Modeling deformation modulus of a stratified sedimentary rock mass using neural network, fuzzy inference and genetic programming
Introduction
The deformation modulus of a rock mass is one of the most significant properties used by a number of designers (Gurocak et al., 2007, Gurocak et al., 2008, Alemdag et al., 2008, Gurocak, 2011, Kaya et al., 2011, Singh et al., 2012, Aksoy et al., 2012, Ajalloeian and Mohammadi, 2014, Alemdag et al., 2014, Nejati et al., 2014, Alemdag, 2015, Feng and Jimenez, 2015) for estimating deformation behavior of rock masses encountered in civil engineering projects, such as design of foundations, tunnels and slopes. The deformation modulus of a rock mass can only be determined by employing large-scale in-situ tests on the rock mass, itself, for example, pressuremeter, plate loading, flat dilatometer, plate jacking, and Goodman jacking. It is sometimes difficult to apply the large scale in-situ tests because of time consuming processes and installation required. Therefore, the modulus of deformation may be determined from other rock properties using empirical estimations for the indirect estimations, which may be acquired more easily and cost effective application.
A number of researchers have developed various empirical relationships for estimating the deformation modulus, based on different classification schemes including Rock Mass Rating (RMR) (Bieniawski, 1974), Tunneling Quality Index (Q) (Barton et al., 1974), Geological Strength Index (GSI) (Hoek and Brown, 1997) and Rock Mass Index (RMi) (Palmstrom, 1995), and RQD (Rock Quality Designation) (Deere, 1964). The first empirical equation for the rocks with RMR > 50 was proposed by Bieniawski (1978). Later, Serafim and Pereira (1983) developed an equation for rock masses with RMR < 50. Nicholson and Bienawski (1990) released an equation based on both RMR and Ei values. Read et al. (1999), Gokceoglu et al. (2003), Chun et al. (2006) and Chun et al. (2009) suggested RMR based equations, whereas Mitri et al. (1994), Kayabasi et al. (2003), Ramamurthy (2004), Gokceoglu et al. (2004) and Sonmez et al. (2006) utilized both RMR and Ei values. RQD and Ei values were employed for the deformation modulus of rock by Zhang and Einstein (2004). Alemdag et al. (2015) evaluated different rock masses, results of in-situ test and existing empirical equations and suggested a new regression equation for estimating the deformation modulus of rock mass.
The present study investigates the applications of artificial neural network (ANN), neuro fuzzy (NF), and genetic programming (GP) for estimating the deformation modulus of a stratified sedimentary rock mass (Em). Success of ANN, NF, and GP applications in various engineering disciplines including geotechnical engineering have already been proven in the literature (Ying et al., 2006, Sawmliana et al., 2007, Singh et al., 2008, Gokceoglu et al., 2009, Cabalar et al., 2009, Cevik and Cabalar, 2009, Cabalar and Cevik, 2009a, Cabalar and Cevik, 2009b, Cabalar et al., 2010, Cevik et al., 2010, Verma and Singh, 2010, Cabalar and Cevik, 2011, Gurocak et al., 2012, Cabalar et al., 2012, Edincliler et al., 2010, Singh et al., 2013). In this study, these modeling techniques have been employed by proposing various equations to indicate the relationships between Em (deformation modulus of rock mass), RMR (rock mass rating) and Ei (elasticity modulus of intact rock), RMR and UCS (uniaxial compressive strength), RMR and Ei/UCS, RQD (rock quality designation) and Ei, RQD and UCS, and RQD and Ei/UCS.
Section snippets
Field studies and testing
The study area is located at approximately 40 km southeast of Elazig in eastern Turkey. Maestrichtian–Late Paleocene aged siltstones, known as Simaki Formation, outcrop out in the region (Fig. 1).
The siltstones are light gray and well-bedded (Fig. 2), and the geotechnical properties of the siltstones were determined by field and laboratory studies. During the field studies, the weathering, spacing, aperture, persistence, filling and roughness of discontinuities were defined using the scan-line
Development of empirical equations
Neural network (NN), neuro fuzzy (NF), and genetic programming (GP) approaches have been employed to determine the relationships between the deformation modulus of rock mass (Em) and the rock mass rating (RMR), rock quality designation (RQD), uniaxial compressive strength (UCS), and modulus of elasticity (Ei) parameters. During the analyses, the pairs of RMR–Ei, RMR–UCS, RMR–Ei/UCS, RQD–Ei, RQD–UCS and RQD–Ei/UCS were considered as the independent variables.
Conclusions
Rock mass deformation modulus (Em) has a very important place in rock engineering design due to a parameter represents the best the mechanical behavior of pre-failure of rock mass. Therefore, design engineers need to design the parameter which can be determined using empirical methods or in-situ tests. The Em requires large scale sophisticated in-situ testing equipments. Thus, it is sometimes difficult, due to the high costs, time consuming, and having operational difficulties, to determine the
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