Artificial neural network ann prediction of one-dimensional consolidation

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 4, Issue 4, July-August (2013), © IAEME
135
ARTIFICIAL NEURAL NETWORK (ANN) PREDICTION OF ONE-
DIMENSIONAL CONSOLIDATION IN HOMOGENEOUS CLAY UNDER
UNIFORM APPLIED LOAD
Hyeong-Joo Kim1
, Jose Leo Mission2
, Jeong-Hee Ko3
1
Ph.D. Professor, Department of Civil Engineering, Kunsan National University,
Kunsan City, South Korea,
2
Ph.D, Geotechnical Engineer, SK Engineering and Construction (SK E&C), Seoul, South Korea,
3
Ph.D. Candidate, Department of Civil and Environmental Engineering, Kunsan National University,
Kunsan City, South Korea.
ABSTRACT
The prediction of one-dimensional (1D) consolidation in homogeneous clay is typically
performed by lengthy calculations using the Finite Difference Method (FDM) or manually using
tables and design charts. In addition, numerical solutions by FDM are typically made in a stepwise
progressing manner in which the needed computational resources in terms of processing time,
memory, and storage requirements accumulates due to the large number of iterations involved. This
study presents the application of Artificial Neural Network (ANN) in the prediction of 1D
consolidation in homogeneous clay under uniform applied load. Aside from predicting consolidation
results comparable to the FDM, ANN offers several advantages as an accurate, direct, and quick tool
for prediction of 1D consolidation with less needed computational resources. Two ANN models were
being developed and presented in this study: net1 for consolidation in single drainage boundary
conditions, and net2 for double drainage conditions, which were further validated in a deployed
environment for the prediction of excess pore water pressure and settlement in field conditions.
Keywords: Artificial Neural Network (ANN), One-dimensional consolidation, Finite difference
method (FDM), Homogeneous clay, Single drainage, Double drainage
1. INTRODUCTION
In one-dimensional (1D) consolidation problems, the typical solution procedure for the
prediction of soil settlement and excess pore water pressure profile at any specific time during the
consolidation process is performed by numerical analysis of the 1D consolidation equation using
finite difference method (FDM) or manually using tables and design charts. In FDM, solutions are
started at the initial time and incrementally marched forward at a small time-step up to the final time
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of interest. For longer consolidation time having a small time-step interval and a thick clay layer
deposit, a large number of iterations is usually involved than can consume a lot of computer memory
and having huge sizes of data file, which can slow down the computational process and may take
longer computer processing time to finish (Kim et al., 1995). With this method, it is therefore not
possible to directly predict the future conditions of the soil without first chronologically solving the
current and sequential conditions that lead to the final conditions. Hazzard and Yacoub (2008)
presented a hybrid computational scheme for the numerical solution of 1D consolidation, based on
the method described by Booker and Small (1975), to speed up the required computational time by
increasing the time-step gradually as the solution progresses while maintaining the required stability
and accuracy. However the suggested method still suffer from the chronological or sequential type of
solution in which the needed computational resources such as computer memory, output file size,
and the processing time accumulates as the solution progresses.
This study presents an alternative method using Artificial Neural Networks (ANN) for the
direct estimation and prediction of the consolidated state of a homogeneous clay soil layer under a
uniformly distributed surcharge loading. Over the last decades, ANN has been used successfully for
modeling most aspects of geotechnical engineering problems as summarized by Shahin et al. (2001;
2008), but no model has yet been presented and applied for the prediction of 1D consolidation over
time. With sufficient training of the ANN model and without resorting to a stepwise progressing and
sequential solution procedure, the method can provide reliable and direct estimates of the excess pore
pressures and settlement in the clay layer at any time during the progress of consolidation, and at a
much less needed computational resources compared to FDM. Numerical examples are presented to
validate the prediction performance and demonstrate the advantages of the ANN in comparison with
the conventional finite difference method.
