Neural network forecast model in deep excavation

Neural Network Forecast Model in Deep Excavation

J. C. Jan

; Shih-Lin Hung, M.ASCE

; S. Y. Chi

; and J. C. Chern

Abstract: Diaphragm wall deflection is an important field measurement in deep excavation. The monitoring data are applied to evaluate the construction performance to avoid a supporting system failure or damages incurred to adjacent structures. Despite the numerous case histories of construction projects and several forecasting methods, no method accurately forecasts the performance of construction due to the complicated geotechnical and construction factors affecting the behavior of the diaphragm wall. This work predicts the diaphragm wall deflection by using the adaptive limited memory–Broyden-Fletcher-Goldfarb-Shanno supervised neural network. Eighteen case histories of deep excavations with four to seven excavation stages are selected for training and verification. In addition, the knowledge represen-tation adopts measured wall deflections of previous excavation stages as inputs to the network. Doing so substantially reduces the importance of soil parameters, which are often extremely fluctuating and difficult to assess. Simulation results indicate that the artificial neural network can reasonably predict the magnitude, as well as the location, of maximum deflection of the diaphragm wall.

DOI: 10.1061/共ASCE兲0887-3801共2002兲16:1共59兲

CE Database keywords: Neural networks; Excavation; Geotechnical engineering; Sensitivity analysis; Algorithm; Diaphragm wall.

Introduction

In urban areas, braced diaphragm walls are generally applied to deep excavations in soft soil. A satisfactorily braced diaphragm wall not only provides for a safe excavation but also minimizes deformations in the surrounding ground, which are of utmost im-portance in avoiding costly damages to adjacent buildings. Obser-vational methods are frequently employed in deep excavation

projects to ensure safe construction. Peck 共1969b兲 first compiled

the observational data in deep excavations and tunneling in soft grounds. By adopting various construction methods, he

summa-rized the feasibility of excavations. Peck 共1969a兲 also

recom-mended the observational method not be adopted unless the de-signer has a plan of action for every unfavorable situation that may arise.

The estimation of lateral wall deflections and ground settle-ments has received substantial attention from practicing engineers and researchers. Finite element analyses are extensively applied to estimate wall deflections in deep excavations. Clough and

Hansen共1981兲 demonstrated how anisotropy clay affects braced

wall systems by performing finite element analyses. Powrie and

Li共1991兲 employed finite element analyses to investigate the ef-fects of soil/wall/prop stiffness and the preexcavation earth

pres-sure coefficient. Hashash and Whittle共1996兲 conducted a series of

numerical experiments, that applied nonlinear finite element analyses to investigate how the embedment length, support con-ditions, and stress history profile affect the undrained deforma-tions around a braced diaphragm wall in a deep excavation.

The accuracy of ground movement prediction through finite element analyses heavily depends on the constitutive behavior of the soil. The soil parameters applied in constitutive models are generally obtained from laboratory tests. However, the test results are often not representative of the in situ soil behavior due to factors such as sample disturbance, change of in situ environment and effects of construction. To minimize the effects of soil

param-eters and construction factors, Gioda and Sakurai共1987兲 proposed

back analysis procedures to obtain modified soil parameters through the fitting of computed wall deformations and field

mea-surements. For example, Whittle et al. 共1993兲 implemented a

fi-nite element analysis with an MIT-E3 soil model to simulate the top-down construction of a seven-story, underground parking ga-rage on Post Office Square in Boston, Mass. According to their results, soil deformation measurements provide valuable informa-tion on how to evaluate the constitutive model for describing soil behavior. In addition, several mathematical optimization ap-proaches have been utilized to determine modified soil

param-eters. Ou and Tang 共1994兲 employed optimization techniques to

determine soil parameters for finite element analysis in deep

ex-cavation. Chi et al.共1999兲 developed an information construction

approach for deep excavation. Their investigation applied an op-timization process to calculate back analyzed soil parameters, which were then used to predict the wall deflection of subsequent excavation stages. Although back analysis combined with finite element analysis provides an effective numerical approach for engineers to estimate wall deflections and surface settlements in excavations, the back analysis technique is limited to the number of soil parameters and the soil model applied.

Artificial neural networks共ANNs兲 form a class of systems that

are derived from biological neural networks. Learning is an im-portant feature of artificial neural networks. Several supervised 1_{PhD, Dept. of Civil Engineering, National Chiao Tung Univ., 1001}

Ta Hsueh Rd., Hsinchu Taiwan 300, R.O.C.

