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املؤمتـر الدوىل العاشر للهندسة اإلنشائية واجليوتقنية

٢٠٠٣إبريل ٢٤-٢٢ القاهرة-جامعة عني مشس

Tenth International Colloquium on Structural and

Geotechnical Engineering April 22-24, 2003

Ain Shams University, Cairo, Egypt

NEURONET PREDICTION OF TUNNELING-INDUCED SETTLEMENTS

ALI A. AHMED1 HOSSAM E. ALI2 SAYED M. EL-SAYED2

SHADY M. NOUR EL-DIN3

ABSTRACT Recent proliferation of tunnels in urban congested areas necessitates the continual updating of subsidence prediction techniques using settlement records of tunnel monitoring programs. This paper concerns with characterization of the surface settlement trough associated with soft ground tunneling through a new model based on the Artificial Neural Networks (ANN). The key element of the employed paradigm is the novel combined topology of the information processing system to cover the different sizes of the learning database. The neural network has been trained using the monitoring and geotechnical data of many tunneling projects in Egypt and abroad. The training database covers a wide spectrum of construction techniques, geotechnical data and the tunnel geometrical data. The main benefit of this approach is to avoid the computational complexities of satisfying all the constraints of constructional details, geotechnical conditions and tunnel configurations in order to obtain a rigorous assessment of settlements associated with tunneling. The proposed model was practiced in analyzing the present and future status of Hydroshield tunneling in Greater Cairo. Keywords: Artificial Neural Network (ANN), tunnels, monitoring programs, settlement trough, trough width, Gaussian distribution, Standard Penetration Test (SPT), Hydroshield, Greater Cairo Metro, Al-Azhar Road Twin Tunnels.

1 Professor of Geotechnical Engineering, Ain Shams University, Cairo Egypt 2 Assistant Professor of Geotechnical Engineering, Ain Shams University, Cairo Egypt 3 M.Sc. Graduate Student, Ain Shams University, Cairo Egypt

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INTRODUCTION Tunneling specifications demand preservation of the surrounding buildings and lifelines by taking necessary measures to avert potential ground settlements. These deformations are attributed to the ground loss at the tunnel, which trigger off a chain of movements up to ground surface leading to the formation of subsidence troughs. Based on analysis of observations made on several tunneling projects, Peck (1969) proposed the double-curved settlement trough. The trough is characterized by means of a reversed Gaussian error function curve as shown in Fig. 1. Accordingly, the settlement trough is determined by two main parameters: the maximum surface settlement at the point above the tunnel centerline (Smax) and the width parameter (i) which is defined as the distance from the tunnel centerline to the inflection point of the trough. Using Peck’s settlement distribution, the spatial settlement (S) is evaluated using the following equation:

−⋅= 2

2

max 2exp

ixSS (1)

where x is the coordinate distance measured from the tunnel centerline. Settlement data compiled from monitoring programs of soft ground tunnels around the world confirmed Peck’s postulation of Gauss-function settlement troughs (Attewell et al., 1986).

FIG. (1) Surface Settlement Profiles (after Peck, 1969)

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To date, the finite element method provides the most powerful tool to simulate tunneling especially with the quick improvement in computer efficiency and availability of very powerful codes (Ahmed, 1991; Esmail, 1997, and El-Sayed, 2001). Yet, complications in developing finite element models covering the contemporary tunneling operations and intricate model parameters encourage the use novel simplified models such as artificial neural networks (ANNs). The objective of this paper is to introduce the ANN techniques in prediction of the settlement troughs induced by soft ground tunneling by making use of the monitoring data complied during the construction of tunnels.

NEURO-MODELING The use of artificial neural networks (ANNs) in geomechanics has significantly increased in the last decade. 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 application (Ali, 2000; Fayed, 2002). Artificial Neural Network (ANN) was inspired by the mechanism of biological nervous systems, such as the human brain. ANN can be defined as is a simulation of human-like response within the computer hardware and specialized software using multiple layers of interconnected processing elements called neurons, which are linked to their neighbors with varying coefficients of connectivity that represent the strengths of these connections. The analogy between the biological neural systems and Artificial Neural Networks exists only at the physical level. However, they have less in common concerning the algorithms ruling these two structures. Figs. 2 & 3 show the biological neurons and the artificial computer neuron. Artificial Neural Networks made their first appearance in the 1940s in the work of McCulloch and Pitts (1943). Nevertheless, Neural Computing has emerged as a practical alternative to algorithmic computation only in the past few years especially after the introduction of the backpropagation algorithm in the late 1980s. Neural networks can be used to extract patterns and detect trends that are too complex to be noticed by either humans or other computer techniques. A trained neural network can be thought of as an "expert" in the category of information it has been given to analyze; this expert can answer "what if" questions when dealing with a new situations of interest (Haykin, 1994).

