Predicting the strength anisotropy in uniaxial compression of some laminated sandstones using multivariate regression analysis

In this study, uniaxial compressive strength (UCS) tests were carried out to investigate the anisotropic strength behavior of laminated sandstones selected from submarine fan deposits in the Neogene Adana Basin of Southern Turkey. The core specimens were prepared at orientation angles (β) of 0°, 30°, 45°, 60°, and 90° with respect to the planes of lamination. U-type strength anisotropy with strength anisotropy ratios (Rc = σ₉₀/σ_min) varying between 1.29 and 1.74 were found, referring to a low degree of anisotropy. An attempt has been made to estimate the anisotropic UCS behavior taking into account orientation angles, unit weight (γ) and porosity (n) as independent variables by multivariate regression analysis. The second orders of each independent variable as well as the third order of the orientation angle values were also considered in regression analyses to take into consideration their nonlinear relationships on UCS. The prediction performance of the best fit regression model was evaluated by the standard error of estimate (SEE), the coefficient of multiple determination (R ²), and the adjusted coefficient of multiple determination (R_a² R_{a}^{2} ), which were obtained as 2.27, 0.927, and 0.923, respectively, indicating high prediction capacity.