Laboratory and Numerical Modeling of the Effects of Width-to-Height Ratio on the Strength and Deformation Behavior of Pillars Composed of Porous, Weak Limestone

The impact of the width-to-height ratio (w/h ratio) on rock strength and deformation behavior of rock pillars has been studied extensively since the 1950s through laboratory tests, in-situ tests, and numerical modeling, with the goal of achieving safe and economical designs. However, most previous studies have focused on hard, brittle, and low porosity rocks, leaving a gap in understanding the effect of the w/h ratio on the porous, weak rock. This study aims to fill this gap by using both laboratory tests and numerical modeling to investigate the relationship between mechanical parameters, strength, and failure processes at different w/h ratios for a weak and porous rock called Texas Cream limestone. Uniaxial Compressive Strength (UCS) tests were conducted on cuboidal samples with a constant cross-section of 15  × 15 cm and varying heights. The results showed that strength parameters [Crack Initiation (CI), Crack Damage (CD), peak strength, and residual strength] increased as the w/h ratio increased. Additionally, the failure pattern changed from a full shear mechanism for slender specimens (w/h = 0.5 and 1) to progressive failure for squatter (w/h = 2 and 3) specimens. To further understand the impact of the w/h ratio on rock strength and deformation, a Voronoi Bonded Block Model (BBM) was calibrated to the laboratory data sets and used to quantify confining stress and the effect of plate-specimen friction angle, which is difficult to measure through laboratory tests alone. From the BBMs, a brittle–ductile transition was inferred to occur at a w/h ratio of 5.2. Finally, a relationship was established between UCS, w/h ratio, and interface friction coefficient obtained through sensitivity analysis on calibrated BBM and validated with previous laboratory results.