Topology, Optimization and Generalization of the ANN Model ANNs are formed by clustering of the primitive artificial neurons into layers, which are then connected to one another. Some of the neurons interface with the external environment to receive the inputs and other neurons provide the network’s outputs. All the rest of the neurons are included in a number of hidden layers between the input and the output layers. The utilized paradigm is a Multi-Layer Perceptron type (MLP) comprising only one hidden layer. Errors between the network predictions and the desired outputs are reduced iteratively using the backpropagation algorithm (Werbos, 1974; Rumelhart et al., 1986). The model topology is composed of two-staged ANN as shown in Fig 4. The first stage (A), indicated by light solid arrows, is used to estimate the maximum settlement employing the following input parameters: the diameter of tunnel, the depth of the tunnel, depth of the groundwater table, thickness of different soil layers, and the average values of the standard

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penetration test (SPT) counted in each layers. The SPT results were selected because they represent raw geotechnical data that indicate the soil strength and stiffness (Terzaghi and Peck, 1967). The second stage (B), indicated by bold dashed arrows, is used to estimate the trough width from the following input variables: the tunnel depth, the excavated diameter of tunnel and, the maximum surface settlement obtained from the first stage.

FIG. (2) Sketch of a Biological Neuron (after Tsoukalas and Uhrig, 1997)

FIG. (3) Artificial Neuron (after Tsoukalas and Uhrig, 1997)

Input

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FIG. (4) ANN Configuration

(* indicates multiple records)

*

*

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Most instrumentation programs exercise frequenter measurements of the longitudinal maximum settlement than acquiring the transverse troughs (Murray, 1990). The difference in the available data sizes of the maximum settlements and trough widths was the key motive to divide the ANN model into two stages. Optimization of ANN topology has many performance criteria (e.g. learning rate, compactness, generalization, and noise resistance). These criteria are hard to implement concurrently because of their complex interactions. The problem of establishing the best architecture of the ANN has been tackled using the Genetic Algorithms (GAs). GAs are general-purpose search algorithms based upon the principles of evolution observed in nature. GAs combine selection, crossover, and mutation operators with the goal of finding the best solution to a given problem (Bishop, 1995).

The introduction of GA in ANNs is implemented by introducing both structure and parameters of the neural network as a fixed-length string which is evolved to minimize the error between the predicted outputs and the training set. There are four stages in the genetic search process: initialization, evaluation and selection, crossover and mutation. In the initialization stage, populations of randomly distributed genetic structures are selected as the starting point of the search. In the second stage, each structure is evaluated using a fitness function. On the basis of their relative fitness values, structures in the current population are selected for reproduction. The selected structures are recombined using crossover. A mutation operator, which arbitrarily alters one or more components of a selected structure, provides the means for introducing new information into the population (Nour El-Din, 2003). It is important to ensure that the network performs well on data that is has not been trained on. This principal is called “generalization” of ANN. The standard method of ensuring good generalization is to divide the training data into multiple data sets; namely, the training, testing (cross-validation), and validation data sets. The ANN is as good as the training data, so increasing the size of the training data enhances the performance of the ANN. The testing (cross-validation) data set is used to determine when the network has been trained as maximum as possible without over-training. If the network is starting to over-train on the data, the cross-validation performance will begin to degrade. For a true test of the performance of the network, the validation set is used. It provides a true indication of how the network will perform on new data. The network is “optimal” when the error in the validation set is at its minimum position (Patterson, 1996). Databases of Tunneling-induced Settlements The databases were collected from measured tunneling-induced surface settlements and the corresponding geotechnical information. The records cover a wide range of variation in geotechnical data and the tunnel geometrical data (depth and diameter) are detailed in Table 1. The considered cases comprise the following tunneling techniques: Hydroshield Tunneling (Greater Cairo Metro, Al-Azhar Road Tunnels and El-Salam Syphon), Earth Pressure Balance Shield (Alexandria Wastewater Tunnel), Compressed Air Shield (Cairo Wastewater Tunnel) and Open Face Shield (Alberta Experimental Tunnels). Additionally, the databases include tunnel diameters ranging between 2.5 and 9.45m with depth ranging between 5 and 25m. The geotechnical conditions vary substantially between soft alluvial deposits with shallow groundwater depths for Cairo projects, marine geological deposits of soil and limestone for Alexandria waste water projects, and glacial till for Alberta tunnels.

