Prediction of compressive and tensile strength of limestone via genetic programming

Abstract

Accurate determination of compressive and tensile strength of limestone is an important subject for the design of geotechnical structures. Although there are several classical approaches in the literature for strength prediction their predictive accuracy is generally not satisfactory. The trend in the literature is to apply artificial intelligence based soft computing techniques for complex prediction problems. Artificial neural networks which are a member of soft computing techniques were applied to strength prediction of several types of rocks in the literature with considerable success. Although artificial neural networks are successful in prediction, their inability to explicitly produce prediction equations can create difficulty in practical circumstances. Another member of soft computing family which is known as genetic programming can be a very useful candidate to overcome this problem. Genetic programming based approaches are not yet applied to the strength prediction of limestone. This paper makes an attempt to apply a promising set of genetic programming techniques which are known as multi expression programming (MEP), gene expression programming (GEP) and linear genetic programming (LGP) to the uniaxial compressive strength (UCS) and tensile strength prediction of chalky and clayey soft limestone. The data for strength prediction were generated experimentally in the University of Gaziantep civil engineering laboratories by using limestone samples collected from Gaziantep region of Turkey.

Introduction

The uniaxial compressive strength (UCS) and tensile strength of rocks are widely used in the design stage of geotechnical structures. There are basically two methods for determining these strength properties, one of the approaches is to collect and test the specimens in the laboratory or making use of the previously derived empirical equations from the literature. The first approach is the direct approach and the second approach can be called as indirect approach. Testing procedures for the direct approach have been standardized by ASTM D 2938-95, ASTM D 3967-95a, ISRM, 1981. Due to simpler, faster and more economical solution aspects, indirect methods for UCS and tensile strength predictions are frequently required to be driven particularly at the conditions of limited laboratory facilities. In the indirect approach the empirical equations for strength are usually derived from simple tests such as Schmidth rebound number, point load tests, impact strength and sound velocity (Fener et al., 2005, Singh et al., 2001). Soft computing based techniques especially artificial neural networks (ANN) are also gaining a considerable attention in estimating both UCS and tensile strength (Meulenkamp, 1997, Meulenkamp and Alveraz Grima, 1999, Nie and Zhang, 1994, Singh et al., 2001). ANN being recently more popular especially at the circumstances of less correlation coefficient of regression equations required more input variables to completely define rock characteristics and more flexible operations between input and output variables (Garret, 1994, Huang and Wänstedt, 1998). ANN is a fundamentally different approach which has to learn and generalize interactions among many variables. Because of this ability, ANN technology has a big potential in modeling the material behaviour from experimental data (Ellis et al., 1992, Ghabousi et al., 1991). In the literature, Meulenkamp and Alveraz Grima, 1999, Meulenkamp, 1997 applied ANN for the prediction of compressive strength on the rock samples containing sandstones and granodiorites. Singh et al. (2001) used ANN to predict both UCS and tensile strength for schistose rocks. All those past studies showed that using neural network models for the prediction of strength properties concluded more accurate predictions than conventional statistical models. However, the problem with ANN is their black box like working characteristic. It is not easy to relate inputs of an ANN with its outputs in an analytical equation form. Another branch of soft computing approaches from the family of evolutionary programming that is known as genetic programming is also a promising candidate for solving complex prediction problems. The main advantage of genetic programming based approaches is their ability to generate prediction equations which can be easily manipulated in practical circumstances. Genetic programming based approaches are not yet applied to the prediction of UCS and tensile strength of limestone in the literature. In this research paper a promising set of genetic programming techniques, which are known as multi expression programming (MEP), gene expression programming (GEP) and linear genetic programming (LGP) approaches are applied to the UCS and tensile strength of chalky and clayey soft limestone. The limestone samples which are used to produce data sets for genetic programming techniques were collected from Gaziantep city of Turkey (see Fig. 1).

The rock characteristics which function as the training input of genetic programming are ultrasonic pulse velocity (UPV), density, water absorption, dry density, saturated density and bulk density, while the corresponding UCS and tensile strength are the outputs for which prediction equations are derived by using LGP, GEP and MEP. The present study makes also a contribution by comparing these three effective genetic programming techniques on a real life problem.