Application of Response Surface Methodology to Model Dependence of Strength and Deformabilty of Limestone Rock on Intact Specimens Shape Deviations

It is known from earlier and recent research that mechanical properties of intact rock like uniaxial compressive strength (UCS), Young's modulus (E) and Poisson's ratio (ⱱ) are influenced by shape deviations of test specimens as deviations from the ideal cylinder. That impact can be significant at certain level of inaccuracy of specimen preparing, and it should be objectively evaluated and controlled in testing. The effects of intact specimens side straightness, ends flatness, ends parallelism and perpendicularity to the specimen axis, on UCS, E, and ⱱ, measured in several actual ways during laboratory compression tests, were determined by previous research on 90 homogeneous specimens of limestone. In this paper, we subject these new experimental results to Response Surface Methodology (RSM) to model the mentioned dependence, to identify significant connections of variables and to evaluate the conclusions obtained directly from experimental phase. This study indicates how the responses of the model (outputs) – parameters UCS/E/ ⱱ of limestone rock depend on factors (inputs) – parameters of specimen shape deviations like flatness R, parallelism P and perpendicularity O, assuming modern test machines with spherically seated upper platen. Starting from general RSM model with three factors (R, P, and O), we investigated the multiple linear regression models of specific mechanical property (UCS, E, and ⱱ). Using the NCSS program ("NCSS 2004 and PASS 2005") in several steps, final models with very high coefficients of determination were developed for properties with the most evident effects of specimen shape deviations: nine models for strength UCS and UCS₅₀ (equivalent UCS for specimen with 50 mm diameter), and three models for ⱱ _L(Poisson's ratio calculated from axial deformations measured on the entire specimen length). These statistical models with their response surfaces further strengthen and confirm the results and conclusions from the experimental phase. The critical values of R, P, and O are established using an additional statistical analysis to determine the lower and upper engineering limits. These findings set the basis for the new eligibility criteria for specimens of limestone (and similar rock with UCS about 100–150 MPa) in further testing of strength and deformability.