Keywords: neural network, back propagation, rock-socketed pile, bearing capacity, soil, rock.

Rock-socketed piles have been widely used in civil engineering for recent decades. Some researches were undertaken to explore them[1,2,3]. However, it is difficult to summarize the relationship between bearing capacity and the interacting factors including length-diameter ratio, socketed length, soil property, and rock property. The relative importance of factors influencing rock-socketed pile bearing capacity hasn't been known precisely. Therefore, the main objective of this paper is to compare the effects on bearing capacity of rock-socketed piles quantificationally by artificial neural networks.

The growing interest in neural networks among geotechnical engineers is due to its excellent performance in modelling nonlinear multivariate problems[4,5]. It has been proved that a three-layer neural network can be used to represent an arbitrary continuous function. Artificial neural network consists of a number of interconnected processing elements, commonly referred to as neurons. The neurons interact with each other via weighted connections. These scalar weights determine the nature and strength of the influence between the interconnected neurons. The relationship between input layer and output layer of neurons is represented by sigmoid nonlinear transfer function. It is generally named B-P network when the neural network paradigm adopted the back-propagation learning algorithm. Multi- layers B-P network has the following advantages: firstly, because nonlinear hyperplane area is given out, the result is more accurate and reasonable, and then this network has good fault-tolerance. Secondly, the transfer function is continuously differential, so the process of weight study is very clear.

Using above theorem, a suitable back-propagation neural network model for studying the bearing characteristics is proposed on the basis of 27 static vertical loading tests of rock-socketed piles in China. The data was used as the input signals of B-P network. The established B-P network can describe the complex relationships on pile bearing capacity. Four principal factors affecting bearing capacity of rock- socketed piles were taken into accounted: length-diameter ratio, the ratio of diameter to socketed length, soil property, and rock property. Through study training, the case data of static tests of rock-socketed piles is input into the weights of neural. Therefore, the relative importance of above four factors can be calculated via the trained neural network. Because a three-layer neural network can be used to represent an arbitrary continuous function, one hidden layer and 8 units of hidden layer are chosen in this research after several experiments. In order to accelerate the network astringency and avoid concussion, the momentum gene and the learning rate is involved into study training procedure. According to the actual error, and may be taken as and respectively.

Computation results indicate the connection weights and relative importance of the various interacting factors. The relative importance of the various input factors can be assessed by examining these connection weights. The results suggest that the more important input factors are the rock property and length-diameter ratio. The model also demonstrates that neural network theory can be applied to describe the complex geotechnical engineering system reasonably after learning from actual test data. This method has the advantage over other more conventional methods in that it can be readily retrained as additional data from actual field records are acquired.

1

X. Shu, Z. C. Chen, "Discussion on the sudden failure mechanism of long rock-socketed bored pile", in "3rd International Geotechnical Seminar on Deep Foundations on Bored and Auger Piles", Van Impe, W. F. and Haegeman, W. , (Editors), A. A. Balkema, Rotterdam, 505-509, 1998.

2

J. P. Seidel, C. M. Haberfield. "The Axial Capacity of Pile Sockets in Rocks and Hard Soils", Ground Engineering, 28 (2), 33-38, 1995.

3

E. C. Leong, M. F. Randolph, "Finite-Element Modeling of Rock-Socketed Piles", International Journal for Numerical and Analytical Methods in Geomechanics, 18 (1), 25-47, 1994. doi:10.1002/nag.1610180103

4

A.T.C. Goh, "Seismic Liquefaction Potential Assessed by Neural Networks", Journal of Geotechnical Engineering, ASCE, 120(9), 1476-1480, 1994. doi:10.1061/(ASCE)0733-9410(1994)120:9(1467)

5

A.T.C. Goh, "Neural-Network Modeling of CPT Seismic Liquefaction Data", Journal of Geotechnical Engineering, ASCE, 122(1), 70-73, 1996. doi:10.1061/(ASCE)0733-9410(1996)122:1(70)

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