Numerical Study of the Mechanical Response and Failure Evolution of Layered Cemented Tailings Backfill under Biaxial Confinement

Technical Summary: Numerical Study of the Mechanical Response and Failure Evolution of Layered Cemented Tailings Backfill under Biaxial Confinement

Problem Statement
As mining operations extend to greater depths, backfill materials face higher in-situ stresses and mining disturbances, necessitating robust bearing capacity and long-term stability. Staged filling is a common practice where a high-cement bottom layer is followed by a lower-cement layer, creating a layered structure with significant mechanical property contrasts. The interface between these layers often exhibits weaker bonding and higher porosity, acting as a potential stress-concentration zone for crack initiation. While uniaxial behavior of such materials has been studied, triaxial or biaxial research remains limited due to the difficulty of specimen preparation and deformation measurement for low-strength materials. Furthermore, existing numerical studies often fail to account for stochastic variability, particle packing differences, and the specific effects of layer order under confinement. This study addresses the need to understand the mechanical response and mesoscopic bond-break evolution of layered cemented tailings backfill under biaxial confinement using a high-resolution numerical approach.

Methodology
The study employs the Particle Flow Code (PFC2D) based on discrete-element theory. The methodology is structured in three phases:

1. Calibration against Published Data: No new uniaxial experiments were conducted. Instead, the authors utilized existing uniaxial compression data from Huang et al. (2022) for homogeneous cement-to-tailings ratios of 1:4 and 1:8, and a layered "Combination I" (U1:8/L1:4). A high-resolution PFC2D model containing approximately 38,700 particles was calibrated using a specific random realization (S10001). The calibration focused on matching the Uniaxial Compressive Strength (UCS) and peak strain of the 1:4 and 1:8 materials.
2. Independent Verification: Once parameters were fixed, two independent random realizations (S20001 and S30001) were generated to verify the model without further retuning. This ensured that the model could reproduce experimental means within a stochastic framework.
3. Biaxial Confinement Simulations: The calibrated parameters were applied to strictly mirrored horizontal layered assemblies (Combination I: U1:8/L1:4; Combination II: U1:4/L1:8). Simulations were run at target confining pressures of 0.2, 0.4, and 0.6 MPa. The study utilized three random seeds for each configuration to quantify variability.
   • Interface Assumption: Contacts crossing the horizontal layer boundary were assigned the properties of the weaker 1:8 material, as no independent interfacial shear data were available.
   • Loading: Biaxial loading was applied with lateral stress control active. A rate-sensitivity check was performed on one case to assess inertial effects, though the authors explicitly note that the numerical strain rates were significantly faster than experimental rates.

Key Contributions

• High-Resolution Calibration: The study establishes a high-resolution PFC2D model calibrated against specific uniaxial benchmarks, verifying its predictive capability through independent random realizations.
• Strict Mirroring Protocol: By creating strictly mirrored assemblies (CI and CII) with identical particle contacts and wall conditions, the study isolates the effect of layer order from stochastic variability and boundary artifacts.
• Mesoscopic Bond-Break Analysis: The research provides a detailed statistical analysis of bond-break evolution (tensile vs. shear) under biaxial confinement, specifically focusing on the early post-peak stage to avoid the complexities of severe late-stage failure.
• Quantification of Variability: The use of three random seeds allows for the reporting of mean values and standard deviations, providing a more robust statistical basis than single-realization studies.

Results

• Model Accuracy: The independent verification realizations (S20001, S30001) yielded mean UCS values with errors of -5.14% (1:4) and -2.88% (1:8) relative to published experimental means, confirming the model's validity for the calibrated parameters.
• Stress-Strain Response: Under biaxial confinement, the peak deviatoric stress did not increase monotonically with target confinement. For both CI and CII configurations, peak stress generally decreased or remained stable as confinement increased from 0.2 to 0.6 MPa.
• Layer Order Effect: Reversing the layer order (CI vs. CII) did not produce a reproducible strength advantage. The differences in peak stress between mirrored configurations varied in sign and magnitude depending on the random seed and confinement level, suggesting no inherent mechanical superiority to a specific layer sequence under the symmetric model conditions.
• Bond-Break Evolution:
  • As confinement increased, the mean total bond-break count at the matched early post-peak stage (80% of peak stress) decreased significantly (e.g., from ~8,956 to ~3,762 for CI).
  • Tensile bond breaks dominated the failure process, accounting for 97.8% to 99.2% of total breaks. Shear breaks were minor.
  • Interface-labelled breaks were a small, non-exclusive subset of the total breaks, indicating that failure was not exclusively localized at the interface in the early post-peak stage.
• Rate Sensitivity: A representative check indicated that reducing the numerical strain rate from 0.50 to 0.10 s⁻¹ resulted in negligible changes to peak stress (<0.24%) and strain (<0.46%), suggesting the peak response was not dominated by inertia within the tested numerical range. However, this did not establish equivalence to the experimental loading rate.

Significance and Claims
The paper modestly frames its findings as numerical predictions and descriptive comparisons within the bounds of the model's assumptions. The authors explicitly state that:

• The study extends previously published experimental work through high-resolution numerical calibration and biaxial confined prediction.
• The observed reduction in bond-break counts with increased confinement is consistent with lateral restraint suppressing tensile bond opening, but this is not a validated physical mechanism due to the lack of independent confined laboratory data.
• The absence of a reproducible strength advantage for either layer order challenges the assumption that layer sequence alone dictates capacity under symmetric conditions; a substantial effect would require unmeasured asymmetries (e.g., density gradients or curing variations).
• The results are descriptive trends derived from three realizations and should not be interpreted as establishing a universal constitutive law or a general interface-controlled shear mechanism.

In summary, the study provides a rigorous numerical framework for analyzing layered backfills, demonstrating that while confinement suppresses bond breaking, it does not necessarily increase peak deviatoric stress in a monotonic manner, and layer order does not inherently dictate strength under the specific symmetric conditions modeled.