2. FINITE DIFFERENCE SOLUTION OF THE 1D CONSOLIDATION EQUATION
Terzaghi (1943) derived the one-dimensional consolidation equation for a homogenous layer
of clay with thickness Hc under a uniformly distributed surcharge load q that is given as,
2
2v
u u
C
t z
∂ ∂
=
∂ ∂
Eq. (1)
where u is the excess pore water pressure, t is the consolidation time, z is the depth, and Cv is the
coefficient of consolidation. Equation (1) is based on the assumption that the coefficient of
consolidation Cv remain constant during the consolidation process, the effect of self-weight
consolidation is neglected, the soil profile is fully saturated, and the consolidation settlements are
small or infinitesimal. The finite difference form of equation (1) for numerical analysis in time (t+∆t)
is written as,
( ) ( ) ( )






+−
∆
∆
+=
∆−∆+∆+ tzztztzz
v
tzttz
uuu
z
tC
uu
,,,
2
,,
2 Eq. (2)
In equation (2), ∆t = time-step and the depth increment∆z = Hc/n, where n is the number of
sublayer elements in the finite difference grid. Equation (2) is applied using the following initial and
boundary conditions with respect to the excess pore pressure at the depth and time coordinates u(z,t)
in which;
u (z,0) = q (initial condition) Eq. (3)

137
u (0,t) = 0 (at a permeable top surface boundary) Eq. (4)
u(Hc,t) = 0 (at a permeable bottom surface boundary) Eq. (5)
u
z
∂
∂
(Hc,t) = 0 (at an impermeable bottom surface boundary Eq. (6)
The impermeable boundary condition defined by equation (6) means that there can be no
flow in the perpendicular direction. Equation (6) is implemented numerically by creating a dummy
node in the finite difference grid after the bottom surface, which can be expressed in finite difference
form as;
( ) ( )
( ) ( )0 , or
2
c c
c c
H z H z
H z H z
u u
u u
z
+∆ −∆
+∆ −∆
−
= =
∆
Eq. (7)
Equation (2) implies that if the solution for u has been determined at time t, then the values at time
(t+∆t) can be calculated by marching the solution downward with depth and forward in time as
shown in Fig. 1. To ensure that the approximate solution of equation (2) must converge to the exact
solution as ∆t and ∆z approaches zero, the following criteria should be satisfied in determining the
time and depth increments, ∆t and ∆z, respectively (Forsythe and Wasow, 1960).
Figure 1: Finite difference nodes in the numerical solution of the 1D consolidation equation
( )
2
1
2
vC t
z
β
∆
= ≤
∆
Eq. (8)
The total settlement S can be calculated using the coefficient of compressibility mv and excess
pore pressure u by numerically integrating along the depth profile as follows:
( ) ( )1
12
c
nH
v
v v c n n
o
n
m z
S m q u dz m qH u u +
=
∆
= − = − +∑∫ Eq. (9)

138
3. ARTIFICIAL NEURAL NETWORK (ANN) MODEL FOR PREDICTION OF 1D
CONSOLIDATION
Table 1: Range of input parameters for ANN training data
Input parameter Range
Thickness of clay, Hc (m) 1, 10, 20, 30
Coefficient of consolidation, Cv (m2
/year) 1, 10, 50, 100, 150
Surcharge load, q (kPa) 5, 10, 50, 100, 150, 200
Time factor, Tv 0.0 - 2.0
Drainage condition One-way (single), Two-way (double)
Neural networks are composed of simple elements called neurons operating in parallel to a
set of input signals whose connections largely determine the network function. The neural network is
trained to perform a particular function by adjusting the values of the connections or weights
between elements so that a particular input leads to a specific target or output with the minimum
error (Fausett, 1994; Zurada, 1992). The number of neurons or nodes in the input and output layers
are restricted by the number of model inputs and outputs. Based on Terzaghi's 1D consolidation
theory (equations 1-6), it can be seen that the relevant input factors affecting the degree of
consolidation are the total thickness of the clay layer (Hc), the consolidation coefficient (Cv), the
magnitude of the uniformly applied surcharge load (q), and the actual consolidation time (t), while
the model output consists of the distribution of the excess pore pressure isochrones u along the depth
profile z. Since the type of boundary conditions are considered as extreme cases of 1D consolidation,
it is presumed that there cannot be any unique ANN model for both. Therefore, separate ANN model
was formulated for each case, that is, the network model net1 for single-drainage condition and net2
for double-drainage conditions. Preliminary output data for training, testing, and validation was
provided from the numerical results of 1D consolidation by FDM using the combination of the range
of input parameters as shown in Table 1 that are typical for 1D consolidation problems encountered
in the field. To ensure that the predicted results by FDM are accurate and always stable, the time-step
∆t was determined from equation (8) using a solution criteria β = 0.25 and a depth increment ∆z
determined from n = 20 elements of the total thickness Hc. Although more accurate predictions can
be provided by selecting a smaller value of β and smaller depth increments by having more number
of elements, the chosen values of β and n for the training model can be sufficient to produce
predicted results that are almost similar to those calculated by analytical solutions (Verruijt, 2001).
