⚡ electrical engineering

Height ratio‑dependent creep failure of coal‑rock composites: A multi‑scale analysis integrating stepwise creep, AE monitoring, and SEM characterization

This study integrates multi-scale analyses to demonstrate that the rock-to-coal height ratio critically governs the creep behavior of coal-rock composites, revealing that a 1:1 ratio offers optimal long-term stability and identifying a consistent failure stress threshold of approximately 90% of peak strength alongside a transition from shear- to tension-dominated cracking mechanisms as rock proportion increases.

Original authors: Fei Ke, Yanlong Chen, Peng Wu, Hai Pu, Yuheng Wang, Pengjiao Zhang

Published 2026-06-24

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CC BY 4.0

Original authors: Fei Ke, Yanlong Chen, Peng Wu, Hai Pu, Yuheng Wang, Pengjiao Zhang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are building a tower out of alternating layers of soft, squishy clay (coal) and hard, rigid bricks (sandstone). This is essentially what happens underground in mines: coal pillars are often sandwiched between layers of rock. The big question this study asks is: How does the ratio of bricks to clay affect how long the tower can stand under its own weight without slowly crumbling over time?

The researchers didn't just build the tower and wait; they used a "step-by-step" stress test, a high-speed camera for sound (Acoustic Emission), and a powerful microscope (SEM) to see exactly how the materials failed. Here is what they found, translated into everyday terms:

1. The "90% Rule" for Long-Term Strength

Think of the "Peak Strength" as the maximum weight the tower can hold before it instantly collapses if you drop a heavy box on it. The "Creep Failure" is the weight it can hold if you leave it there for days or weeks, slowly squishing down until it gives way.

The study found a simple, reliable rule: No matter how you mix the clay and bricks, the tower will eventually fail under a load that is about 90% of its maximum instant-breaking weight.

The Analogy: If a bridge can hold 100 tons if you drop a truck on it, it will likely collapse if you leave a 90-ton truck sitting on it for a long time. This ratio holds true whether the bridge is made mostly of clay, mostly of bricks, or a mix.

2. The "Goldilocks" Mix (The 1:1 Ratio)

The researchers tested different recipes:

All Clay: Weak and squishy.
Mostly Clay, Few Bricks: Better, but still weak.
Mostly Bricks, Little Clay: Strong, but the clay layer gets squeezed so hard it fails quickly.
All Bricks: Very strong, but brittle.
The 1:1 Mix (Equal parts clay and bricks): This was the winner.

Why? Imagine the hard bricks acting like a supportive hug for the soft clay.

If there are too few bricks, the clay has nothing to hold it back, so it squishes out the sides easily.
If there are too many bricks, they squeeze the thin layer of clay so tightly that the clay cracks immediately under the pressure.
The 1:1 ratio is the "Goldilocks" zone. The bricks provide just enough support to stop the clay from bulging out, but not so much pressure that they crush the clay. This mix lasted the longest, deformed the least, and was the most stable over time.

3. How the Tower Breaks: Shearing vs. Tearing

The study listened to the "cracks" using Acoustic Emission (like listening for the sound of snapping twigs). They discovered that the way the tower breaks changes depending on the mix:

All Clay: The tower fails by slipping (shearing). Imagine a deck of cards sliding sideways until the bottom card slips out.
All Bricks: The tower fails by splitting (tension). Imagine a piece of chalk snapping straight down the middle.
The Mix: As you add more bricks, the failure style shifts from "slipping" to "splitting."
The 1:1 Mix: This ratio created the most "splitting" (tensile) cracks and the fewest "slipping" (shear) cracks. The study suggests that splitting is a slower, more stable way for the material to fail, which is why the 1:1 mix lasted longer. It's like a slow, controlled tear rather than a sudden, violent slide.

4. The Microscopic View

Using a microscope, the researchers saw that the "clay" (coal) is full of tiny holes and cracks, like a sponge. The "bricks" (sandstone) are dense and solid, like a block of wood.

When you mix them, the solid bricks help cover up the weak spots in the sponge.
However, the study also noted a trade-off: While the 1:1 mix was the strongest overall, it actually lost a slightly higher percentage of its strength over time compared to the other mixes. It started very strong but degraded a bit more noticeably under long-term pressure.

Summary

The paper concludes that if you are designing a coal pillar underground, mixing the rock and coal in equal heights (1:1) is the best strategy for long-term stability. It creates a "supportive hug" that prevents the soft coal from squishing out, delays the formation of dangerous cracks, and ensures the structure lasts as long as possible before failing.