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It should be noted that the width parameter (i) cannot be achieved directly from the measured settlements. Nonlinear Newton-Raphson regression analysis (Chapra and Canale, 1990) was performed on the settlement measurements in order to obtain the trough width parameter (i) assuming Gauss settlement distribution (Nour El-Din, 2003). The database was randomly divided into three subsets: training data set (50% of the data), testing data set (25% of the data) and validation data set (25% of the data) in order to train the ANN and benchmark its performance. TABLE (1) Database of the Tunneling Projects Used to Develop the ANN

Project and Location (Reference)

Depth to springline

(m)

Tunnel Diameter

(m)

No. of Cases

(A*)/(B**) Greater Cairo Metro – Egypt

(Hamza Associates, 1995 & 1997) 13.4-25 9.45 17/2

North Tunnel – Al-Azhar Road Tunnels – Egypt

(Campenon Bernard-SGE, 1999) 19.5-23 9.45 2/1

Alberta Experimental Tunnels – Canada

(El-Nahhas, 1980) 27& 11.7 2.56 & 6.2 2/2

Alexandria Wastewater Tunnel – Egypt

(Kotait, 2001) 14 2.81 1/1

Spinal Tunnel – Cairo Wastewater Tunnel – Egypt

(El-Nahhas et al., 1990) 15.6 5.15 1/1

First Tunnel – Al-Salam Syphon – Egypt

(Esmail, 1997) 24 6.6 1/1

Soft Soil Tunnels (after Lee et al., 1999) 5 2.5 0/7

* Used in stage (A) ** Used in stage (B) Model Validation The most important criterion that has to be fulfilled in developing successful ANN is to attain a good performance in the validation set which was previously unseen by the model. The coefficient of correlation (R2), as defined by Chapra and Canale (1990), is considered as the key factor to evaluate the performance of analytical models. The value of R2 generally ranges between zero and one. The model behavior can be categorized according to the value of (R2) as shown in Table 2. Tables 3 and 4 show that the correlation between the validation set and ANN results are generally less the correlation between the training or testing sets and the outputs of the ANN. However, the correlation observed between all data sets and ANN can be classified as “strong”.

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The plots of the measured and predicted settlements for all data sets are shown in Figs 5 and 6. The results indicate that the model performs well in obtaining the characteristics of the Gaussian settlement distribution. TABLE (2) Performance Criterion (Chapra and Canale, 1990)

Category Value of R2 Strong correlation More than 0.8 Medium correlation Between 0.2 and 0.8 Weak correlation Less than 0.2

TABLE (3) Correlation Coefficient for Stage (A); Estimation of Maximum Settlement.

Data set Value of R2 All data 0.92 Training data 0.95 Testing data 0.98 Validation data 0.80

TABLE (4) Correlation Coefficient for Stage (B); Prediction of Trough Width.

Data set Value of R2 All data 0.97 Training data 0.99 Testing data 0.99 Validation data 0.84

FIG. (5) Results of Stage (A)

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FIG. (6) Results of Stage (B)

