Comparative analysis on plastic zone in deep soft rock roadway surrounding rock considering rheology or not

Technical Summary: Comparative Analysis on Plastic Zone in Deep Soft Rock Roadway Surrounding Rock Considering Rheology or Not

Problem Statement
Deep mining in China frequently encounters roadways in soft rock formations that exhibit pronounced rheological (time-dependent) behavior. Traditional elastoplastic analyses of roadway surrounding rock often rely on the peak compressive strength of rock specimens as the failure criterion, neglecting the rheological characteristics of the rock mass. This approach frequently leads to theoretical results that overestimate the strength of the surrounding rock and underestimate the extent of deformation and the plastic (loosening) zone, resulting in designs that deviate from engineering reality and compromise long-term stability. The core problem addressed is the discrepancy between theoretical predictions of the plastic zone and actual field observations in deep soft rock roadways, specifically caused by the omission of rheological effects and the misidentification of the peak stress state in stabilized surrounding rock.

Methodology
The study utilizes a multi-faceted approach combining field monitoring, laboratory testing, theoretical derivation, and numerical simulation, centered on the -848 m charging rectifier chamber test roadway in a mine.

1. Field Investigation: The study site was selected because the surrounding rock had reached a stable state after severe initial deformation. Monitoring sections measured surface displacements (arch springing, roof-to-floor convergence, floor corners) to confirm stability. Ultrasonic wave velocity tests were conducted to determine the actual depth of the loosening zone (plastic zone) in the field, which ranged from 2.7 to 3.2 m at the ribs.
2. Laboratory Testing: Rock cores were tested to determine mechanical parameters.
   • Triaxial Compression: Specimens were tested under confining pressures of 0, 4, 8, 12, and 16 MPa to obtain complete stress-strain curves and peak strengths ($\sigma_{pk}$).
   • Creep Tests: Step-loading creep tests were performed under the same confining pressures.
   • Long-term Strength Determination: Using the "creep termination trajectory theory," the intersection of the fitted creep termination trajectory and the complete stress-strain curve was used to determine the long-term strength ($\sigma_{\infty}$) for each confining pressure.
3. Theoretical Analysis: An elastic-brittle-plastic model was established. The study derived analytical solutions for the plastic zone radius under two conditions:
   • Case A (Considering Rheology): The peak stress of the surrounding rock ($\sigma_s$) was defined as the long-term strength ($\sigma_{\infty}$).
   • Case B (Neglecting Rheology): The peak stress was defined as the peak compressive strength ($\sigma_{pk}$).
   • Solutions were derived for both axisymmetric conditions ($\lambda = 1$) and biaxial unequal stress fields ($\lambda = 0.86$) using the stress construction method.
4. Numerical Simulation: ABAQUS finite element software was used to simulate the roadway. Two models were run: one using the long-term strength parameters (cohesion $c_0 = 5.58$ MPa) and one using peak strength parameters (cohesion $c_0' = 11.26$ MPa).

Key Contributions

• Redefinition of Peak Stress Criterion: The paper proposes that for stabilized deep soft rock roadways, the peak stress of the surrounding rock should be equated to the rock's long-term strength under a given confining pressure, rather than its short-term peak compressive strength. This is based on the premise that if stress exceeds the long-term strength, unstable rheological deformation will continue until the stress drops to a stable level.
• Analytical Solutions: The study provides explicit elastoplastic analytical solutions for the plastic zone radius and stress distribution, distinguishing between scenarios where rheology is considered (using long-term strength) and ignored (using peak strength).
• Comparative Validation: By integrating field data, the study quantitatively demonstrates the magnitude of error introduced by ignoring rheology.

Results

• Field Observations: The measured loosening zone depth at the roadway ribs was 2.7–3.2 m.
• Theoretical Comparison:
  • Neglecting Rheology: Using peak strength, the calculated plastic zone radius was approximately 2.83 m (for $\lambda=1$) and 2.93–3.22 m (for $\lambda=0.86$). The resulting plastic zone depth at the ribs was only ~0.68 m, suggesting the rock remained largely elastic. This significantly underestimated the actual loosening zone.
  • Considering Rheology: Using long-term strength, the calculated plastic zone radius was 4.96 m ($\lambda=1$) and 4.69–5.24 m ($\lambda=0.86$). The resulting plastic zone depth at the ribs was 2.42 m to 2.70 m, which aligned closely with the field-measured range of 2.7–3.2 m.
• Numerical Simulation: The simulation results mirrored the theoretical findings. Ignoring rheology yielded a small, horseshoe-shaped plastic zone (~0.58 m depth), while considering rheology produced an elliptical distribution with a depth of ~2.12 m, much closer to field reality.
• Stress Distribution: Neglecting rheology led to a significant overestimation of surrounding rock strength and an unconservative assessment of stability.

Significance and Claims
The paper claims that the rheological characteristics of rock mass are a dominant factor in the deformation and stress distribution of deep soft rock roadways. The primary significance lies in the finding that neglecting rheology leads to a substantial overestimation of surrounding rock strength, resulting in plastic zone calculations that deviate significantly from engineering practice and pose safety risks.

The authors assert that for the long-term stability assessment and support design of deep soft rock roadways, the rheological characteristics must be fully considered. Specifically, the peak stress in theoretical models should be based on the long-term strength of the rock mass rather than its instantaneous peak strength. This approach ensures that theoretical analyses and engineering designs are consistent with the actual deformation evolution and stability conditions observed in the field. The study concludes that while exact analytical solutions for biaxial unequal pressure remain complex, the proposed approximate method considering rheology provides a reliable and safer basis for engineering applications.