Multivariate Adaptive Regression Spline and Least Square Support Vector Machine for Prediction of Undrained Shear Strength of Clay

This study adopts Multivariate Adaptive Regression Spline (MARS) and Least Square Support Vector Machine (LSSVM) for prediction of undrained shear strength (su ) of clay, based Cone Penetration Test (CPT) data. Corrected cone resistance (qt ), vertical total stress (σv ), hydrostatic pore pressure (u0 ), pore water pressure at the cone tip (u1 ), and pore water pressure just above the cone base (u2 ) are used as input parameters for building the MARS and LSSVM models. The developed MARS and LSSVM models give simple equations for prediction of su. A comparative study between MARS and LSSSM is presented. The results confirm that the developed MARS and LSSVM models are robust for prediction of su. DOI: 10.4018/jamc.2012040103 34 International Journal of Applied Metaheuristic Computing, 3(2), 33-42, April-June 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 1975; Schmertmann, 1975). There are numerous empirical correlations between qc and su reported in literature (Lunne et al., 1976; Koutsoftas & Fischer, 1976; Stark & Delashaw, 1990). This article adopts Multivariate Adaptive Regression Spline (MARS) and Least Square Support Vector Machine (LSSVM) for developing correlations between su and CPT test data. MARS is a flexible, more accurate, and faster simulation method (Friedman, 1991; Salford Systems, 2001). It has been successfully used to solve different problems (MacLean & Mix, 1991; Veaux et al., 1993; Ekman & Kubin, 1999; Prasad & Iverson, 2000; Jin et al., 2000; Ko et al., 2004; Sharda et al., 2008; Okine et al., 2003, 2009). LSSVM is proposed by Suykens and Vandewalle (1999). In LSSVM, the training is expressed in terms of solving a set of linear equations in the dual space instead of quadratic programming. Researchers have successfully used to solve different problems in engineering (Pahasa & Ngamroo, 2011; Deng & Yeh, 2010; Huang et al., 2009; Bin et al., 2008). This article uses the database obtained from Sandven (1990) and Chen (1994) that included data from clay sites located in several countries around the world. The dataset contains information about the corrected cone resistance (qt), vertical total stress (σv), hydrostatic pore pressure (u0), pore pressure at the cone tip (u1), pore pressure just above the cone base (u2) and su. The reference values of su were estimated from isotropically and anisotropically consolidated undrained triaxial compression (CIUC and CAUC) tests and in situ field vane shear tests. A comparative study has been done between the developed LSSVM and MARS. The organization of the work is as follows. The details of MARS are proposed in the upcoming section. Then the LSSVM technique is described. The results from the developed MARS and LSSVM are presented afterwards. The conclusions are given in the last section. DETAILS OF MARS MARS is a flexible modeling method for highdimensional data (Friedman, 1991). A brief overview of the MARS model will be given here. MARS uses the following equation for prediction of output(y). y B x m m m M = + ( ) = ∑ α α 0 1 (1) Where Bm(x) is basis function, αm is the coefficient of Bm(x), x is the input variables, M is the number of basis functions and α0 is constant. In this study, the input parameters are qt, σv, u0, u1, u2. The output of the MARS model is su. So, x q u u u t v =    , , , , σ 0 1 2 and y su =     . MARS adopts the following truncated spline function as basis function (Sekulic & Kowalski, 1992).