2_{Associate Professor, Dept. of Civil Engineering, National Chiao} Tung Univ., 1001 Ta Hsueh Rd., Hsinchu Taiwan 300, R.O.C. 共corre-sponding author兲. E-mail: slhung@cc.nctu.edu.tw

3_{Researcher, Geotechnical Researcher Center, Sinotech Engineering} Consultants, Inc., Basement No. 7, Ln. 26, Yat-Sen Rd., Taipei Taiwan 105, R.O.C.

4_{Manager, Geotechnical Researcher Center, Sinotech Engineering} Consultants, Inc., Basement No. 7, Ln. 26, Yat-Sen Rd., Taipei Taiwan 105, R.O.C.

Note. Discussion open until June 1, 2002. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on May 22, 2000; approved on January 3, 2001. This paper is part of the Journal of Computing in Civil Engineering, Vol. 16, No. 1, January 1, 2002. ©ASCE, ISSN 0887-3801/2002/1-59– 65/$8.00⫹$.50 per page.

and unsupervised neural network learning algorithms have been

developed and explored in a number of various domains 共Adeli

and Hung 1995; Haykin 1994兲. ANN learning models can effec-tively deal with qualitative, uncertain, and incomplete informa-tion. Therefore, ANN is highly promising for modeling compli-cated problems in which the governing equations are difficult to

define. Flood and Kartam共1994a,b兲 provided a discourse on the

understanding, usage, and potential for application of artificial neural networks in civil engineering. According to their study, artificial neural networks can be implemented in mapping, transi-tory, and optimization problems, as well as model dynamic pro-cesses. Based on supervised learning algorithms, several other researchers have applied neural network learning models in civil

engineering共Hajela and Berke 1991; Ghaboussi et al. 1991; Kang

and Yoon 1994; Stephen and Vanluchene 1994; Elkordy et al. 1994兲. In geotechnical engineering, Ni et al. 共1996兲 applied ANN

to evaluate failure potential of slopes, and Goh共1994兲 introduced

the application of neural networks to evaluate liquefaction

poten-tial. Juang et al. 共1999兲 presented a technique of training ANNs

with the aid of fuzzy sets theory. The technique involved modules for preprocessing input parameters and postprocessing network output. They indicated that the fuzzy set-based ANN models could be trained with greater efficiency.

This work attempts to predict the diaphragm wall deflection in deep excavation using a supervised limited

memory–Broydon-Fletcher-Goldfarb-Shanno共L-BFGS兲 ANN learning model 共Hung

and Lin 1994兲. The training data are collected from the construc-tion projects in the Taipei basin. For comparison, the convenconstruc-tional finite element analysis, which involves optimization back analysis to calculate soil parameters, is also applied to evaluate these dia-phragm wall deflections in deep excavation.

Artificial Neural Networks„ANNs…

The ANNs form a class of systems that are derived from biologi-cal neural networks. The topology of an ANN model consists of a number of simple processing elements, called nodes, that are in-terconnected to each other. Interconnection weights that represent the information stored in the system are used to quantify the strength of the interconnections; these weights hold the key to the functioning of an ANN. ANNs have been used in a broad range of applications, including classification, pattern recognition, function approximation, optimization, prediction, and automatic control. Among the many different types of ANN, the feedforward, mul-tilayered, supervised neural network with the error

back-propagation共BP兲 algorithm, the so-called BP network 共Rumelhart

et al. 1986兲, is by far the most commonly applied neural network learning model owing to its simplicity. The architecture of BP networks, displayed in Fig. 1, consists of an input layer, one or more hidden layers, and an output layer.

Before an ANN can be used in the application, it needs to learn or be trained from an existing training set that consists of pairs of input-output elements. The training of a supervised neural net-work using BP learning algorithm usually involves two stages. The first stage is the data feed forward. The output of each node is defined as netj⫽

兺

where Wi j⫽weight associated with the ith node in the preceding

layer to the jth node in the current layer; oi⫽output of ith node in

the preceding layer; ␪j⫽threshold value of node j in the current

layer; oj⫽output of node j in the current layer; and function

f⫽activation function, which has to be differentiable. Herein, the sigmoid function is used as the activation function and is defined as

f共x兲⫽ 1

1⫹e⫺x (3)

The second stage is error back-propagation and adjustment of the weights through the network. In the training process, system error function is used to monitor the performance of the network. This system error function is defined as

E⫽1 2p

兺

兺

where P⫽number of instances in the training set; and dpkas well

as opk⫽desired and calculated output of the kth output node for the pth instance, respectively. The standard BP algorithm uses a

gradient descent approach with a constant step length 共learning

ratio兲 to train the network

W_{i j}共k⫹1兲⫽W_{i j}共k兲⫹⌬Wi j (5)

⌬Wi j⫽⫺␩

⳵E ⳵Wi j

(6)

where␩⫽learning ratio, which is a constant in the range of 关0,1兴.

