# Catastrophic instability criterion for roadway roof and sidewall rock mass under deep-hole roof blasting in Songshan coal mine

## TL;DR

This study uses catastrophe theory to analyze rock instability in coal mine roadways caused by deep-hole blasting, offering a method to predict and control such instability.

## Contribution

A novel instability criterion for layered roof and sidewall rock masses under deep-hole roof blasting is proposed using cusp catastrophe theory.

## Key findings

- A critical maximum explosive charge of 93.3 kg was calculated for the roadway in Songshan Coal Mine.
- Field monitoring showed minimal roof subsidence and sidewall convergence after blasting, indicating slight impact.
- Theoretical models were developed to predict instability based on potential energy and mechanical criteria.

## Abstract

To investigate the catastrophic instability mechanisms of roadway roof and sidewall rock masses under deep-hole roof blasting in coal mines, this study establishes potential energy functions and instability criteria models for layered roof and sidewall strata based on cusp catastrophe theory. First, the layered roof is idealized as a simply supported beam. Considering the coupling effects of deep-hole blasting loads, rock mechanical properties, and support resistance, a total potential energy equation for the system is derived, and the cusp catastrophe equation along with sufficient and necessary conditions for instability are obtained. Second, for the roadway sidewall, a tensile-shear coupled sliding failure mechanical model is proposed to analyze the influence of blasting loads on sidewall stability, and a corresponding catastrophe instability criterion is developed. Through theoretical derivation, the critical maximum explosive charge for both the layered roof and sidewall rock masses is formulated, along with a mechanical criterion for instability judgment. Finally, taking the lower roadway of the 2205 working face in Songshan Coal Mine as the engineering background, theoretical calculations indicate that the maximum critical explosive charge for the roadway is 93.3 kg. Field monitoring shows that, within 1 day after blasting, the roof subsidence increased by 5 mm and the convergence of the two sidewalls increased by 11 mm, indicating that the roadway was only slightly affected by roof deep-hole blasting.This work provides a theoretical basis and engineering guidance for the prediction and control of roadway rock instability under deep-hole roof blasting conditions.