What does this research mean for the field?

In saturated Hoek-Brown rock masses, the critical depth-to-span ratio separating shallow and deep tunnel roof collapse mechanisms ranges from 0.15 to 2.0, and neglecting pore water pressure significantly compromises structural stability evaluations. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish a three-dimensional stability evaluation framework for tunnel roofs at varied burial depths within saturated rock masses governed by the Hoek–Brown failure criterion.

September 5, 2026Applied SciencesOpen Access

Three-Dimensional Stability Analysis of a Tunnel Roof at Varying Burial Depths in Saturated Hoek–Brown Rock Masses

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To establish a three-dimensional stability evaluation framework for tunnel roofs at varied burial depths within saturated rock masses governed by the Hoek–Brown failure criterion.
Formulated a 3D kinematic collapse mechanism within limit analysis theory that directly incorporates pore water pressure.
Conducted numerical optimization across tunnel geometry, rock-mass parameters, and burial depth to derive stability charts linking support pressure and factor of safety.
Determined that the critical depth-to-span ratio (C/R) dividing shallow- and deep-buried failure mechanisms ranges approximately from 0.15 to 2.0 based on rock properties, pore pressure, and geometry.
Showed that omitting pore water pressure leads to significant underestimation of required stability support, confirming the need to integrate hydrogeological conditions into underground structural design.

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Implication

Computational limit analysis evaluates roof collapse mechanisms across burial depths in saturated Hoek–Brown rock masses, highlighting the necessity of accounting for pore water pressure in design.

Cite This Study

Xu et al. (2026) studied this question.

synapsesocial.com/papers/6a9bd4436b95aff0620ebc4f https://doi.org/10.3390/app16178769

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Implication

Computational limit analysis evaluates roof collapse mechanisms across burial depths in saturated Hoek–Brown rock masses, highlighting the necessity of accounting for pore water pressure in design.

Three-Dimensional Stability Analysis of a Tunnel Roof at Varying Burial Depths in Saturated Hoek–Brown Rock Masses

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Discussion

Implication

Cite This Study

Three-Dimensional Stability Analysis of a Tunnel Roof at Varying Burial Depths in Saturated Hoek–Brown Rock Masses

Key Points

Discussion

Implication

Cite This Study

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