Soft computing-based modeling of high strain rate-controlled rock compressive strength: a comparative analysis of ANN and metaheuristic algorithms optimized ANN models

Accurate estimation of the dynamic or high-strain-rate-controlled rock strength characteristics parameters, such as the uniaxial compressive strength (UCS), is essential in several areas of geomechanics, including earthquakes, rock bursts, hydraulic fracturing, tunneling, and aseismic design of important rock engineering structures. This study appraises the applicability of soft computing or machine learning (ML) techniques to estimate the strain rate-controlled UCS of rocks. To achieve this aim, three ML algorithms were employed: an artificial neural network learned or fitted using the Levenberg–Marquardt algorithm (ANN-LM) and two optimized variants incorporating metaheuristic frameworks—a Grasshopper Optimization Algorithm-enhanced ANN (ANN-GOA) and a Salp Swarm Algorithm-tuned ANN (ANN-SSA) to estimate the strain rate-controlled UCS of rocks. For this purpose, 94 direct laboratory measurements database comprising six input parameters, including rock sample diameter (D), thickness (L), strain rate (Ɛ), bulk density (ρ), static UCS (σc), and P-wave velocity (PWV) was used for the model development. A multivariate regression model was also developed to compare with the ML models. Among the developed models, the ANN-SSA 6–10-1 model demonstrated superior performance, achieving a correlation coefficient (R) of 0.99270, a relative root mean square error (RRMSE) of 0.07384, a variance accounted for (VAF) of 98.49%, and an a20-index of 1.0000. The ANN-GOA 6-10-1 and ANN-LM 6-10-1 models followed closely, with R values of 0.99146 and 0.98176, RRMSE values of 0.08117 and 0.09482, VAFs of 98.29 and 96.26%, and a20-indices of 0.9285 for both, respectively. The models were converted into intuitive and explicit equations for practical engineering and large-scale implementation. A variable importance analysis showed that the static UCS and strain rate are the most sensitive parameters to the high-strain rate-controlled UCS of rocks. Hence, the developed models can provide an accurate and easy means of determining the high strain rate-controlled UCS of rocks without laborious and expensive experimental methods.