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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

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Abstract

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.

Highlights

  • Uniaxial compressive strength tests were conducted on porous, weak limestone at different width-to-height ratios.

  • Calibrated bonded block model was used to evaluate confining stress and effect of platen–specimen interface friction angle at different w/h ratios.

  • Strength parameters, such as crack initiation, crack damage, peak strength, and residual strength, increase as w/h ratio increases.

  • Confining stress increases with w/h ratio, having higher value in the center of the specimen.

  • Peak strength increases for squatter specimen (w/h = 2, and 3), as interface friction angle increases.

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Data Availability

The data used in this study can be made available upon reasonable request from Akash Chaurasia.

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Acknowledgements

The authors would like to thank Bruce Yoshioka, Brent Duncan, Jim DesRochers, and Muthu Vinayak from the Colorado School of Mines for their help in the initial experimental setup. Special thanks to Dr. Sankhaneel Sinha for providing valuable insight into the BBM model setup and calibration.

Funding

This study was sponsored by the Alpha Foundation for the Improvement of Mine Safety and Health, Inc. (ALPHA FOUNDATION, Grant no. AFC820-52). The views, opinions, and recommendations expressed herein are solely those of the authors and do not imply any endorsement by ALPHA FOUNDATION, its directors, and its staff.

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    Akash Chaurasia & Gabriel Walton

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AC planned the study, set up and ran the laboratory tests and simulate the numerical model, analyzed the data, and wrote the paper. GW assisted in planning the study and data analysis and edited the paper.

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Correspondence to Akash Chaurasia.

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Chaurasia, A., Walton, G. 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. Rock Mech Rock Eng 57, 719–738 (2024). https://doi.org/10.1007/s00603-023-03579-7

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