Predicting the uniaxial compressive strength and elasticity modulus of sandstones from physical and mechanical properties using statistical analyses and artificial intelligence-based techniques

This study develops predictive models for the uniaxial compressive strength (UCS) and elasticity modulus (E) of sandstones by integrating statistical analyses with artificial intelligence (AI) techniques. Comprehensive laboratory tests were performed on 20 sandstone samples from four Iranian formations, measuring key physical (dry unit weight γₐ = 23.34–26.10 kN/m³, porosity nₑ = 2.07–10.16%) and mechanical properties (UCS = 55.46–104.16 MPa, E = 39.86–57.03 GPa). Statistical analyses revealed strong correlations, with dry unit weight showing the highest Pearson correlation to UCS (R = 0.947) and E (R = 0.971), while porosity exhibited significant negative relationships (R = −0.918 and −0.916 respectively). Among the evaluated AI models, Artificial Neural Networks (ANN) demonstrated superior predictive capability, achieving the highest accuracy for both UCS and E predictions (e.g., UCS-Hs: R² = 0.992, RMSE = 1.562; E-Hs: R² = 0.947). In contrast, Random Forest (RF) and K-Nearest Neighbors (kNN) models provided acceptable but comparatively lower performance, with their best models attaining R² values of 0.909 and 0.906, respectively. Sensitivity analysis identified Schmidt hammer rebound (H₅) as the most influential predictor (Univariate Regression score = 3406.678), followed by point load index (PLI). The PDH formation demonstrated superior mechanical properties (UCS = 97.21 MPa, E = 54.82 GPa) linked to its high density (γₐ = 25.52–25.99 kN/m³) and low porosity (nₑ = 2.48–4.84%), while the HZD formation showed the weakest performance (UCS = 60.25 MPa) due to high porosity (nₑ = 8.02–10.16%). These findings provide a robust framework for predicting sandstone mechanical properties using non-destructive methods, offering significant advantages for geotechnical applications where direct testing is impractical.