Key Takeaway: Don't just pile on more rock to make it stronger; the balance is what matters. Equal parts rock and coal create the most durable, long-lasting pillar.

Technical Summary: Height Ratio‑Dependent Creep Failure of Coal‑Rock Composites

Problem Statement
The long-term stability of coal pillars in underground stopes and open-pit slopes is critically dependent on the creep behavior of coal–rock combinations. While the rock-to-coal height ratio ( $K_{rc}$ ) is recognized as a governing parameter for the mechanical response of these composites, its specific influence on long-term creep deformation, strength attenuation, and the underlying mechanisms of creep damage accumulation remains insufficiently characterized. Existing research has largely focused on instantaneous failure mechanisms under conventional loading rates, leaving a gap in understanding how $K_{rc}$ modulates time-dependent failure and crack evolution under sustained loading.

Methodology
This study employed a multi-scale experimental approach integrating stepwise uniaxial creep tests, real-time acoustic emission (AE) monitoring, and scanning electron microscopy (SEM) characterization. Five distinct specimen groups were prepared with varying rock-to-coal height ratios ( $K_{rc}$ ): pure coal (0:1), three composite configurations (1:3, 1:1, and 3:1), and pure sandstone (1:0).

Creep Testing: Specimens underwent stepwise loading protocols where stress levels were incrementally increased and held constant to observe creep deformation until failure.
AE Monitoring: An AE system tracked ring counts and energy release to characterize internal microcrack evolution, distinguishing between crack initiation, propagation, and coalescence. Parameters such as Average Frequency (AF) and Rising Angle (RA) were utilized to differentiate between tensile and shear cracking mechanisms.
Microstructural Analysis: SEM observations were conducted on fresh fracture surfaces of coal and sandstone to verify microstructural defects and their role in stress concentration.

Key Results

Strength Relationship: A robust, linear relationship was established where the creep failure stress ( $\sigma_{cr}$ ) consistently approximated 90% of the peak uniaxial compressive strength ( $\sigma_c$ ) across all $K_{rc}$ configurations. This finding suggests that long-term strength can be reliably estimated from short-term static strength tests.
Optimal Configuration (1:1 Ratio): The composite specimen with a 1:1 rock-to-coal height ratio ( $K_{rc} = 1:1$ ) demonstrated superior creep resistance compared to other configurations. It exhibited the longest time to creep failure, the smallest instantaneous and time-dependent strains, and the lowest steady-state creep rate.
Non-Monotonic Thresholds: The crack initiation stress ( $\sigma_{ci}$ ) and crack damage stress ( $\sigma_{cd}$ ) followed a non-monotonic trend relative to $K_{rc}$ . These thresholds peaked at the 1:1 ratio before declining as the rock proportion increased further, indicating that the 1:1 configuration offers the widest stable crack growth regime.
Failure Mechanism Transition: As the proportion of rock increased, the failure mechanism shifted from shear-controlled to tension-controlled. The proportion of shear cracks decreased (from 25.56% in pure coal to 11.97% in pure rock), while tensile cracks became dominant. The 1:1 ratio exhibited the lowest shear crack proportion among composites, correlating with its enhanced stability.
Microstructural Influence: SEM analysis revealed that coal possesses a fragmented microstructure with interconnected microcracks and pores, whereas sandstone exhibits a rigid, dense grain skeleton. The stiffer rock layer in the composites provided lateral confinement to the coal, suppressing lateral expansion and delaying unstable crack growth, an effect that was maximized at the 1:1 ratio.

Significance and Claims
The authors posit that these findings provide quantitative guidance for the rational geometric design of coal pillars in underground mining and open-pit operations. Specifically, the study claims that identifying the 1:1 height ratio as an optimal configuration for creep resistance can inform the dimensioning of coal pillars to ensure long-term structural stability. Furthermore, the established 90% ratio between creep failure stress and peak strength offers a practical predictive tool for engineers assessing the long-term safety of existing pillar structures. The research bridges the gap between static mechanical properties and time-dependent failure behaviors, offering a theoretical foundation for understanding how structural geometry influences the transition from stable to unstable creep in heterogeneous rock–coal systems.

1. The "90% Rule" for Long-Term Strength

2. The "Goldilocks" Mix (The 1:1 Ratio)

3. How the Tower Breaks: Shearing vs. Tearing

4. The Microscopic View

Summary

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