Keywords: artificial neural network (ANN), back propagation (BP), ultimate bearing capacity (UBC), mean squared error (MSE), training patterns, testing patterns, multi-layer perceptron (MLP).

An artificial neural network (ANN) model is usually employed when the relationship between the input and output is complicated or application of another available method takes a long computational time and effort. An ANN has potential of learning; creating and flexibility. Artificial neural networks basically simulate the behaviour of the human brain [2]. The architecture of a multilayer feed forward neural network consists of an input layer, an output layer, and hidden layers [1].

This study deals with the development of multi-layer feed forward ANN models for predicting the ultimate bearing capacity of soil. The computer code has been written in Basic language based on the principle of artificial intelligence. The back propagation concept has been used in writing the computer code [3].

In this investigation nine effective parameters have been considered as input parameter in order to determine the ultimate bearing capacity of soil with three different layers. These parameters are the width of the foundation (B), the friction angle in each layer (), the cohesion of the layers (C₁,C₂,C₃) and the depth of each layer (H₁,H₂). The depth of the third layer is considered infinite and the output of the network is the ultimate bearing capacity of soil.

Moreover a computer program which is based on classical method on ultimate bearing capacity of the soil suggested by Hansen [4,5] has been written to generate the soil data needed to train the ANN developed in this investigation. Training is the process of changing the weights systematically in order to achieve some desired results for a given set of inputs. The initial weights are adjusted by small amounts. Since the initial values play important role in this procedure, the training process has been conducted several times, each time with different random weights values to reach results with minimum error. In this study:

• The mean square error (MSE) is used to determine the error of resulting function.
• One hidden layer has been selected and in this layer, good convergence has been achieved with 45 neurons.
• Sig (x) in the output layer and tanh (3x) in the hidden layer has a minimum error and has been selected as activation functions.
The best value for learning rate is obtained 0.085 and for momentum of inertia 0.70

After the ANN was trained, an attempt has been made to test the trained ANN to see how well it would recognize various ultimate bearing capacities. This goal was achieved by generating 400 new sets of data. After several adjustments to the network parameters, the network converges to a minimum error. The trained model prediction was in good agreement with the actual gains.

A comparison between the ultimate bearing capacity of soils predicted through the ANN and that evaluated using Hansen's method shows that the results of the ANN were very close to the Hansen's method [4,5] and the artificial neural network was successful in training the relationship between the input and output data with a MSE of 10 percent.

Based on the study it can be concluded that:

(i)

An artificial neural network model has been developed for predicting the ultimate bearing capacity in shallow foundation in multilayer soils.

(ii)

With the availability of a good training data set, neural networks can offer a good alternative for predicting the ultimate bearing capacity.

(iii)

Learning the relationship between inputs and outputs, comparing the results obtained from the proposed network model with their corresponding values obtained from the empirical (Hansen's formula) there is an average 10 percent difference.

1

M.H. Baziar, A. Ghorbani, "Evaluation of Lateral Spreading Using Artificial Neural Networks", Journal of Soil Dynamics and Earthquake Engineering, 25, 1-9, 2005. doi:10.1016/j.soildyn.2004.09.001

2

R.V. RaikarKumar, D. Nagesh, S. Dey, "End Depth Computation in Inverted Semicircular Channels Using ANNs", Flow Measurement and Instrumentation Journal, 15, 285-293, 2004. doi:10.1016/j.flowmeasinst.2004.06.003

3

T. Kerh, D. Chu, "Neural Network Approach and MicroTremor Measurement in Estimating Peak Ground Acceleration due to Strong Motion", Advances in Engineering Software, 33, 733-742, 2002. doi:10.1016/S0965-9978(02)00081-9

4

J.E. Bowles, "Physical and Geotechnical Properties of Soils", Published by McGraw- Hill, New York, U.S.A, 1984.

5

M. Bolton, "A Guide to Soil Mechanics", Published by Macmillan Press Ltd, London, U.K. 1979.

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