Predicted ultimate capacity of laterally loaded piles in clay using support vector machine Pijush Samui* Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India (Received 17 May 2007; final version received 07 December 2007) The determination of ultimate capacity of laterally loaded pile in clay is a key parameter for designing the laterally loaded pile. The available methods for determination of ultimate resistance of pile in clay are not reliable. This study investigates the potential of a support vector machine (SVM)-based approach to predict the ultimate capacity of laterally loaded pile in clay. The SVM, which is firmly based on statistical learning theory, uses a regression technique by introducing an "-insensitive loss function. A sensitivity analysis has been carried out to determine the relative importance of the factors affecting ultimate capacity. The results show that SVM has the potential to be a practical tool for prediction of the ultimate capacity of pile in clay. Keywords: pile foundation; support vector machine; statistical learning theory; sensitivity analysis 1. Introduction Piles are structural members of timber, concrete and/or steel that are used for a variety of structures including heavy building, transmission lines, power stations and highway structures. In many cases, piles are often subjected to considerable lateral forces such as wind loads in hurricane-prone areas, earthquake loads in areas of seismic activity and wave loads in offshore environments. So the determination of the ultimate capacity of laterally loaded piles is an essential task in geotechnical engi- neering. There are several methods available for prediction of ultimate capacity (Q) of laterally loaded piles in clay (Czerniak 1957, Hansen 1961, Broms 1964, Mayerhof, 1981). Recently, an artificial neural network (ANN) has been successfully used for pile analysis (Chan et al. 1995, Goh 1995, Chow et al. 1995, Lee and Lee 1996, Kiefa, 1998, Nawari et al. 1999). However, there are some limitations in using ANN: 1. Unlike other statistical models, ANN does not provide information about the relative importance of the various parameters (Park and Rilett 1999). 2. The knowledge acquired during the training of the model is stored in an implicit manner and it is very difficult to come up with a reasonable interpretation of the overall structure of the network (Kecman 2001). 3. In addition, ANN has some inherent drawbacks such as slow convergence speed, less generalising performance, arriving at a local minimum and over-fitting problems. As a result, alternative methods are needed which can predict Q more accurately. In this study, the support vector machine (SVM), as a novel type of learning machine based on statistical learning theory, has been used to predict the Q of laterally loaded pile in clay. SVM uses 44 load test data that have been taken form literature (Rao and Kuma, 1996). The dataset contains information about the diameter of pile (D), embedded length of pile (L), load eccentricity (e), shear strength of clay (C u ) and Q. The founda- tions of the SVM were developed by Vapnik (1995). It provides a new, efficient approach to improve generalisation perfor- mance and can attain a global minimum. In general, SVMs have been used for pattern recognition problems (Osuna et al. 1997, Gualtieri and Cromp 1998, Dibike et al. 2001, Huang et al. 2002, Zhu and Blumberg 2002, Belousov et al. 2002). Recently it has been used to solve non-linear regression estima- tion and time series prediction by introducing an "-insensitive loss function (Vapnik 1995, Mukherjee et al. 1997, Muller et al. 1997, Vapnik et al. 1997). The SVM implements the structural risk minimisation principle (SRMP), which has been shown to be superior to the more traditional empirical risk minimisation principle (ERMP) employed by many of the other modelling techniques (Osuna et al. 1997). SRMP minimises an upper bound of the generalisation error, whereas ERMP minimises the training error. In this way, it produces a better generalisation than traditional techniques. In SVM, the number of support vectors is determined by algorithm rather than by trial-and- error, which has been used by ANN for determining the number of hidden nodes. This paper has the following aims: Geomechanics and Geoengineering: An International Journal Vol. 3, No. 2, June 2008, 113--120 *Email: pijush.phd@gmil.com ISSN 1748-6025 print=ISSN 1748-6033 online Ó 2008 Taylor & Francis DOI: 10.1080=17486020802050844 http:==www.informaworld.com