Semester

Summer

Date of Graduation

2025

Document Type

Thesis

Degree Type

MS

College

Statler College of Engineering and Mineral Resources

Department

Mining Engineering

Committee Chair

Deniz Tuncay

Committee Member

Deniz Talan

Committee Member

Guilherme Pereira

Abstract

Recent catastrophic collapses in U.S. limestone mines have exposed the limitations of traditional empirical design formulas for brittle rock masses. These events, especially those involving slender pillars, underscore that traditional methods often fail to account for progressive, spalling-dominated failure, highlighting a crucial gap in our understanding. This research addresses this issue by conducting a comprehensive investigation into the mechanics of spalling in rectangular stone mine pillars, utilizing advanced three-dimensional numerical modeling with FLAC3D combined with LiDAR-based geometric modeling.

The stability of a pillar is governed by a complex interaction between the in-situ stress field, rock mass properties, and pillar geometry. In shallow to moderate depths typical of stone mines, the horizontal stress component is often much higher than the vertical component, resulting in high tangential compressive stresses on the pillar walls that lead to spalling failure. The failure process is primarily determined by the pillar's shape, especially the width-to-height ratio. Slender pillars (w/h < 1.5) lack a significantly confined inner core and are prone to sudden, brittle collapse with little warning. In contrast, squat pillars (with a high w/h ratio) develop a confined core, which allows for a more ductile, strain-softening response even after the outer surface has failed. To simulate this behavior accurately, a constitutive model should reflect the progressive nature of brittle fracture. Classical failure criteria, such as the Mohr-Coulomb model, are conceptually flawed for this purpose because they assume the simultaneous mobilization of cohesion and friction, which is physically impossible since friction can only be mobilized on a surface that has already formed after the loss of cohesion.

To overcome this limitation, this research employs the Cohesion-Weakening Friction-Strengthening (CWFS) theory. The CWFS model describes a more physically realistic, sequential failure process: (1) as the rock is loaded beyond its damage initiation threshold, micro-cracks form and merge, resulting in a gradual reduction of the rock's cohesive strength; (2) only after significant damage and the development of fracture surfaces can the frictional component of strength activate and increase as fragments interlock under confinement. This framework is conceptually better suited for modeling spalling, a cohesion-loss-focused process that occurs at the low-confinement pillar surface.

The core of this thesis comprises a series of three-dimensional numerical simulations using FLAC3D, which incorporates both idealized block models and realistic pillar shapes derived from LiDAR scans processed with CloudCompare and Rhino 3D software. The models are designed to analyze the initiation and development of spalling under realistic geomechanical conditions. The CWFS behavior is implemented using the built-in strain-softening Mohr-Coulomb model, with parameters selected and calibrated based on a comprehensive review of published case studies for brittle rocks.

The numerical simulations successfully captured the brittle nature of the stone pillars. The results provided a detailed, mechanistic view of how failure initiates and leads to a critical stress redistribution into a confined inner core. The modeling clarified the critical role of the w/h ratio in determining the failure mode. It provided insight into the "length benefit" of rectangular pillars by mechanistically exploring the concept behind the effective pillar width formula. This analysis will enhance understanding of the failure mechanisms of stone mine pillars.

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