PARAMETRIC ANALYSIS OF HYDROSHIED TUNNELING IN GREATER CAIRO As Cairo began its rapid population explosion, the need for new mass transportation systems was inevitable. The National Tunneling Authority (NAT) promoted two underground solutions. The first solution was Greater Cairo Metro railway tunnel and the second solution was Al-Azhar Road Twin Tunnels. Greater Cairo Metro comprises a regional line and two urban lines as shown in Fig. 7. The regional line was completed in 1989 and was the first subway metro line in Africa and the Middle East. It is 42.5 km long from El-Marg at the North of Cairo to Helwan at the South with about 4.5 km underground part through downtown area using cut-and-cover technique. Line 2 extends from Shubra El-Kheima to Giza suburban areas connecting the east and west banks of the Nile (Madkour et al., 1999). Line 3 is expected to connect Imbaba to Cairo Airport through Cairo downtown and Heliopolis district. The geology of Cairo has been outlined by Shata (1988). He concluded that Cairo is underlain by tertiary sedimentary rocks and quaternary soils, both underlain by older basement rocks. Tunnels that were driven through Cairo lie totally within the geomorphic unit known as the young alluvial plain that represents the majority of the lowland portion of the Nile Valley in the Cairo area. The Nile River deposits governed the subsurface and groundwater conditions. The Pleistocene age sediments in the alluvial plain are generally fairly consistent with depth, but vary somewhat laterally as a result of the long history of river meanders, and alternate cycles of sedimentation and erosion before the construction of Aswan High Dam in Upper Egypt in the 1960's. These sediments are approximately 60-90 meters thick in the Cairo area.

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Tunnels constructed in Greater Cairo are usually characterized by excavation through non-plastic permeable deposits usually sand with a variable content of silt as shown in Fig. 8. Such geological formations limit the tunnel construction methods to pressurized full face tunneling machines. Two identical Herrenknecht BS TBMs (Hydroshields) of 9.45m diameter were selected to drive the tunnel in Line 2. The details of the employed TBM are shown in Fig 9. One of the these TBMs was also used to drive AL-Azhar north and south tunnels to connect Salah Salem Road to Opera Square as shown in Fig 10.

FIG. (7) Greater Cairo Metro Network (after Madkour et al., 1999)

FIG. (8) Gradation of the Excavated Deposits in Line 2 of Greater Cairo Metro

(after Richards et al, 1997)

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FIG. (9) Hydroshield Details (after El-Nahhas, 1999)

FIG. (10) Layout of Al-Azhar Road Tunnels

(after Ramond and Guillien 1999)

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The ANN model was used to conduct a parametric analysis to study the settlement associated with tunneling through sand deposits with the characteristic SPT values. The diameter of the tunnel is set equal to the diameter of the Hydroshields used in driving Line 2 - Greater Cairo Metro and Al-Azhar Road Tunnels (i.e. 9.45m). Maximum settlements were calculated for various values of SPT and tunnel depth. Fig 11 shows the attenuation relation of the maximum settlement by increasing the tunnel depth. The analysis shows that loose sand tends to have approximately constant value of maximum settlement regardless of the tunnel depth while dense sand has much pronounced attenuation trend with depth. The available monitoring data concerning Line 2 – Greater Cairo Metro and Al-Azhar Road Tunnels are also marked in Fig 11. Most of the observed data tend to be located in the zone between (SPT=30) curve and (SPT=50) curve. This remark is justified by the fact that most of the considered monitoring data of Greater Cairo Metro and Al-Azhar Tunnels lies in dense granular deposits.

FIG. (11) Maximum Settlement Attenuation with Depth

Another parametric study was conducted to relate the width parameter of the trough (i) to the tunnel depth for various values of maximum settlement. The results of the analysis are shown in Fig 12. Based on the data shown in Fig 5, two levels of maximum settlement were chosen to express the tunneling status in Greater Cairo Metro (Smax=16mm) and Al-Azhar Road Tunnels (Smax ≤ 10mm). Fig 12 also shows the expected trough width limits according to Schmidt (1969) and the available monitoring data. The data conforms very well to the ANN curves but have a poor correlation with Schmidt bounds. This may be attributed to the complex relation of soil strength and stiffness versus depth that was unaccounted in Schmidt’s fitting method.

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FIG. (12) Variation of Width Parameter (i) with Springline Depth

PREDICTION OF SETTLEMENTS ASSOCIATED WITH HYDROSHIELD TUNNELING IN GREATER CAIRO METRO - LINE 3

A substantial part of Greater Cairo Metro - Line 3 is anticipated to have geological and constructional conditions similar to Line 2. Using the results of the ANN parametric analysis shown in Figs. 11 and 12, the maximum settlement is expected to range between 4mm and 15mm and the trough width is expected to range between 4m and 10m for dense sand tunneling under shallow groundwater table. Fig. 13 shows the expected settlement envelope for Line 3 based on the previous values.