The superscript index k denotes the kth learning iteration. BP supervised neural network learning models, however, al-ways take a long time to learn. Moreover, the convergence of a

BP neural 共BPN兲 network is highly dependent upon the use of a

learning rate, ␩. Thus, several different approaches developed to

enhance the learning performance of the BP learning algorithm have been applied. One approach is to develop more effective learning algorithms with the objective of reducing the learning

time. Moller共1993兲 developed a scaled conjugate gradient

algo-rithm for fasting the supervised learning. Adeli and Hung共1994兲

developed an adaptive conjugate gradient neural network

共Ad-CGN兲 learning algorithm and applied it to structural engineering.

Sanossian and Evans共1995兲 used a gradient range-based heuristic

method for accelerating neural network. Another approach is to develop a parallel algorithm on multiprocesser computers with the objective of reducing the overall computing time. For

in-Fig. 1. Feedforward network with one hidden layer

stance, Adeli and Hung 共1993兲 presented a concurrent Ad-CGN learning algorithm to a large-scale pattern recognition problem. Significant improvement for the BPN algorithm in computing time was reported in their work. The third approach is the devel-opment of hybrid neural network learning algorithms. Hung and

Adeli 共1994兲 presented a parallel hybrid genetic/neural network

learning algorithm. They reported a superior convergence prop-erty of the parallel hybrid neural network learning algorithm as compared with a BPN learning algorithm. Besides, the perfor-mance of neural networks in engineering applications can be sig-nificantly improved by selecting a suitable representational

frame-work to present the training input/output pattern pairs.

Gunaratnam and Gero共1994兲 discussed the effect of

representa-tion of input/output pairs for training instances on the learning performance of the BPN learning algorithm in the problems of structural design. The dimensionless representation is reported to result in a simpler mapping function and makes it possible to train network on a small training set and still have the capability for reasonable accurate predictions.

Hung and Lin 共1994兲 developed a more effective adaptive

L-BFGS learning algorithm based on the approach of a L-BFGS

quasi Newton second-order method共Nocedal 1980兲 with an

inex-act line search algorithm. In the conventional BFGS method, the

approximation Hk⫹1 to the inverse Hessian matrix of function

E(W) is updated by Hk_⫹1⫽共I⫺␳kskyk T_兲 Hk共I⫺␳kyksk T_兲⫹␳ ksksk T_⬅V k T HkVk⫹␳ksksk T (7) where ␳k⫽1/yk T_s k; Vk⫽I⫺␳kyksk T_{; s} k⫽Wk⫹1⫺Wk; yk⫽gk⫹1

⫺gk; and gk⫽⳵E/⳵W. Instead of forming the matrix Hk in

BFGS method, we save the vectors sk and yk. These vectors first

define and then implicitly and dynamically update the Hessian approximation using information from the last few iterations, say m in the work. Therefore, the final stage of the adjusting weights in a BP-based ANN is modified as

W共k⫹1兲_⫽W共k兲_⫹␣

kdk (8)

The search direction is given by

dk⫽⫺Hkgk⫹␤kdk⫺1 (9)

where␤k⫽关y(kT⫺1)H(k⫺1)g(k⫺1)/关y(kT⫺1)d(k⫺1)兴

The step length ␣k is adapted during the learning process

through a mathematical approach—the inexact line search algo-rithm. This is used in the L-BFGS learning algorithm instead of a

constant learning ratio 共Hung and Lin 1994兲. The inexact line

search algorithm is based on three sequential approaches— bracketing, sectioning, and interpolation. The bracketing

ap-proach brackets the potential step length,␣, between two points,

through a series of function evaluations. The sectioning approach then uses the two points of the bracket as the initial points, reduc-ing the step size piecemeal, and locatreduc-ing the minimum between

points, e.g.,␣1 and␣2, to a desired degree of accuracy. Finally,

the quadratic interpolation approach uses the three points, ␣1,

␣2, and (␣1⫹␣2)/2, to fit a parabola to determine the step length,

␣k. Consequently, the step length ␣k is required to satisfy the

following conditions in each iteration共Hung and Lin 1994兲:

E共Wk⫹␣kdk兲⭐E共Wk兲⫹␤␣k关ⵜE共Wk兲Tdk兴;

␤苸共0,1兲 and ␣k⬎0 (10)

ⵜE共Wk⫹␣kdk兲Tdk⭓␪关ⵜE共Wk兲Tdk兴;

␪苸共␤,1兲 and ␣k⬎0 (11)

ⵜE共Wk⫹␣kdk兲Td共k⫹1兲⬍0 (12) Hence, the problem of trial and error selection of a learning ratio in the BP algorithm was circumvented in the adaptive L-BFGS learning algorithm.

Knowledge Representation of Wall Deflection Problem

Deep excavations are widely conducted in the construction of underground structures and the foundations of high-rise buildings. Therefore, a large amount of monitoring data has been accumu-lated. However, due to the complexity of factors that affect the behavior of deep excavation, the information cannot be applied effectively to solve new problems. Herein, supervised ANN with adaptive L-BFGS learning models are adopted to accurately pre-dict the diaphragm wall deflections employing accumulated moni-toring data. The measurement data and wall deflections from deep excavations, are collected for training purposes. The underlying notion of applying ANN model to predict staged construction problems is that during an excavation, an accurate prediction of the succeeding stage can be derived from the information of two or more previous stages as input to the network. In doing so, the causes and effects of factors that determine the behavior of the modeled problems do not need to be fully understood.

Fig. 2 depicts a wall structure system, where the wall length is assumed to be 1.8 times the final excavation depth, H; R, an index of the observation point, is the normalized depth of the measuring point; and W and D denote the thickness of the diaphragm wall and the depth of the current excavation, respectively. Combining the aforementioned terms with monitored data, each instance con-sists of seven inputs and one output.

Inputs

• Wall thickness: W

• Depth of excavation surface: D

• Equivalent SPT-N value between the depth of D⫺0.25H and

D⫹0.25H: N¯

• Index of observation point: R

• Wall deflection of observation point in (i⫺3)th excavation

stage:⌬_Ri⫺3

Fig. 2. Illustration of diaphragm wall structure

• Wall deflection of observation point in (i⫺2)th excavation

stage:⌬_Ri⫺2

• Wall deflection of observation point in (i⫺1)th excavation

stage:⌬_Ri⫺1

Output

Wall deflection of observation point in ith excavation stage⌬Ri .

Notably, in these instances, if i equals 1,⌬_Ri⫺1,⌬_Ri⫺2and⌬_Ri⫺3are

zero; if i equals 2,⌬_Ri⫺2and⌬_Ri⫺3are zero; and if i equals 3,⌬_Ri⫺3

is also zero.

In this study, 18 case histories of deep excavation with 4 –7 excavation stages each, resulting in a total of 93 sets of wall deflection, are used to establish the instance base. Each dia-phragm wall is discretized into 18 uniform subintervals with 19

nodal points. Therefore, a total of 1,767 共93⫻19兲 instances are

generated and employed to train and verify the learning perfor-mance of the network.

Computational Results

A hidden layer feed-forward network with 7 input nodes, 15 hid-den nodes, and 1 output node was used to solve the diaphragm wall deflection problem. Fig. 3 displays the flow chart of the verification process, as summarized in the following:

1. Select a case history for verification;

2. Train the neural network with other case histories;

3. Predict the wall deflection of subsequent excavation stage;

4. After the excavation stage is completed, append the

mea-sured wall deflection of the excavation stage to the training instances;

5. Retrain the neural network; and

6. Repeat Steps 3–5 until the prediction is complete.

The 18 case histories of deep excavation in the Taipei Basin are sequentially used to verify the prediction accuracy of a neural

network. Herein, only the third to seventh excavation stages 共57

sets of wall deflection兲 are of concern, because engineering fail-ures seldom occur in the first and second excavation stages.

Hence, a total number of 1,083共57⫻19兲 instances are adopted for

verification. Fig. 4 presents the forecasted maximum deflections of the 57 sets of wall deflection. The correlation coefficient be-tween predicted and measured maximum wall deflections is 0.9081. The number of cases with relative error of predicted

maximum wall deflection in the range of关0,10%兴, 关10,20%兴, and

greater than 20% are 28, 16, and 13, respectively. If we define that the prediction is failed as the relative percentage error ex-ceeds 20, then 77% of cases are acceptable predictions.

