MineGeotech

Pillar Spalling Calculations User Guide

Introduction

Pillar spalling is a key factor in assessing the long-term stability of coal pillar systems. It refers to the progressive loss of material from the ribs of coal pillars over time. As the pillar’s effective width reduces due to spalling, its strength reduces, which ultimately lead to failure. The phenomenon is driven by:

Mechanical and Environmental Factors: Changes in loading conditions, weathering, and the natural degradation of coal material.
Geometrical Limits: Spalling progresses until the remaining core reaches a critical dimension, reducing the factor of safety below acceptable levels.
Time-Dependent Failures: Even pillars designed with high initial factors of safety (e.g., FoS 2.11) may ultimately fail due to long-term spalling effects.

Therefore, we provide a comprehensive analysis that evaluates the long-term stability of pillars by cincorporating spalling rates and multiple failure modes. Our approach captures the time-dependent behaviour of pillar spalling through Stochastic Modelling, which predict the evolution of the pillar's effective width and its corresponding factor of safety over time.

1. Analytical Model

Factor of safety (FoS)

FoS is a measure comparing a pillar’s strength to the load it support. A higher FoS means a greater safety margin against failure. It is defined as:

FoS = \frac{Strength}{Load}

where Strength is calculated using the UNSW pillar formula, and Load is the mean stress acting on a pillar (the tributary area load).

where b₁ and b₂ is the roadway width; w and l are the original pillar dimension; C₁ and C₂ are the centre distances w₁ and w₂ are the pillar dimension after spalling;

2. Input Parameters

Cover depth H (Unit: m)

Cover depth is the vertical distance from the top of the pillar to the ground surface. It is used to determine the tributary load.

Mining Height h (Unit: m)

The mining height is the height of the layer being removed during extraction. This value is shown in Plot Area.

Unit weight γ (Unit: MPa/m³)

The unit weight of the overburden rocks is set to a default value of 0.025 MPa/m³.

Roadway Width 1 b₁ (Unit: m)

This is the roadway width along the x-axis. This value is shown in Plot Area.

Roadway Width 2 b₂ (Unit: m)

This is the roadway width along the y-axis. This value is shown in Plot Area.

Pillar Width w (unit: m)

Original pillar width along the x-axis. This value is shown in Plot Area.

Pillar length l (unit: m)

Original pillar width along the y-axis. This value is shown in Plot Area.

Angle of Response α (unit: ^o)

Angle of response is set to 35^o.

(a) Touch Caes
(b) No Touch Caes

where c is peeled off material distance (m); α is angle of repose (default as 35^o); d is amount of scaling on one side (m); C₁ is centre distance (m); X is amount of overlap.

Bulking Factor B

Bulking Factor is set to 1.35.

Pillar Spallng Rate (unit: m/year)

Bulking Factor is set to 0.05.

Roof Spallng Rate (unit: m/year)