# Uniaxial Compressive Failure Characteristics and Constitutive Modeling of Fractured Coal Mass Under Different Strain Rates

## TL;DR

This paper studies how strain rates and fractures affect coal's mechanical behavior and develops a model to predict coal failure under different conditions.

## Contribution

A novel statistical damage constitutive model for fractured coal is proposed, incorporating strain rate and fracture density effects.

## Key findings

- Compressive strength increases with strain rate but decreases with fracture density.
- Fractal dimension of fragmented coal particles increases with higher strain rates.
- Weibull parameters show distinct variation patterns based on strain rate and fracture density thresholds.

## Abstract

To investigate the effects of different strain rates and fracture densities on the mechanical behavior of coal, CT scanning was employed to quantify fracture content in coal specimens. Uniaxial compression tests were conducted to analyze the mechanical characteristics of coal, followed by the establishment of a statistical damage constitutive model for fractured coal. The results demonstrate: (1) The compressive strength of coal specimens shows a positive correlation with increasing strain rate, while the elastic modulus exhibits an initial decrease followed by an upward trend. Compressive strength displays a negative correlation with fracture density. Under a strain rate of 0.001 s−1, the elastic modulus decreases significantly with increasing fracture density, whereas this trend becomes less pronounced at higher strain rates. Notably, compressive strength demonstrates greater sensitivity to fracture density variations. (2) Within the dynamic strain rate range of 0.001 s−1~0.05 s−1, the fractal dimension of fragmented coal particles ranges from 1.0 to 1.3. Both the average mass of ejected fragments and the mean fractal dimension of fractured particles increase progressively with strain rate elevation, indicating enhanced non-uniformity in particle size distribution. (3) Significant correlations exist between Weibull distribution parameters (F0, m) and strain rate/fracture density. A critical threshold emerges at 0.01 s−1 strain rate, where F0 and m exhibit opposite variation trends before and after this threshold. Similarly, a fracture density threshold between 0.3%~0.45% is identified, with F0 and m demonstrating contrasting evolution patterns below 0.3% and above 0.45% fracture density under increasing strain rates. (4) Based on the established relationships between Weibull parameters (F0, m), strain rate, and fracture density, the dynamic statistical damage constitutive model for coal was modified. A systematic methodology for determining parameters in the revised model was subsequently proposed.