To improve training and performance, the original input-output dataset were preprocessed by
normalizing the output excess pore pressure u profile in terms of the applied surcharge load q, that is,
u/q, and normalizing the actual consolidation time t from the input in terms of the time factor Tv
defined as,
Tv = Cv.t/H2
Eq. (10)
Where t = actual consolidation time, H = length of the longest drainage path, and in which H
= Hc for single drainage and H = Hc/2 for double drainage.

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online) Volume 4, Issue 4, July
Table 2: Sensitivity analysis for the relative importance of the input variables in a preliminary ANN
model with four inputs (
network
H
net1 0.0055
net2 0.0011
In an attempt to identify which of the
on the consolidation predictions, a sensitivity analysis is carried out by training a preliminary ANN
model with four inputs (Hc, Cv, q, and
technique proposed by Garson (1991) is u
variables by examining the connection weights of the trained network. The method is also illustrated
and applied by Shahin et al. (2002). The results of the sensitivity analysis
model having three neurons in the single hidden layer
time factor Tv has the most significant effect on the prediction of consolidation having a relative
importance factor almost equal to 100% and the rest of t
importance. With the normalization of the time
and likewise with the normalization of the output excess pore pressure
load q, the inputs Hc, Cv, and q are
number of input variables may be reduced
where n = 20, corresponding to the profile of the normalized excess pore pressure
spaced at the normalized depth z/Hc
of 1D consolidation is then shown in Fig. 2.
(a)
Figure 2: Typical architecture of the ANN model for 1D consolidation prediction:
(a) Original ANN input-output model, and (b) normalized ANN input
From the various combinations of the range of input parameters shown in Table 1, the
original number of input-output dataset for ANN training consisted of a total of 384,000 samples for
net1 and 96,000 samples for net2, corresponding to the total number of
the final time factor Tv = 2.0 for each case.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online) Volume 4, Issue 4, July-August (2013), © IAEME
139
Sensitivity analysis for the relative importance of the input variables in a preliminary ANN
model with four inputs (Hc, Cv, q, and Tv) and normalized outputs u/q
Relative importance of input variables (%)
Hc Cv q Tv
0.0055 0.0062 0.0003 99.9880
0.0011 0.0026 0.0025 99.9938
In an attempt to identify which of the original input variables has the most
, and Tv) and normalized outputs u/q. A simple and innovative
technique proposed by Garson (1991) is used to interpret the relative importance of the input
and applied by Shahin et al. (2002). The results of the sensitivity analysis for the preliminary ANN
model having three neurons in the single hidden layer are shown in Table 2. It can be seen that the
has the most significant effect on the prediction of consolidation having a relative
importance factor almost equal to 100% and the rest of the input variables having negligible relative
With the normalization of the time t into the time factor Tv as defined by
and likewise with the normalization of the output excess pore pressure u in terms of the surcharge
are indeed not required in the ANN model and thereby the original
may be reduced from four to one. The number of output variables is (
= 20, corresponding to the profile of the normalized excess pore pressure u
c. The typical architecture of the final ANN model for prediction
of 1D consolidation is then shown in Fig. 2.
