

neglected due to the following reasons:

a)The transformation (model) error is relatively negligible compared to the inherentvariability and the measurement error, andb) Lack of data related to the scatter or regression error.4.5 Soil Geotechnical Parameters at Lot 42

In the light of the above mentioned analyses, Table (8) illustrates the findings of the

geostatistical analysis.

Table (8): Soil Geotechnical Parameters at Lot 4275

Clay Sand Layer (1) Sand Layer (2)Property

Distribution Mean S.D. Mean S.D. Mean S.D.

Mod. Of Elasticity,

Eref(kPa)

Variable min. 9E+03 max 20E+03

1.25E+04 5.52E+03 6.49E+04 5.52E+03

Angle of Friction, Normal N/A N/A 360 20 410 20

Cohesion, C (kPa) Normal 60 20 N/A N/A N/A N/A

It is worth mentioning that simplifying assumptions are essential from a practical point

of view. According to El-Ramly [7] and ElKateb [6], simplifying assumptions are often

adopted for the inherent soil variability. Principal assumptions can be made according

to the geometry of the project. In projects with significant extent (e.g. long

embankment) soil properties can be averaged vertically in each borehole and the

averaged values are used to estimate the horizontal autocovariance function. However,

in cases where the vertical function is more important (e.g. compressibility), averages ofmeasurements at the same elevation in different boreholes are used to estimate the

vertical autocovariance function.

In analyzing the stability of the dykes of the James Bay project, Christian et al. [14]

adopted a single isotropic autocorrelation distance for all soil properties and layers. This

study has been limited to studying the soil inherent variability in the vertical direction

due to a) the absence of a well defined plan for the soil investigation program in the

horizontal direction, b) focusing on the soil vertical variability which is the major factor

affecting deformations and straining actions associated with tunneling. This study is

limited to investigating the inherent variability in the vertical direction.

5 ARTIFICIAL NEURAL NETWORK (ANN)/ MONTE CARLOSIMULATION (MCS) HYBRID SYSTEM

The use of Artificial Neural Networks (ANNs) in geomechanics has significantly

increased in the last decade [12 and 13]. Moreover, their successful applications in other

fields of decision-making and in computer and electrical engineering is expected to lead

to further interest and confidence in their applications in all fields of civil engineering.

The expert judgments that must routinely be made in geotechnical engineering make it

an excellent field for ANN applications. The objective of this paper is to utilize the

ANN technique in obtaining an A.I. based expression that approximately represents the

performance function. A Hybrid Model Using ANN/ MCS is developed to calculate the


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statistical moments of the performance function (the mean and variance of the

performance function).

The Hybrid ANN/ MCS technique was innovated by virtue of generating and compiling

a Dynamic Link Library file (DLL) for the ANN and embedding it to a macro

application written in Microsoft Visual Basic Language, Figure (6). This linkage,

as illustrated in Figure (6), overcame a major shortcoming of ANNs. This shortcoming

is related to information storage. The information acquired during training is stored in

the connection weights in a complex manner that is often difficult to interpret. In

general, the rules governing the relationships between the network input/output

variables are difficult to quantify, and thus ANNs are often criticized for being black

boxes. The technique presented in this paper is considered a utility to overcome this

black box limitation. Other techniques used to overcome the shortcomings of ANNs

using neuro-fuzzy techniques have been tackled by Shahin [17].

The technique utilized for reaching the optimal neural network for the study conducted

in this paper is an Evolutionary Generalized Feedforward Network "EGFFN" which is ageneralization of the Multilayer Perceptron (MLP), such that connections can jump over

one or more layers. In theory, a MLP can solve any problem that a Generalized

Feedforward Network can solve. In practice, however, EGFFNs often solve the problem

much more efficiently. A standard MLP requires hundreds of times more training

epochs than the EGFFNs containing the same number of processing elements, Figure

(7).

