Statistical Models to Predict Tensile Strength from Unconfined Compressive Strength: Case Study from Southern Iraq

Abstract

Tensile strength (To) is an important parameter for creating geomechanical models, especially when tensile failure is the failure of interest. The most common way to estimate the tensile strength is by utilizing Brazilian tests. However, due to material limitation, cost, or time, To is sometimes assumed or estimated empirically. In this work, laboratory test data of To and Unconfined Compressive Strength (UCS) conducted for three zones in southern Iraq (Zubair sandstone, Zubair shale, and Nahr Umr shale) were utilized to create three regression models to estimate To from UCS. The reason for selecting UCS as the independent parameter is that static UCS, in most cases, has to be estimated from laboratory tests to create robust geomechanical models. In other words, UCS will be given the preference over Towhen there is the material limitation, cost, or time involved. The data of each zone were divided into training (80%) and testing (20%) to ensure the models can generalize for new data and avoid overfitting. Multiple least squares fits were tested, and linear least squares regression was selected since it provided the highest R2 and the lowest error. The models yielded training R2 of 0.983, 0.988, and 0.965 while the testing R2 were 0.978, 0.990, and 0.993 for Zubair sandstone, Zubair shale, and Nahr Umr shale, respectively. The errors were assessed using root mean squared error (RMSE) and mean absolute error (MAE), and they both have shown an acceptable margin of error for all three models. In short, the created three models showed the ability to estimate To from UCS when material limitation, cost, or time factors are involved or when executing a Brazilian test is not applicable. The proposed models can contribute to robust geomechanical models as well as minimizing cost, time, and material usage.