(b)
Typical architecture of the ANN model for 1D consolidation prediction:
output model, and (b) normalized ANN input-output model
output dataset for ANN training consisted of a total of 384,000 samples for
, corresponding to the total number of required iterations to reach
= 2.0 for each case. In other words, it takes about 4 times as much the
Sensitivity analysis for the relative importance of the input variables in a preliminary ANN
u/q
99.9880
99.9938
input variables has the most significant effect
. A simple and innovative
sed to interpret the relative importance of the input
for the preliminary ANN
are shown in Table 2. It can be seen that the
has the most significant effect on the prediction of consolidation having a relative
he input variables having negligible relative
as defined by equation (10),
in terms of the surcharge
not required in the ANN model and thereby the original
The number of output variables is (n+1),
u/q that is equally
ANN model for prediction
Typical architecture of the ANN model for 1D consolidation prediction:
output model
output dataset for ANN training consisted of a total of 384,000 samples for
required iterations to reach
In other words, it takes about 4 times as much the

140
required time for single drainage conditions compared to that of double drainage conditions to attain
the same degree of consolidation as can be seen in equation (10). In order to speed up the network
training and learning process, only one sample was arbitrarily chosen for every 20th
time-step or
iteration from the database results in double drainage, and only one sample for every 80th
time-step
was arbitrarily taken for training from the database results in single drainage. The total number of
reduced samples used for training in each case is 4,800 and it had been justified that this number was
sufficient based on the observed prediction performance.
Table 3: Optimization of the final ANN model architecture
Trial
Number of
hidden layers
Number of
hidden layer nodes
Coefficient of correlation, R
net1 net2
1 1 3 0.9995 0.999
2 1 4 0.999 .0999
3 2 [4 2] 0.9995 0.9995
4 2 [6 3] 0.999 0.999
The training process of the network was based on supervised learning (Masters, 1993), where
the network was presented with the historical set of model inputs and their corresponding targets or
outputs as shown in Fig. 2. In addition, back-propagation learning algorithm (Rumelhart et al., 1986)
was used in which the connection between the processing elements through their weights were
adjusted both in the forward and backward directions until the error between predicted and measured
outputs are minimized based on performance criteria. Using cross-validation (Stone, 1974) as a
stopping criterion, the database is randomly divided into three sets and proportions as follows:
training (70%), testing (15%), and validation (15%). Although a single hidden layer may be
sufficient to model any solution of practical interest (Cybenko, 1989; Hornik et al., 1989; Hecht-
Nielsen, 1990), there is no unified approach for determination of an optimal ANN architecture,
which is generally achieved by fixing the number of hidden layers and choosing the number of nodes
in each. Keeping the number of hidden layers and hidden nodes to a minimum is preferable for
reduced training time, better generalization performance, prevents over fitting, and allows the
network to be easily analyzed (Shahin, 2008). The best approach by Nawari et al. (1999) was to start
with a small number of hidden layer and nodes and to slightly increase the number until no
significant improvement in model performance is achieved. For this purpose several trials were made
as shown in Table 3, where the main criteria that is used to evaluate the prediction performance of
the optimal ANN model is the coefficient of correlation (R), which is a measure that is used to
determine the correlation and the goodness-of-fit between the predicted and observed data. A
performance goal of 10-6
was chosen and based on the trial with the highest coefficient of correlation
(R) and minimum number of layers and nodes for both cases as presented in Table 3, the final size of
the selected network architecture for the model shown in Fig. 2 has then one input layer, one hidden
layer with four neurons, and 21 neurons in the output layer. This is also the optimum network size
which produces the minimum number of epochs and iteration during the training process and thus
producing the least required learning time and consequently the fastest processing time in terms of
producing the estimated and predicted output. For both cases, the networks net1 and net2 were
modeled and trained using the Matlab function 'newff'' that is used to create a feed-forward back-
propagation network and the 'train' function that is used to train the neural network (Demuth et al.,
2009). Figure 3 shows the regression plot of the training data, validation, and testing of the
respective ANN model in Matlab. The high correlation coefficient (R = 0.999) for each case proves

141
the satisfactory prediction performance of the model and network architecture. The general
performance of the trained networks, net1 and net2, were then further validated individually in the
deployed environment and field conditions as described in the following sections.
