Application of fuzzy inference system and nonlinear regression models for predicting rock brittleness

Abstract

Brittleness is one of the most crucial rock features for underground excavation and design considerations in rock mass. Direct standard testing method for measuring rock brittleness, the combination of rock properties rather than only one rock parameter have not available yet. Therefore, it is indirectly calculated as a function of some rock properties such as rock strength by using various ratios and prediction tools. The aim of this study is to estimate the rock brittleness by constructing fuzzy inference system and nonlinear regression analysis. For this purpose, a dataset established by utilizing the relevant laboratory rock tests (i.e., punch penetration, uniaxial compressive strength, Brazilian tensile strength and unit weight of rock) at the Earth Mechanics Institute of Colorado School of Mines in the USA on the rock samples assembled from 48 tunnels projects throughout the world. Running the established models, the performance values such as RMSE, VAF, absolute error and coefficient of cross-correlation were computed for developed models. The VAF and RMSE indices were calculated as 89.8% and 2.97 for the nonlinear multiple regression model and 83.1% and 3.82 for fuzzy model, respectively. As a result, these indices revealed that the prediction performance of the nonlinear multiple regression model is higher than that of the fuzzy inference system model. However, it is concluded that both constructed models exhibited a high performance according to the obtained prediction values.

Introduction

Rock brittleness is the combination of rock properties rather than only one parameter; therefore, it is very crucial rock parameters for underground projects like tunneling. Different researchers describe and measure rock brittleness using various rock testing methods; however, there is no agreement on the measurement of the brittleness in rock mechanics community except indirect measuring it as a function of rock strength such as uniaxial compressive and Brazilian tensile strength (Schwartz, 1964, Cook et al., 1984, George, 1995, Gong and Zhao, 2007, Kahraman, 2002, Yagiz, and Ozdemir, 2001, Eberhardt et al., 1988, Protodyakonov, 1963, Hucka and Das, 1974, Altindag, 2002, Bieniawski, 1967, Yagiz, 2004, Pang and Goldsmith, 1990). In fact a general law to define the brittleness is that a more brittle rock breaks at very little deformation. The brittleness only describes the behavior of rock deformation and failure subjected to the concrete loading condition, the measurement of the brittleness has not yet been standardized (Gong & Zhao, 2007). At present, various empirical relations were obtained in the literature to estimate and compute the rock brittleness with different approaches (Table 1).

Schwartz (1964) conducted a series of triaxial tests on intact rock specimens of the Indian limestone and concluded that the transition from brittle to ductile behavior appears at a principal stress ratio of approximately 4.3. Hetenyi (1966) defined the brittleness as the lack of ductility. Ramsay (1967) stated that as the internal cohesion of rock is destroyed, the rock can be accepted as brittle. Hucka and Das (1974) stated that the higher ratio of uniaxial compressive to Brazilian tensile strength defines the higher brittleness value; then they introduced various strength ratios to define the brittleness. Further, Goktan (1991) stated that brittle rock should have a lower specific energy than a less brittle one. George (1995) defined the rock brittleness is the ability of rock material to deform continuously without permanent deformations along with the application of stress surpassing the necessary stresses for micro-cracking rock of the materials. Altindag (2002) suggested a brittleness index as a function of uniaxial compressive strength and Brazilian tensile strength of rock, but he has not give any method how to make decision to describe the degree of the brittleness with findings. Even though the brittleness is often calculated by using Brazilian tensile and uniaxial compressive strength of rock in engineering practices, several special tests are also used for some special purposes such as tunneling performance estimation. Blindheim and Bruland (1998) introduced brittleness value that equals to the percentage of material passing the 11.2 mm mesh after the aggregate has been crushed in the mortar is one of the main rock parameters to estimation of TBM performance in the prognosis model at the Norwegian University of Science and Technology (NTNU). Similarly, the punch penetration test, originally intended to provide a direct method for estimating the normal load on disc cutters was developed in late 1960s to provide direct laboratory method to investigate rock behavior under the indenter (Hamilton & Handewith, 1971). Since its initial development, a number of major modification and improvements were made on the test procedures and data evaluations. Szwedzicki (1998) employed the test for measuring rock hardness and stated that this test could be used for predicting cutability of rocks. Further, the punch penetration test also could provide qualitative data for investigating rock toughness and brittleness under the indentor to estimate TBM penetration rate (Dollinger et al., 1998, Yagiz, 2002, Yagiz, 2003, Yagiz, 2006, Yagiz, 2008). Yagiz (2002) utilized the punch penetration test for investigating rock brittleness and toughness that is one of the input rock properties in the Modified Colorado School of Mines Model (CSM) to estimate penetration rate of tunneling machines. Consequently, the rock brittleness classification has been introduced by using brittleness index generated as a result of punch penetration test (Yagiz, 2009a). Copur, Bilgin, Tuncdemir, and Balci (2003) introduced brittleness index based on the ratio of force increment to decrement period of the punch penetration (indentation) test results.

In addition to conventional regression techniques, some soft computing techniques such as fuzzy inference systems and artificial neural networks for the prediction purposes have been used in rock engineering for the last decade (Finol et al., 2001, Alvarez Grima and Babuska, 1999, Alvarez Grima, 2000, Gokceoglu, 2002, Meulenkamp and Alvarez Grima, 1999, Nefeslioglu et al., 2006, den Hartog et al., 1997, Singh et al., 2001, Gokceoglu and Zorlu, 2004, Tutmez and Hatipoglu, 2007, Singh et al., 2007, Sonmez et al., 2006, Zorlu et al., 2008). The purpose of the present study is to construct both a fuzzy inference system and nonlinear regression models for predicting the rock brittleness and to make comparison of prediction levels between developed models by using the related prediction values and results.