# Characterization of dip effect on strength for gently inclined rock pillar

## TL;DR

This study explains how the strength of rock pillars in mines decreases as the angle of the ore deposit increases, offering a new model to predict this effect.

## Contribution

A new mathematical model using a compression-shear coefficient to quantify the dip effect on rock pillar strength.

## Key findings

- Pillar strength decreases as the dip angle increases.
- The compression-shear coefficient effectively captures the dip effect.
- Model results align well with numerical simulations.

## Abstract

In underground mining operations, rock pillars play a crucial role as load-bearing elements whose structural integrity exhibits strong correlation with the inclination angle of the ore deposit. While the dip effect on pillar strength is widely acknowledged, quantifying this effect remains challenging. This study addresses this issue through theoretical and numerical approaches. A failure criterion for inclined rock was applied to establish the relationship between flat and inclined rock pillar strength. A dimensionless compression-shear coefficient (incorporating in-situ stress factors) was introduced to bridge this relationship, enabling the development of a mathematical model for estimating pillar strength based on the ore-body dip angle. This model integrates rock strength criteria with empirical formulas, extending the application of rock strength theory. The model’s results were validated against numerical simulations, showing strong agreement. Both methods demonstrated that pillar strength decreases as the dip angle increases. The compression-shear coefficient effectively quantifies the dip effect, revealing a consistent decline in strength with higher dip angles. This research not only provides a theoretical framework for assessing inclined pillar strength but also enhances the practical application of rock strength theory in geomechanical applications.