Furthermore, the average error of wall deflection for all veri-fication instances is 5.3 mm. The average error of the seven larg-est deflection points of each excavation stage of case histories is 6.4 mm. The average error of wall deflection of embedded points is 4.8 mm. As a result, the largest prediction error occurs near the maximum wall deflection nodal point. Additionally, for maximum wall deflection, 38.6% of computed case histories occur at the same nodal point, as compared with measured case histories; 49.1% of maximum wall deflection of computed case histories are only inaccurate by one nodal point. These results imply that more than 87% of the predicted maximum deflection point is less than one nodal point from the observed location. Furthermore, the wall shape of predicted wall deflection resembles that of the measured wall deflection.

For comparison, the finite element analysis involving optimi-zation back analysis calculating soil parameters, proposed by Chi

et al.共1999兲, is employed as a reference. The hyperbolic

stress-strain relationship and Mohr-Coulomb plasticity are adopted for the soil model. Four most important soil parameters are obtained by optimization back analysis calculation. The four soil param-eters are the ratio of Young’s modulus of clay over undrained shear strength, the ratio of Young’s modulus of sand over SPT-N, the variation of undrained shear strength, and the undrained shear strength at ground level.

Three excavation projects are adopted to compare the compu-tational performances of ANN prediction model and the reference approach. Both Cases A and B applied a 0.6-m thick diaphragm wall, however, the depths of the wall were 23 and 21.5 m, respec-tively. Furthermore, the walls were constructed with the bottom-up construction method. The third case, Taipei National

Enterprise Center 共TNEC兲 Case, is the construction project in

Taiwan. Ou et al. 共1998兲 studied this case, and Chi et al. 共1999兲

investigated optimization of back analysis by incorporating it into a finite element analysis. Case TNEC used a 0.9-m thick and 35-m depth diaphragm wall as the earth-retaining structure. Dif-fering from the other cases, however, a top-down construction method was applied.

Fig. 3.Flow chart of verification

Fig. 4. Computational results of predicted maximum wall deflection

Figs. 5共a and b兲 depict the back analysis results and ANN prediction model of Case A, where the back analysis results are curve fittings rather than predictions of measured wall deflections. According to these figures, the optimization back analysis has acceptable convergence in fitting measured wall deflections. Also, the ANN model performs acceptable predictions. Similarly, Figs. 6共a and b兲 illustrate the back analysis results and ANN prediction model of Case B. The optimization back analysis in this case has a poor convergence in fitting measured wall deflections. For ex-ample, the magnitudes of maximum wall deflections of excava-tion stages 4 and 5 are visibly larger than the measured results, and the deflection shapes of excavation stages 3, 4, and 5 are markedly dissimilar to the measured wall deflections. However, the predicted wall deflections from the ANN model are accept-able.

In Case TNEC, the back analyzed soil parameters from previ-ous excavation stages are applied for finite-element analysis to predict wall deflections of the subsequent excavation stage. In

doing so, the prediction begins at the second excavation stage. For comparison, soil parameters based on local empirical formu-las are also employed herein. Figs. 7共a and b兲 display the com-puted wall deflections from ANN prediction model and the finite-element analysis. The ANN model gives acceptable prediction of wall deflections, except for excavation stages 2 and 3. Analysis results obtained from finite-element analysis, based on local em-pirical formulas, markedly differ from those of measured wall deflection in all excavation stages. In addition, analysis results obtained from the finite-element analysis, using back analyzed soil parameters, satisfactorily predict the maximum wall deflec-tion except for excavadeflec-tion stages 2 and 3. However, the predicted wall deflections of the embedded points are inaccurate except for excavation stages 2 and 7.

Sensitivity Analysis

After an ANN model is successfully trained, the relative strength of effect for input element on output data can be derived based on Fig. 5. 共a兲 Back analysis results and artificial neural network 共ANN兲

prediction of case A共excavation stages 1–4兲 and 共b兲 Back analysis results and ANN prediction of case A共excavation stage 5兲

Fig. 6. 共a兲 Back analysis results and artificial neural network 共ANN兲

prediction of case B 共excavation stages 1–4兲 and 共b兲 Back analysis results and ANN prediction of case B共excavation stage 5兲

the weights stored in the network 共Yang and Zhang 1997兲. This

work adopted an importance index, Iik, to express the degree of

sensitivity for each input parameter xi on one of data in output

ok. Hereinafter, the process of sensitivity analysis is summarized

as follows:

1. ABP-based ANN model has been successfully trained. The

computed output for any node then can be yielded through the network and expressed as

ok⫽f共netk兲, netk⫽

兺

兺

兺

where xiis ith input parameter; and ok, ojn, and oj1 denote

the computed output for output node j, hidden node jn, and

input node j1, respectively.