FIG. (13) Probable Settlement Envelope for Greater Cairo Metro - Line 3

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SUMMAY AND CONCLUSION In the present study, a back-propagated supervised ANN model enhanced by the evolution capabilities of GA was employed to predict the settlement characteristics associated with tunneling. A novel combined topology was implemented due to the different data sizes of the maximum settlement and trough width databases. Many projects in Egypt and abroad were utilized to train, test and validate the proposed model. The database used in model training covers a wide spectrum of geological conditions, configurations and construction techniques. The model shows good results compared with settlement observed during construction especially for pressurized tunneling techniques. A parametric analysis was conducted using the ANN-based technique to reveal the geotechnical and geometric factors affecting application of the Hydroshield technique in Greater Cairo. The analysis shows that depth of the tunnel affects profoundly the settlement characteristics in dense deposits but have less influence in loose deposits. It was also shown that the width factor of the trough (i) does not necessarily increase with the increase of the tunnel depth. The proposed ANN model was used to predict the future tunneling-induced settlements for Line 3 – Greater Cairo Metro in dense sand deposits under shallow groundwater table and it was found that the probable maximum settlement is 15 mm and trough may extend to about 30m depending on the tunnel depth.

REFERENCES

1. Peck, R.B., 1969, "Deep Excavation and Tunneling in Soft Ground", State-of-the-Art, Proceeding of the 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico City, Mexico, pp. 225-290.

2. Attewell, P., Yeates, J. and Selby, A., 1986, "Soil Movements Induced by Tunnelling and Their Effects on Pipielines and Structures", Blackie & Sons Ltd., Glasgow, UK.

3. Ahmed, A.A., 1991, "Interaction of Tunnel Lining and Ground", Ph. D. Thesis, Ain Shams University, Cairo, Egypt.

4. Esmail, K.A., 1997, "Numerical Modeling of Deformation around Closed Face Tunneling", Ph. D. Thesis, Ain Shams University, Cairo, Egypt.

5. El-Sayed, S.M., 2001, "Elasto-Plastic Three-Dimensional Analysis of Shielded Tunneling with Special Application on Greater Cairo Metro", Ph.D. Thesis, Ain Shams University, Faculty of Engineering, Cairo Egypt.

6. Ali, H.E., 2000, "Neuronet Based Liquefaction Potential Assessment and Stress-Strain Behavior Simulation of Sandy Soils", Ph. D. Thesis, Kansas State University, Manhattan, Kansas, USA.

7. Fayed, A.L., 2002, “Interaction Between Deep Braced Excavation and Ground for Metro Subway Stations”, Ph.D. thesis, Ain Shams University, Faculty of Engineering, Cairo, Egypt.

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8. Mcculloch, W.S. and Pitts, W., 1943, "A Logical Calculus of the Ideas Immanent in Nervous Activity", Bullettin of mathematical Biophysic, 5: pp.115 – 133.

9. Tsoukalas, L.H. and Uhrig, R.E., 1997, "Fuzzy and Neural Approaches in Engineering", John Wiley & Sons Inc, NY, USA.

10. Haykin, S., 1994, “Neural Networks: A Comprehensive Foundation,” Macmillan Publishing, NY, USA.

11. Werbos, P.J., 1974, "Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences", Ph.D. thesis, Dept. Applied Mathematics, Harvard University, Cambridge, Mass, USA.

12. Rumelhart, D.E., Hinton, G.E. and Williams, R.J., 1986, “Learning Internal Representations by Error Propagation,” in Parallel Distributed Processing, Rumelhart and McClelland (Eds.), Vol 1, Cambridge, MA: MIT Press, USA.

13. Terzaghi, K. and Peck, R.B., 1967, "Soil Mechanics in Engineering Practice", John Wiley & Sons, Inc., New York, USA.

14. Murray, R.T., 1990, "Rapporteur's Paper", in Geotechnical Instrumentation in Practice, Proceedings of the conference of geotechnical instrumentation in civil engineering projects, Thomas Telford, London, UK, pp. 75-85.

15. Bishop, C., 1995, “Neural Networks for Pattern Recognition,” Oxford University: University Press.

16. Nour El-Din, S.M., 2003, "Neuronet Prediction of Settlement Associated with Soft Ground Tunneling", M.Sc. Thesis, In Progress, Ain Shams University, Faculty of Engineering, Cairo, Egypt.

