Comparison of the reliability of experimental methods for determining the strength limit of prismatic samples of mining rocks

Purpose. Development of a mathematical model for calculating the parameters of stress-strain diagrams of tall prismatic rock samples with a high internal friction angle to evaluate their strength and destruction characteristics under load. Methods. Analytical modeling of the destruction process of tall prismatic samples was conducted using experimental values of four rock properties: shear strength limit, internal and contact friction coefficients, and elastic modulus. The model accounts for stress distribution and crack development characteristic of tall samples. Results. The proposed method allows determining the strength limit of prismatic samples depending on their height. A hyperbolic relationship between sample height and strength limit was identified, demonstrating that doubling the sample height reduces its strength by approximately 30%. The method also describes the influence of crack formation on the contact surfaces on the deformation properties of the samples. Scientific novelty. For the first time, a mathematical model has been developed to describe the destruction mechanisms of tall prismatic rock samples, taking into account the influence of a high internal friction angle. The model provides an analytical basis for the reduction in sample strength with increasing height and the redistribution of stresses. Practical significance. The developed model can be used to calculate the mechanical parameters of tall prismatic rock samples in mining enterprises. The obtained results contribute to assessing rock stability and optimizing mining operations, ensuring their efficiency and safety.