(a) (b)
Figure 3: Regression plot of the ANN model showing the prediction performance and correlation
coefficient (R) of the training data, validation, and testing in Matlab: (a) net1 - single drainage
condition, and (b) net2 - double drainage condition
4. NUMERICAL VALIDATION CASE EXAMPLES
Table 4: Case 1 - properties of marine clay profile under fill
Thickness of clay, Hc (m) 25.0
/year) 70.0
Coefficient of compressibility, mv (m2
/kN) 0.00025
Surcharge load, q (kPa) 112.70
Drainage boundary condition
single (one-way)
drainage
4.1. Validation Case 1: 25 m thick marine clay under reclamation fill (Bjerrum et al., 1969)
Bjerrum et al. (1969) reported results of a consolidation test on a land that was reclaimed
from the sea by placing about 8 m of fill over the sea bed at the Heroya site, Norway. The
consolidating soil consists of about 25 m of marine clay. Table 4 shows the chosen properties for the
clay profile in which the consolidation parameters and magnitude of the applied surcharge load were
deduced from the published data (Poulos and Davis, 1980; Alonso et al., 1984; Fellenius, 2006).
Piezometer measurements indicated that one-way drainage conditions were present at the site. The
total thickness was subdivided into 20 elements for consolidation analysis by FDM using a solution
criteria β = 0.25 for the time and depth increment as described in Section 2. ANN prediction was
performed using the network model (net1) that was trained, tested, and validated for single drainage

142
condition. Figure 4(a) shows the predicted excess pore pressure isochrones at different time factor Tv
in which the ANN predictions compare well with FDM results. Figure 4(b) shows the profile of the
excess pore pressure in May 1967 corresponding to a time factor Tv of about 0.38, in which the
predicted results compares fairly with measured data.
(a) (b)
Figure 4: Example 1: (a) Comparison of predicted excess pore pressure isochrones, and (b) Excess
pore pressure (u) profile in May 1967 (Tv = 0.38) and calculated effective stress (σ')
4.2. Validation Case 2: 15.5 m thick stiff clay under embankment fill (Walker et al., 1973)
Walker et al. (1973) reported results of a consolidation test of a highly stratified soil
consisting of a 2 m of recent fill, 7 m of sand overlying a stiff silty clay 15.5 m thick, and underlain
by sandy silt/dense sand layers. Surcharge load was applied by constructing a test embankment 100
m x 200 m x 3 m high and in which monitoring was made for about 8 months. The clay layer was
confined by cohesionless soil layers above and below such that two-way drainage was assumed.
Table 5 shows the chosen properties for the clay profile that were deduced from the published data
(Wong and Teh, 1995; Fellenius, 2006; Kim and Mission, 2009). Numerical analysis of 1D
consolidation was performed using 20 elements and the time-step was determined using a solution
criteria β = 0.25. ANN prediction was performed using the network model (net2) that was trained,
tested, and validated for double drainage condition. Figure 5(a) shows the predicted excess pore
pressure isochrones at different time factor Tv in which the ANN predictions compare well with
numerical results. Figure 5(b) shows the comparison between the measured and predicted total
settlement in which good agreement is observed.
Table 5: Case 2 - properties of stiff clay profile under embankment fill
Thickness of clay, Hc (m) 15.5
/year) 135.0
Coefficient of compressibility, mv (m2
/kN) 0.000042
Surcharge load, q (kPa) 51.0
Drainage boundary condition double (two-way) drainage

143
(a) (b)
Figure 5: Example 2: (a) Comparison of predicted excess pore pressure isochrones, and (b)
Comparison of measured and predicted total settlement
Having validated the accuracy of the ANN for prediction of 1D consolidation whose results
are comparable with the FDM, the advantages in terms of the solution speed and efficiency of the
ANN are then compared with the FDM as shown in Table 6. The FDM and ANN predictions were
implemented using the Matlab program in a 2.83 GHz computer with 6 Gb memory and quad-core
processor. The central processing unit (CPU) time in seconds (s) as well as the size of the output file
in kilobytes (kb) were compared for the range of time factor Tv shown in Table 6. Due to the
sequential nature or time-marching solution process of the FDM, the CPU time and output file sizes
or memory requirements are thus increased especially when consolidation results are needed at
longer consolidation times. In contrast, equivalent and accurate predictions are still being provided
by ANN in which direct and quick results can be made at any consolidation time of interest. As
shown in Table 6, prediction method of 1D consolidation can therefore be reliably made by ANN
that can be more efficient by about 6 % to 278 % compared to the FDM and thus minimizing the
needed computational resources.