17. Patterson, D., 1996, “Artificial Neural Networks,” Prentice Hall, Singapore.

18. Chapra, S.C. and Canale, R.P., 1990, "Numerical Methods for Engineers", McGraw-Hill Publishing Co., NY, USA.

19. Hamza Associate, 1995, "Greater Cairo Metro: Phase (2) Tunnel Monitoring", Comprehensive Report, NAT, Egypt.

20. Hamza Associates, 1997, "Greater Cairo Metro Line 2 Phase 2, Phase 3 Tunnel Monitoring", Lot 42 (El-Dokki/ El-Gezira, NAT, Egypt.

21. Campenon Bernard-SGE, 1999, "Tunneling at the CWO Crossing, Results of Montoring", El Azhar Road Tunnels Project, Detailed Design, NAT, Egypt.

22. El-Nahhas, F.M, 1980, "The Behaviour of Tunnels in Stiff Soils", Ph.D. Thesis, Alberta University, Edmonton, Canada.

23. Kotait, H, 2001, "Effect of Tunneling on Adjacent Structures", Ph.D. Thesis, Alexandria University, Alexandria, Egypt.

24. El-Nahbas, F., El-Kadi, F. and Shalaby, A., 1990, “Field Measurements During Construction of a Compressed Air Tunnel in Cairo”, Proc. of Intl. Congress on Tunnels and Underground Works Today and Future, Chengdu, China.

25. Lee, Chung-Jung; Wu, Bing-Ru; and Chiou, Shean-Yau, 1999, "Soil Movement around a Tunnel in Soft Soils", Proc. Natl. Sci. Counc. ROC (A), Vol. 23, No. 2, pp.235-247.

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26. Madkour, A., Hudson, M. A. and Bellarosa, A., “Construction of Cairo Metro Line 2”, Proc. Inst. Civ. Engrs, Civ. Eng, 1999, 132, May/August, pp. 103-117

27. Shata, A.A., 1988, “Geology of Cairo, Egypt”, Bulletin of the Association of Engineering Geologists, Vol. XXV, No. 2, pp. 149-183.

28. Richards, D.P., Ramond, P. and Herrenkenecht, M., 1997, "Slurry Shield Tunnels on the Cairo Metro", General Report, RETC, Las Vegas, USA.

29. El-Nahhas, F.M., 1999, "Soft Ground Tunnelling In Egypt: Geotechnical Challenges and Expectations", Tunnelling and Underground Space Technology, Vol. 14, No. 3, pp. 245-256.

30. Ramond, P. and Guillien, S., 1999, "El Azhar Road Tunnels", Tunneling and Underground Space Technology, Elsevier Science Ltd., Vol. 14, No. 3, pp.291-317.

31. Schmidt, B., 1969, "Settlement and Ground Movement Associated with Tunneling in Soil", Ph.D. Thesis, University of Illinois, Urbana, Illinois, USA.

ملخص

يتطلب االنتشار الحالى لألنفاق فى المناطق الحضرية المزدحمة التحديث المستمر لطرق التنبؤ بالهبوط ويعنى هذا البحث بتقديم طريقة مستحدثة مبنية على . باستخدام نتائج برامج مراقبة مشاريع األنفاق

ألنفاق عن طريق نموذج مرآب الشبكات العصبية االصطناعية للتنبؤ بالهبوط السطحى المصاحب لتنفيذ اتم تدريب الشبكة . يسمح هيكله بمعالجة البيانات الناتجة عن برامج مراقبة األنفاق على اختالف حجمها

العصبية االصطناعية باستخدام قياسات متعددة للهبوط المصاحبة لتنفيذ األنفاق فى مصر وفى الخارج وقد تميز النموذج المقترح بسهولة . د الهندسية لألنفاقباإلضافة إلى الخواص الجيوتقنية للتربة واألبعا

. أعتبار طرق التنفيذ و الخواص الجيوتقنية للتربة وابعاد النفق مما يتيح الحصول على تقدير دقيق للهبوطوتم استخدام النموذج فى تحليل االنفاق المنفذة او المزمع تنفيذها باستخدام دروع الهيدروشيلد لحفر االنفاق

.منطقة القاهرة الكبرىفى