2. The variance of output with the change of each input

param-eter can be derived. The variance is represented by the fol-lowing differential equation:

⳵ok ⳵xi⫽ ⳵ok ⳵netk ⳵netk ⳵oj . . .⳵neti xi ⫽

兺

兺

兺

where jn, jn⫺1, . . . , and j1denote hidden nodes in the nth,

(n⫺1)th, . . . , and first hidden layer, respectively; Wj_nk

de-notes weight between the kth output node and hidden node

jn; Wj_n⫺1j_n denotes weight between the hidden nodes jn⫺1

and jn; Wi j₁denotes weight between the ith input node and

the hidden node j1; netk, netjn and netj1 denote weighted

sums of kth output node, the hidden node jnand j1,

respec-tively; and f⬘ denotes differential function of the activation

function f.

3. The total variance of training instances as a temporary

vari-able Tikof xiand ok Tik⫽

兺

冏

冉

冊

冏

4. The importance index, Iik, of input parameter xi to output

data ok, therefore, can be calculated as

Iik⫽ Tik Tmax

(18)

where Tmaxis maximum sum of variance.

If the network converges, the terms Iik for each instance also

converge to constants. Obviously, a large value of Iik indicates

more effect on the output data. A positive value of Iikimplies the

positive relation; i.e., the change of output data is proportional to the change of input variable. On the other hand, a negative value

of Iik specifies negative action. The output data have no relation

with the input variable when their Iik equals zero. Herein, the

importance indexes for each input, W, D, N¯ , R, ⌬_Ri⫺3,⌬_Ri⫺2and

⌬R

i⫺1_{, to the output,⌬}

R

i _{, are derived via the aforementioned}

sen-sitivity analysis process. They are 0.3204, 0.121, 0.1313, 0.173, 0.271, 0.3759, and 1, respectively. Revealed from these results,

the input parameters D, N¯ , and R have little influence in the

prediction of the diaphragm wall deflection. Alternately, the wall deflection in the last excavation stage is the most important factor for the prediction. Restated, incorporating the previous excavation stages into the knowledge representation, which reflects both the soil and construction factors for the case to be predicted, has an important effect on the ANN prediction model.

Conclusions

In this work, the adaptive L-BFGS supervised neural network was applied to predict the diaphragm wall deflection of deep excava-tions. Training data were collected from the construction projects in the Taipei Basin. To compare, the conventional finite element analysis involving optimization back analysis calculating soil pa-rameters is also applied to evaluate these diaphragm wall deflec-tions in deep excavation. The conclusions are summarized as fol-lows:

Fig. 7.共a兲 Comparison of back-analysis and artificial neural network

共ANN兲 predictions of the case of the Taipei National Enterprise

Cen-ter 共TNEC兲 共excavation stages 2–5兲 and 共b兲 Comparison of back

analysis and ANN predictions of case TNEC共excavation stages 6 and 7兲

1. This study presents a neural network prediction model for deep excavation in geotechnical engineering to assess the safety of retaining systems during construction. Due to the historical information that is gathered during excavations, the limitation of understanding cause and effect, which in turn determines the behavior of the obstacles being modeled, is avoided. The advantage of the ANN prediction model is that it does not require a rigorous understanding of cause and effect. Moreover, the soil models are not significant to the predictions of wall deflections in deep excavations as com-pared with other factors.

2. In deep excavations, the artificial neural network can

reason-ably predict the magnitude as well as the location of maxi-mum deflection of diaphragm wall. In addition, reliable pre-dictions on wall deflections in the embedded position are also achieved. These results imply that the shape of the pre-dicted wall matches that of the measured wall. As a result, neural network prediction allows engineers to estimate the wall structure system prior to the next excavation stage.

3. Input wall deflections of the three previous excavation stages

provides a more accurate prediction of the ensuing excava-tion stage. Also, as compared with other convenexcava-tional ap-proaches, the importance of soil parameters is markedly re-duced. The simulation results indicate that the monitoring data involving various information reflects both the uncer-tainty and the construction factors of field situations.

Acknowledgment

The writers would like to thank the Sinotech Engineering Con-sultants, Inc. of the Republic of China for financially supporting this research under Grant No. SEC/R-GT-99-01.

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