6 BACK-ANALYSIS USING NON-DETERMINISTIC APPROACH TO

DEMONSTRATE THE STRESS RELEASE CORRESPONDING TO

CONFINEMENT LOSS

The monitored settlement profiles for Cairo Metro Line No. 2 revealed the following

[5]:

a)The back-calculated distance for the point of inflection i varied at different Lotsand different locations between 5.8 m and 8.3 m. Some of the observed relationships

for i/aversus z/2a(ais the tunnel radius) varied between 1.0 and 2.0 for Phase 1 and

between 1.3 and 1.85 for Lots 40, 42 and 46 (Phase 2A).

b) The back-calculated volume losses at the Cairo Metro Line No. 2 at the beginning oftunneling for Phase 1 at Lots 12, 14 and 16 averaged at 0.5% and exceeded 0.8% at

some locations. On the other hand, the back-calculated volume loss for Phase 2A was

estimated at 0.3% average and 0.5% maximum.In order to determine the stress release corresponding to the confinement loss occurred,

an ANN/MCS Hybrid System Back-Analysis Framework HSBAF was used to

express the probabilistic parameters of the stress release under the uncertainty of the soil

parameters including shear strength parameters and the modulus of deformation

following two aspects:

a)Measured surface settlement at the lot under study: HSBAF-1b)Values of volume loss mentioned in literature: HSBAF-2.The test section is analyzed through approximately 300 runs using the geotechnical

finite element code Plaxis version 7.2. The main goal of the FEA is to carry out a


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non-deterministic parametric study for the stress release factor at Lot 42, and to

facilitate a source of input data that can represent the performance of tunneling in the

section under study. The soil was modeled by 127 fifteen-node elements. The Mohr-

Coulomb elastic perfectly plastic model was used to represent the nonlinear, stress-

strain behavior of the soil. The angle of friction (), the cohesion (C), and the modulusof elasticity (E) were introduced to the analysis as random variables with Probability

Distribution Functions (PDFs) as mentioned in Table (8).

Sixty percent (60%) of the FEA runs were used for training, while the rest were divided

equally between the cross validation and testing data sets. The neural network algorithm

was then used to determine the Stress Release Z (, C, E, Smax) & Z (, C, E, Vs),

which represent the stress release occurred as a function of the random variables , C,

Esand, Eclay and the maximum surface settlement at the centerline of the tunnel

Smax or the volume of the settlement profile at the ground surface Vs. The optimal

neural network constituted of six (6) input neurons representing the input variables, one

hidden layer containing four (4) neurons, and one (1) output neuron representing theStress Release factor (1-). EGFFN Model configuration and results are illustrated in

Figure (7) and the evaluation of the ANN model performance is demonstrated in Tables

(9) and (10).

Table (9): HSBAF-1: Data Sets Performance

Performance Training Cross Validation Testing

MSE (Mean Square Error) 0.001 0.001 0.001

NMSE (Normalized MSE) 0.022 0.041 0.036

MAE (Mean Average Error) 0.021 0.025 0.025

Min Absolute Error 0.000 0.000 0.001

Max Absolute Error 0.067 0.141 0.109

r (correlation) 0.990 0.985 0.982

Table (10): HSBAF-2: Data Sets Performance

Performance Training Cross Validation Testing

MSE (Mean Square Error) 0.001 0.001 0.003

NMSE (Normalized MSE) 0.035 0.023 0.089

MAE (Mean Average Error) 0.023 0.021 0.028

Min Absolute Error 0.001 0.001 0.000

Max Absolute Error 0.098 0.072 0.368

r (correlation) 0.989 0.990 0.957

The final forecast charts (Figures 8 and 9) reflect the combined uncertainty of theassumption on the models output. The analysis of both the first and the second

approaches revealed that the stress release occurred has a mean value of 16% and 19%

with a Standard Deviation of 6% and 7% respectively having a best fit of a Gamma

Distribution Probability Distribution Function.


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Fig. (7): Configuration of ANN for Predicting Stress Release Factor

Fig. (8):HSBAF-1, PDF of (1-) Corresponding to max. Surface Settlement of 10 mm,

Gamma Distribution, Loc. =0.09, Scale=0.05, Shape=1.50


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Fig. (9): HSBAF-2, PDF of (1-) Corresponding to Vs=0.30%

Gamma Distribution, Loc. =0.10, Scale=0.05, Shape=1.93

7 SUMMARY AND CONCLUSION:

Tunneling is subject to a diversity of uncertainties compared to other areas of

geotechnical engineering. Accordingly, it is never possible to unerringly predicttunneling conditions. However, it is possible to determine the range over which those

parameters may vary. Such deliverable can in turn serve as a basis for risk analysis and

decision making under uncertainty. It is shown that the prediction of statistical soil

strength and deformation parameters using Geostatistical analysis techniques is the key

to non-deterministic/ reliability/ probabilistic analyses.

