Indirect estimation of uniaxial compressive strength (UCS) and tensile strength (TS) of rocks using physical, abrasion, and mechanical parameters by regression models

Uniaxial compressive strength and tensile strength are key parameters in geotechnical engineering; however, their direct determination is often costly and time-consuming and requires standardized specimens. This study investigates indirect estimation of UCS and Brazilian tensile strength (BTS) using physical, mechanical, and abrasive properties of 14 groups of sedimentary, igneous, and metamorphic rocks from different regions of Iran. Simple and multiple regression analyses and principal component analyses (PCA) were applied to identify the most effective predictors and develop empirical relationships. As expected, the Schmidt hammer rebound value (SCH) provided the strongest univariate relationship with UCS (R 2 = 0.75), whereas the Los Angeles abrasion value (LA) showed the strongest relationship with BTS (R 2 = 0.83). The multivariate model based on SCH and Cerchar abrasion index (CAI) improved the BTS prediction to R 2 = 0.88. PCA extracted two components explaining 90.05% of the total variance, with the first component accounting for 71.15% and showing strong relationships with UCS (R 2 = 0.90) and BTS (R 2 = 0.89). Leave-one-out cross-validation (LOOCV) further confirmed the predictive performance of the developed models, with Q 2 values of 0.853 and 0.775 for PCA-based prediction of UCS and BTS, respectively. The results demonstrate that combining readily measurable mechanical and abrasion parameters can provide practical indirect estimates of rock strength, particularly where direct testing is difficult, costly, or limited by the availability of standard core specimens.