Suggested empirical equations for estimating modulus of elasticity of intact rock

The modulus of elasticity of intact rocks is widely used in many rock engineering projects such as tunnels, slopes, foundations etc. as an input parameter. It is also used in the evaluations of deformation modulus of rock mass based on some empirical models. However, determination of this parameter from laboratory tests requires high-quality core samples and sophisticated testing equipments. Considering this difficulty, the use of empirical models to obtain this parameter has been attractive in rock engineering practice. In rock mechanics literature, some empirical relations exist between modulus of elasticity and other rock properties, such as uniaxial compressive strength (UCS), unit weight (γ), Schmidt hammer, point load index and petrographic composition. The main deficiency of the existing empirical relations is that they either ignore the rock type or use limited rock types. To eliminate these deficiencies, total of 239 UCS, unit weight, tensile strength (Brazilian) and modulus of elasticity (Ei) data were collected from the literature. Besides, total of 80 tests were performed on the greywacke and agglomerate core samples in this study. A total of 319 data set representing 37 different rock types were used throughout the analyses. To assign the rock type, the mi constant of the Hoek-Brown criterion was also considered. The UCS and the tensile strength data pairs, and the Hoek-Brown equation for intact rock were used to calculate the mi constant for each rock sample. In the first stage of regression analyses, a series of simple regressions were performed to define type and significance degree of relations between the independent parameters and modulus of elasticity. The simple regression uses one input and one output parameters. Due to this limitation, single value can be obtained from the simple regression based equation for modulus of elasticity depending on the input parameter. In other words, two different rocks may have same input parameter, although their elasticity moduli values are different. Considering this limitation, a series of simple regression were also considered by using combined parameter which include two or more input parameters. Finally, two prediction charts were prepared on the based on the empirical equations having coefficient of correlations of 0.863 and 0.872, respectively.