Table 6: Comparison of CPU times and output file sizes for analyses Case 1 and 2
Tv Case
CPU Time (s)
Output file size
(kb)
(FDM-ANN) ANN
(%)
FDM ANN FDM ANN CPU time
Output
file size
0.10
Case 1 0.196 0.007 28 1 27 27
Case 2 0.082 0.007 7 1 11 6
0.50
Case 1 0.734 0.007 140 1 104 139
Case 2 0.254 0.007 35 1 35 34
1.00
Case 1 1.381 0.007 279 1 196 278
Case 2 0.482 0.007 70 1 68 69

144
5. CONCLUSIONS
This paper presents the novel application of Artificial Neural Network (ANN) in the
prediction of one-dimensional consolidation of a homogeneous clay layer under uniform applied load.
ANN can provide accurate and direct estimates of the excess pore pressures and settlement at any
time during consolidation without resorting to the stepwise progressing solution procedure by the
Finite Difference Method (FDM). The prediction performance of the ANN has been validated by the
equivalent results with FDM. Prediction of consolidation by ANN has the advantage that it can be
used as a direct, accurate, and quick tool for estimating excess pore pressures and settlement at any
time without a need to perform any lengthy manual calculations or approximately using tables and
charts. Two ANN models were being developed and presented in this study: net1 for consolidation in
single drainage boundary conditions, and net2 for double drainage conditions, which were further
validated in a deployed environment for prediction of excess pore pressures and settlement in field
conditions. Compared to FDM, ANN offers several advantages with regards to efficiency, speed, and
economy by having lesser computational resources needed and faster time for the calculations and
thus makes it a powerful and practical tool for the prediction of 1D consolidation in homogeneous
clays.
ACKNOWLEDGEMENTS
This paper was supported by research funds of Kunsan National University.
REFERENCES
1. Kim, H.J., S. Hirokane, H. Yoshikuni,. T. Moriwaki, and O.Kusakabe. (1995). “Consolidation
behavior of dredged clay ground improved by horizontal drain method.” Compression and
Consolidation Clay Soils,Vol.1, pp.99 -104.
2. Hazzard, J. and Yacoub, T. (2008). “Consolidation in multi-layered soils: a hybrid
computational scheme.” GeoEdmonton '08 :61st Canadian Geotechnical Conference and 9th
Joint CGS/IAH-CNC Groundwater Conference, pp. 182-189.
3. Booker, J. R. and Small, J. C. (1975). “An investigation of the stability of numerical solutions
of Biot's equations of consolidation.” International Journal of Solids and Structures, Vol. 11,
pp. 907-917.
4. 22. Shahin, M. A., Jaksa, M. B., and Maier, H. R. (2001). “Artificial neural network
applications in geotechnical engineering.” Australian Geomechanics, Vol. 36, No. 1, pp. 49-
62.
5. Shahin, M. A., Jaksa, M. B., and Maier, H. R. (2008). “State of the art of Artificial Neural
Networks in Geotechnical Engineering.” Electronic Journal of Geotechnical Engineering
(EJGE), Vol. 8, pp. 1- 26, http://www.ejge.com.
6. Terzaghi, K. (1943). Theoretical Soil Mechanics. New York: John Wiley and Sons.
7. Forsythe, G. E. and Wasow, W. R. (1960). Finite Difference Methods for Partial Differential
Equations. New York: Wiley.
8. Fausett, L. V. (1994). Fundamentals of neural networks: Architecture, algorithms, and
applications. New Jersey: Prentic-Hall.
9. Zurada, J. M. (1992). Introduction to artificial neural systems. Minnesota: West Publishing
Company.
