Prediction of uniaxial compressive strength of sandstones using petrography-based models
Introduction
Mining engineers request the uniaxial compressive strength more often than any other rock material property (Bieniawski, 1974). The second most sought property is the triaxial strength, although the uniaxial compressive strength is requested nearly nine times more often (Cargill and Shakoor, 1990). The other important intact rock property for rock engineering projects is the modulus of elasticity. Several researchers (for ex. Sachpazis, 1990, Katz et al., 2000, Yilmaz and Sendir, 2002, Sonmez et al., 2006) emphasised on the importance of the modulus of elasticity. However, high quality core samples of regular geometry are needed for the determination of the uniaxial compressive strength and the modulus of elasticity. Such cores cannot always be extracted from weak, highly fractured, thinly bedded, foliated and/or block-in-matrix rocks. To cope with this difficulty, prediction of the some mechanical properties of intact rock became a practical approach. Especially, in the early stages of the engineering designs, such prediction models are highly useful because they are cost effective and provide reproducible data.
Krynine (1948) estimated a 40% share for sandstones in all sedimentary rocks. Ronov (1968) suggested that 24% of world platforms comprises sandstones. Boggs (1993) gives a rather gross values 20–25% for sandstone abundance in stratigraphic record. Considering these abundances declared by various researchers, to encounter a type of sandstone is a usual situation during a tunnel, slope or foundation excavation. When considering these reasons, it is evident that understanding the key petrographical parameters governing the uniaxial compressive strength of sandstones and development of some prediction models for the uniaxial compressive strength of sandstones have crucial importance.
It is expected that various petrographical properties have a control on the uniaxial compressive strength of sandstones. However, a general prediction model for the uniaxial compressive strength of sandstones does not exist in the literature although some rock type-specific empirical models and strength-petrography relationships for different types of sandstones have been proposed. In addition, although there are several petrographic parameters of sandstones, a parameter selection routine for the purposes of strength prediction is not discussed in the literature. For this reason, the main goals of the present study are to discuss the key parameters influencing the uniaxial compressive strength of sandstones, to construct a database as large as possible, to develop some general prediction models for sandstones and to check the validity of the developed prediction models. For the purposes of the study, after compilation of the data from the previous studies, the Ankara sandstone was selected in the first stage in accordance with the purpose of the study, and the uniaxial compressive strength tests and the thin-section analyses were performed. Employing the results of these analyses and the data obtained from the literature, the key parameters were selected and some multiple prediction models were developed using multiple regression analyses and ANN.
Section snippets
Previous studies
The uniaxial compressive strength of sandstones is controlled by several inherent and environmental parameters. The inherent parameters can be characterized by petrographical properties. Petrographic characteristics known to affect mechanical properties of sandstones include grain size, packing density, packing proximity, degree of grain interlocking, void space, and mineral composition (Shakoor and Bonelli, 1991). However, conflicting results have been reported relating to the influence of
Laboratory studies
In this study, the sandstones collected from Ankara and its southern vicinity were used. These sandstones belong to the Karakaya Complex of Triassic age and extend from west to the east throughout the North Anatolia in patchy outcrops (Okay and Goncuoglu, 2004). Karakaya complex is supposed to have been formed in a short-lived extensional trough (Kocyigit, 1987, Genc and Yılmaz, 1995) and mainly comprises gravity-laden siliciclastics, intercalated volcanogenic rocks and reef limestones. This
Construction of database
A total of 61 samples including uniaxial compressive strength and petrographical parameters of the Ankara sandstone were prepared. In addition, a database including the data of different authors (Bell, 1978, Shakoor and Bonelli, 1991, Ulusay et al., 1994, Bell and Lindsay, 1999) was compiled to apply statistical analyses and to construct ANN model. Bell (1978) performed both the uniaxial compressive strength tests and thin-section petrographical studies on 29 samples taken from the Fell
Parameter selection routine
When constructing a prediction model having multiple inputs, the selection of input parameters has a crucial importance. Standard statistical procedures consider only redundancy among the input parameters. In this study, not only redundancy was taken into account but also a logical procedure including physical meanings of the petrographical parameters and ease of determining them were considered. The petrographical parameters were divided into two main groups such as mineralogy and microfabric.
Multiple regression analyses
Most of the problems in geology involve complex and interacting forces, which are impossible to isolate and study individually (Davis, 1973). For this reason, the multivariate regression analysis was applied for the generalized model in this study because they allow us to consider changes in several properties simultaneously.
Fahy and Guccione (1979), Ulusay et al. (1994) and Zorlu et al. (2004) developed some multiple regression equations (Eqs. (3), (4), (5), respectively) for the prediction of
Construction of artificial neural network model
In the last decade, some soft computing methods such as fuzzy inference systems and ANN models have been used in engineering geology literature to construct some multiple prediction methods for estimation of some rock parameters. den Hartog et al. (1997), Alvarez Grima and Babuska (1999), Finol et al. (2001), Gokceoglu (2002), Gokceoglu and Zorlu (2004), Nefeslioglu et al., 2003, Nefeslioglu, H.A. et al., 2006, Tutmez and Hatipoglu (2007) employed some fuzzy inference systems for predicting
Assessment of the prediction performances and selection of the best models
Total 10 prediction models (5 of them are multiple regression and 5 of them are ANN) were developed in the present study. When considering the testing data sets as well, total 20 coefficients of correlations were obtained. The high performance for the training data sets shows good learning of the prediction model while that for the testing data sets indicates good generalization ability of the models. For this reason, when selecting the best model among the models developed herein, some
Conclusions
The conclusions obtained from the present study can be drawn as follows:
Considering the previous empirical equations among the uniaxial compressive strength and petrographic parameters of sandstones, some contradictions were detected. One of the important causes of these contradictions is sourced from selection of input parameters for multiple prediction models. In this study, to eliminate this problem, a new logical parameter selection routine for petrographic parameters is introduced.
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