Analysis of Young's modulus for Carboniferous sedimentary rocks and its relationship with uniaxial compressive strength using different methods of modulus determination

Abstract

Young’s modulus (E) is one of the basic geomechanical parameters used in rock engineering in practice. It is determined based on uniaxial compressive test (UCS). However, according to International Society of Rock Mechanics it can be calculated by three different ways: as the tangent, secant and average modulus. The results from each method are significantly different. The UCS tests was carried out on 237 rock specimens with the slenderness ratio 2 of Carboniferous claystones, mudstones and sandstones. The axial deformation was always measured automatically by the displacement measurement device (LVDT) built into the testing machine and connected to the hydraulic piston. Then the Young’s modulus was calculated for each test by all three methods. The analysis of the results is presented in this paper to show the difference between all the three moduli calculated for each specimen, and to recommend the best method of Young’s modulus determination. First, the typical range of the elastic linear deformability for the chosen rock types was determined as 25–75% of the peak strength at confidence interval 95% for these sedimentary rocks. The modulus value distributions obtained from each calculation method were compared using statistical parameters: mean value, median, minimum, maximum, standard deviation, mean difference at confidence interval 95%, and non-uniformity coefficient. The proportions between average-secant modulus (Eav/Esec) and average-tangent modulus (Eav/Etan) for the rock samples were estimated. For the studied rocks the obtained values were: 1.10–1.32% for Eav/Esec, 1.08–1.25% for Etan/Esec and 1.01–1.06 for Eav/Etan (for Etan with the range of 20–80% of peak strength). These values show low coherence between secant and average modulus (ca. 23% difference) and good consistency of average and tangent modulus. Based on the analysis, tangent Young’s modulus is recommended as the guiding one at the constant range of 30–70% of the ultimate stress. Secant Young’s modulus, as it comprises not only elastic strain but the pore compaction as well, should be named as modulus of deformability. This conclusion was further confirmed by the regression analysis between UCS and E. The highest regression coefficients and the lowest standard error of the regression was obtained for tangent Young’s modulus determination method. In addition, modulus ratio MR for claystones, mudstones and sandstones was studied and determined as 274, 232 and 223 respectively.