10. Verruijt, A. (2001). Soil Mechanics. Delft University of Technology, The Netherlands.
11. Garson, G. D. (1991). “Interpreting neural network connection weights.” AI Expert, Vol. 6,
No. 7, pp. 47-51

145
12. Shahin, M. A., Maier, H. R., and Jaksa, M. B. (2002). “Predicting settlement of shallow
foundations using neural networks.” Journal of Geotechnical and Geoenvironmental
Engineering, Vol. 128, No. 9, pp. 785-793.
13. Masters, T. (1993). Practical neural network recipes in C++. California: Academic Press.
14. Rumelhart, D. E., Hinton, G. E., and Williams, R. J. (1986). “Learning internal representation
by error propagation.” Parallel distributed processing. Vol. 1, Chapter 8, D. E. Rumelhart and
J. L. McClelland, eds., MIT Press, Cambridge, Mass.
15. Stone, M. (1974). “Cross-valedictory choice and assessment of statistical predictions.” Journal
of the Royal Statistical Society, Vol. 36, No. 2, pp. 111-147.
16. Cybenko, G. (1989). “Approximation by superpositions of a sigmoidal function.”
Mathematics of Control, Signals, and Systems, Vol. 3, pp. 303-314.
17. Hornik, K., Stinchcombe, M., and White, H. (1989). “Multilayer feedforward networks are
universal approximators.” Neural Networks, Vol. 2, pp. 359-366.
18. Hecht-Nielsen, R. (1990). Neurocomputing. Massachusetts: Addison-Wesly.
19. Nawari, N. O., Liang, R., and Nusairat, J. (1999). “Artificial intelligence techniques for the
design and analysis of deep foundations.” Electronic Journal of Geotechnical Engineering, Vol.
4, http://www.ejge.com.
20. Demuth, H., Beale, M., and Hagan, M. (2009). Neural Networks ToolBox User Guide. The
Math Works Inc., Natick, Massachusetts.
21. Bjerrum, L., Johannessen, I. J., and Eide, O. (1969). “Reduction of negative skin friction on
steel piles to rock.” Proceedings of the 7th
International Conference on Soil Mechanics and
Foundation Engineering, Mexico City, August 25-29, Vol. 2, pp. 27-34.
22. Poulos, H.G. and Davis, E.H. (1980), Pile Foundation Analysis and Design, New York: John
Wiley Sons, Inc.
23. Alonso, E.E., Josa, A., and Ledesma, A. (1984). “Negative skin friction on piles: a simplified
analysis and prediction procedure.” Geotechnique Vol. 34, No. 3, pp. 341-357.
24. Fellenius, B.H. (2006). “Results from long-term measurement in piles of drag load and
downdrag.” Canadian Geotechnical Journal, Vol. 43, No. 4, pp. 409-430.
25. Walker, L.K., Le, P., and Darvall, L. (1973). “Dragdown on coated and uncoated piles.”
Proceedings of the 8t
International Conference on Soil Mechanics and Foundation Engineering,
August, Vol. 2, Paper 3/41, pp. 257-262.
26. Wong, K.S., and Teh, C.I. (1995). “Negative Skin Friction on Piles in Layered Soil Deposit.”
Journal of Geotechnical and Geoenvironmental Engineering, Vol. 121, No. 6, pp. 457-465.
27. Kim, H. J. and Mission, J. L. (2009). “Negative skin friction on piles based on finite strain
consolidation theory and the nonlinear load transfer method.” Korean Society of Civil
Engineers (KSCE) Journal of Civil Engineering , Vol. 13, No. 2, pp. 107-115.
28. Balamuruga Mohan Raj.G and V. Sugumaran, “Prediction of Work Piece Hardness using
Artificial Neural Network”, International Journal of Design and Manufacturing Technology
(IJDMT), Volume 1, Issue 1, 2010, pp. 29 - 44, ISSN Print: 0976 – 6995, ISSN Online:
0976 – 7002.
29. V. Sugumaran, V. Muralidharan, Bharath Kumar Hegde and Ravi Teja C, “Intelligent Process
Selection for Ntm - A Neural Network Approach”, International Journal of Industrial
Engineering Research and Development (IJIERD), Volume 1, Issue 1, 2010, pp. 84 - 93,
ISSN Online: 0976 - 6979, ISSN Print: 0976 – 6987,

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