The uniaxial compressive strength and modulus of elasticity of intact rocks are vital parameters in many rock engineering projects. However, determination of these mechanical properties from laboratory tests requires high-quality core samples which are sometimes difficult to obtain. Considering this difficulty, the predictive models are often employed for the indirect estimation of these parameters. The purpose of this paper is to describe the use of canonical correlation method for estimating the mechanical properties of intact rocks simultaneously. For this reason, 100 rock samples were collected and several tests including uniaxial compressive strength, Schmidt hammer, point load index, sound velocity, tensile Strength, porosity, dry and saturated density tests have been applied. Current study presents a Canonical correlation capable of predicting the mechanical properties of intact rocks concurrently.
Mechanical properties of rocks such as uniaxial compressive strength (UCS) and modulus of elasticity (E) of intact rocks are of paramount importance in mining and civil activities. Rock engineers extensively utilize the UCS and E in designing tunnels, foundations, slopes and other rock engineering projects. In addition, analytical and numerical solutions require both parameters. Generally, the UCS and E of rock samples are determined using either the laboratory test or index tests but owing to the nature of rock materials, determination of rock properties is cumbersome and time consuming. For this reason, developing of predictive models to estimate the required properties is always an interesting study area among the rock engineers [1–10]. In the past studies, all models were obtained using regression of one variable from one or more variables of engineering indices but it is sometimes essential to recognize the relationship between two or more dependent variables and some independent variables [11]. The purpose of this paper is to describe the use of canonical correlation method for estimating the UCS and E at the same time. For this purpose Different rock types have been tested based on ISRM suggested methods [12]. These tests consist of point load, sound velocity, schmidt hammer, porosity, tensile strength, uniaxial compressive tests, dry and saturated density.
Rock blocks have been collected and 100 sample sets for rock mechanics tests were obtained. Each data set consist of UCS, E, point load index (PL), porosity (n), sound velocity (Vp), schmidt hammer (SHR), tensile strength (T), dry (dry) and saturated (sat) density. The procedures 432 suggested by ISRM for rock mechanics tests were considered. The results obtained from the tests with statistical evaluation are tabulated in table 1.
Canonical correlation originally has been developed by Hotelling [13]. This method is a multivariate statistical model that facilitates the study of interrelationships among sets of multiple dependent and multiple independent variables. Whereas multiple regression predicts a single dependent variable from a set of multiple independent variables, canonical correlation simultaneously predicts multiple dependentvariables from multiple independent variable.
