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A method is presented addressing quantitative assessment of tunnel roof stability, based on the kinematic approach of limit analysis. Long tunnels with both rectangular (flat-ceiling) and circular cross-sections are considered. The rock is considered to be governed by the Hoek-Brown strength envelope and the normality flow rule, and it is assumed to provide enough ductility at failure, making plasticity theorems applicable. A failing block in the collapse mechanism is separated from the stationary rock by a deformation band with a large gradient of velocity across its width. The shape of the block in the critical mechanism is found from the requirement of the mechanism’s kinematic admissibility and an optimization procedure consistent with respective measures of stability. Both the stability number and the supporting pressure needed for tunnel stability are calculated first. Although less commonly used in rock engineering, a procedure is developed for estimating the factor of safety, defined as the ratio of the rock shear strength determined from the Hoek-Brown criterion to the demand on the strength. Curiously, for flat-ceiling tunnels, such definition of the factor of safety yields results equivalent to the ratio of a dimensionless group dependent on the uniaxial compressive strength and the size of the tunnel to the stability number. Such an equivalency does not hold for tunnels with ceilings of finite curvature. Not surprisingly, all measures of tunnel roof stability are strongly dependent on the Geological Strength Index that describes the quality of the rock.
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Spatial Distribution of Rock Disturbance in Assessment of Roof Stability in Flat-Ceiling Cavities
Three-dimensional stability of roofs in deep flat-ceiling cavities is analyzed. The stability number, factor of safety, and required supporting stress are used as measures of roof stability. Despite the simplicity of the flat roof geometry, the three-dimensional stability analysis presents some complexities owed to the shape of the failure surface geometry in the collapse mechanism. The failure mode assumes a rock block moving downward into the cavity, and the study aims to recognize the most critical shape of the failing block. Three specific block shapes are described in some detail, but more have been analyzed. Blocks defined by a special case of a 4th order conical surface (quartic) on a rectangular base, and a 2nd order elliptic surface (quadric) are found to be the most critical in the stability analysis. The kinematic approach of limit analysis was used, with the rock strength governed by the Hoek-Brown failure criterion. The parametric form of the Hoek-Brown function was employed. Interestingly, an absence of diagonal symmetries in the most critical failure mechanisms was observed in roof collapse of square-ceiling cavities. Computational results in terms of dimensionless measures of stability are presented in charts and tables.
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- Award ID(s):
- 1901582
- PAR ID:
- 10524124
- Publisher / Repository:
- ScienceDirect
- Date Published:
- Journal Name:
- Rock Mechanics and Rock Engineering
- Volume:
- 56
- Issue:
- 6
- ISSN:
- 0723-2632
- Page Range / eLocation ID:
- 4445 to 4461
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00603-023-03295-2