The conventional deterministic approach does not account for quantified uncertainty

and relies on conservative parameters to deal with uncertain conditions. Using such

approach, the impact of subjective conservatism cannot be assessed and conservative

design can not be considered as a safeguard.

On the contrary, non-deterministic analysis incorporates uncertainty, and providesgreater insight into design reliability; thus, enhancing the engineering judgment and

improving the decision making process. The next stage in the progress of tunneling

design shall count on non-deterministic tunneling analysis.

Applicability and cost/time effectiveness are key elements in order to effectively convey

and communicate a probabilistic methodology to practicing engineers. An

approximation of the limit state surface is essential for achieving efficient reliability or

probabilistic analysis of geotechnical systems for which their models cannot be

developed explicitly. For nonlinear problems, the use of simple regression functions

may lead to high estimation errors.


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This paper demonstrated an alternative procedure based on the evolutionary neural

network algorithm to develop an approximate limit state surface overcoming most of

the shortcomings of the currently used techniques. By implementing a hybrid system

using ANN/ MCS, it is possible to estimate the probabilistic value of soil unloading/

deformation parameters associated with soft ground tunneling conditions by using apractical technique and an easy to implement number of FEA runs, Figure (10) . The

proposed Hybrid System Backanalysis Framework (HSBAF) has proven to be a

promising technique in probabilistic assessment of non-deterministic factors. However,

coupling both neural networks and Genetic Algorithm (Evolutionary Generalized

Feedforward Network, EGFFN) technique has proven to be reliable, effective and

efficient in refining and improving the performance of neural network architectures.

Figure (10): Decrease in the Overall Number of FEA Runs Required by the

Proposed Hybrid Model

8 ACKNOWLEDGEMENT

We, the authors, would like to express our gratitude to all those who gave us the

possibility to complete this work. We are deeply indebted to Prof. Dr. Fathalla

ElNahhas, Ain Shams University, whose help, stimulating suggestions and

encouragement helped us floating the boat.

We would also like to express our sincere gratitude and appreciation to Gen. Eng.

ElHosseiny Abdel-Salamm and Dr. Ashraf AbuKreisha, Egyptian Tunneling Society/

National Authority of Tunnels NAT, for providing us with their support at all levels.

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[1] Baecher, G.B. And Chritian, J.T., 2003. Reliability and Statistics in GeotechnicalEngineering, John Wiley and Sons.

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[3] Bowles, J., 1996, "Foundation Analysis and Design", Mcgraw-Hill, New York.[4] Christian, J.T., Ladd, C.C., and Baecher, G.B., 1994, Reliability and Probability in

Stability Analysis, Journal of Geotechnical Engineering Division, ASCE, 120, (2): 1071-

1 11 1.


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[5] Coduto, D., 1994, "Foundation Design: Principles and Practices", Prentice Hall,Englewood Cliffs.

[6] Elkateb, T., 2003, "Quantification of Soil Heterogeneity", Ph.D. Thesis, Edmonton,Alberta, Canada.

[7] El-Ramly, H., 2001. Probabilistic Analyses of Landslide Hazards and Risks: BridgingTheory and Practice. Ph.D. Thesis, the Faculty of Graduate Studies and Research,Edmonton, Alberta, Canada.

[8] Goh, Anthony T. C. and Kulhawy, F. H., 2003. Neural Network Approach To Model TheLimit State Surface For Reliability Analysis. Can. J. Geotech., Rev. Can. Geotech. 40(6):

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[9] Hamza Associates, 1997. Greater Cairo Metro Line 2 Phase 2, Phase 3 TunnelMonitoring, Lot 42 (El-Dokki/ El-Gezira). Monitoring Report.

[10] Jones Allen L., Kramer, Steven L., and Arduino, P., 2002, "Estimation of Uncertainty inGeotechnical Properties for Performance-Based Earthquake Engineering", Peer 2002/16.

[11] Laso, E., Sagrario, M., Lera, G., and Alarcon, E., 1995. A Level II Reliability Approachto Tunnel Support Design. Appl. Math. Modeling 1995, Vol. 19.

[12] Noureldin, S.M. 2003. Neuronet Prediction of Settlement Associated with Soft GroundTunneling. M.Sc. Thesis, Ain Shams University, Faculty of Engineering, Cairo, Egypt.

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